Topics not covered here may often be found in the chapters on specific lasers. For example, information on mode structure and coherence length is in the chapter: Helium-Neon Lasers, specifically the sections starting with: Longitudinal Modes of Operation.
Note that throughout this document, I use the term 'dielectric' in reference to most laser mirrors but may use the term 'dichroic' or 'dichro' for mirrors or prisms designed to separate wavelengths. Nowadays, it apppears as though the term 'dielectric' is more popular.
A few on-line references with just a bit more extensive information can be found at:
And, of course, general on-line encyclopedias like Wikipedia.com.
Name Symbol Factor --------------------------- yocto y 10-24 zepto z 10-21 atto a 10-18 femto f 10-15 pico p 10-12 nano n 10-9 micro u 10-6 milli m 10-3 centi c 10-2 deci d 10-1 deka da 101 hecto h 102 kilo k 103 mega M 106 giga G 109 tera T 1012 peta P 1015 exa E 1018 zetta Z 1021 yotta Y 1024
The "u" should really be the Greek symbol for "micro" but I'm too lazy to use the correct HTML code.
They make a big deal out of the special case of kilogram which is the only SI unit with a prefix as part of its name and thus cannot be used with an additional prefix. So, the SI police will come get you if you write something like mkg to mean a gram. :)
(Portions from: Dr. Mark W. Lund (mlund@moxtek.com).)
Put another way, Candelas are a measure of luminous intensity through an imaginary sphere with the light source at its center. For an isotropic point source 1 Candela is equal to 1 lumen per steradian. There are 4 x pi or about 12.6 steradians in a complete sphere around the source. A 12.6 lumen isotropic source would then produce 1 Candela. This doesn't really apply to your typical laser but would be a close approximation to a something like a short-arc xenon lamp. However, it is still possible to define the Candela over a portion of a diverging beam. So, if your laser put out 1 lumen over only .1 steradians, its intensity in Candelas would be 10 Candelas.
I (Mark) was at one time a true expert on photometry and radiometry and I still can't figure out how to compare one LED with another because every company specifies their parts in different ways, not all of which are appropriate. :)
Warren Smith gives an admirable discussion of photometry in his book "Modern Optical Engineering".
Or, check out the Lighting Design and Simulation Glossary for definitions of these and other related terms.
A Radiometry versus. Photometry FAQ by: James M. Palmer (jpalmer@azstarnet.com) is in the final stages of development (to the extent that FAQs are ever fully developed!). (PDF Version also available.)
(From: Ian Ashdown (byheart@direct.ca).)
A foot-candle is a unit of illuminance, which is defined in ANSI/IES RP-16-1996 (Nomenclature and Definitions for Illuminating Engineering), from Illuminating Engineering Society of North America as "The areal density of the luminous flux incident at a point on a surface."
In plain English, illuminance is the quantity of light arriving at a point on a real or imaginary surface. (The point does not have to be located on a physical surface.)
One foot-candle is equivalent to one lumen per square foot (where a lumen is a measure of the luminous flux, or quantity of light).
A wax candle flame has a luminous intensity (or equivalently, candlepower) of approximately one candela. If you hold the candle one foot away from a surface, the illuminance of the surface at this distance due to the light from the candle will be approximately one foot-candle. It will be 1/4 fc at two feet, 1/9 fc at three feet, and so on in accordance with the inverse square law for point light sources.
Brightness is a psychophysiological phenomenon that cannot be measured directly. The term "photometric brightness" used to refer to luminance, but is no longer in scientific or engineering use. (Let me rephrase that: it shouldn't be!)
There is an understandable but technically accurate description of photometric and radiometric terminology at Ian Ashdown's Publications.
(From: Don Klipstein (don@misty.com).)
A lumen is defined as the "luminous flux" of 1/683 of a watt of monochromatic light that has a frequency of 540 Terahertz, or a wavelength of approx. 555.5 nm. One thing worth noting is that a lumen is defined secondarily, in terms of the candela (which is 1 lumen per steradian), and the candela is defined primarily (it's the "beam candlepower" of 1/683 watt per steradian of 540 THz monochromatic light.) Light of wavelengths other than 555.5 nm have a different amount of lumens per watt of radiation. The number of lumens in a watt of wavelength other than 555.5 nm is 683 times the photopic function of the wavelength in question, divided by the photopic function of 555.5 nm (which I believe is very close to but not exactly 1).
A "USA-usual" 100 watt, 120 volt, 750 hour "regular" (A19) light bulb usually produces 1710 lumens.
Lumens per watt is a measure of efficiency in converting electrical energy to light. Multiply this by the watts dissipated in the LED to get lumens. A typical red, orange, or yellow or yellow-green LED has a voltage drop around 2 volts and is getting around .04 watt at the typical "standard" current of 20 milliamps. A blue, white, or non-yellowish-green one typically has a voltage drop of 3.5 volts at 20 mA and gets .07 watt at 20 mA.
A candela is a lumen per steradian, or "beam candlepower". (Actually, as mentioned above, the candela is a primarily defined metric unit, while the lumen is defined in terms of the candela.) So lumens are candelas times the beam coverage in steradians. Candelas are lumens divided by the beam coverage in steradians. Ideally, that is - assuming that all light is within the beam and the "candlepower" is constant within this beam.
So you may now be wondering what a steradian is. It is 1 / (4 * pi) of a whole sphere or 1 / (2 * pi) of a hemisphere or about 3283 "square degrees". To get steradians from the beam angle:
Steradians = 2 * pi * (1 - cos (.5 * (beam angle)))
(NOTE: There are a few other expressions equal to this. Proving that is homework for 12th graders taking trig / "elementary functions".)
So if you determine the steradian beam coverage and multiply that by the candela figure (or 1/1000 of the millicandela figure), you get the lumen light output - very roughly! The beam is not uniform and it does not contain all of the light. Obtaining lumens from beam angle and candela can easily be in the +100 / - 50 percent range. Actual lumens are generally higher than predicted by this formula with smaller beam angles of 8 degrees or less since the nominal beam does not include a secondary "ring-shaped" "beam" that usually surrounds the main one. Also note that some beam angle figures are optimistic and could lead one to expect a lot more lumen light output than actually occurs.
(This info is also available on my Web site at: Converting/comparing lumens, candelas, millicandelas.)
But, what about a laser? Just about any HeNe laser beam can be focused to a microscopic point which your average moron can see is more intense than the discharge inside the bore. :)
I wonder if this is getting into a philosophical question of sorts: Where is the source in a laser? For an incandescent object like the Sun, it is its surface and the radiance law applies. However, there is no similar physical surface in a laser - the beam appears to originate from the lasing medium at a point in space somewhere behind or at the beam waist but there may not actually be anything there! The wavefront curvature implies a source which for a "well behaved laser" :) like a HeNe, is very nearly a diffraction limited point, thus the ability to apparently increase the brightness compared to what is inside the tube's bore.
For "poorly behaved lasers" like those annoying high power laser diodes or laser diode bars, the fast axis is diffraction limited and effectively a point source so it can be focused to a diffraction limited point (or actually a line in this case). The effective source location is inside the laser diode chip but isn't a singularity - it is spread throughout the gain region as with a HeNe laser.
But the slow axis is multimode and options with imaging optics are extremely limited - though squeezing the 1 cm output of a laser diode bar to a couple of mm with usable divergence isn't impossible (there is an example in "Solid State Laser Engineering" by Koechner, fifth edition, and in this case, the refraction at the surface of the laser crystal helps to limit divergence somewhat as well). The benefits of it being a laser don't help since it looks more like a multitude of sources side-by-side. Each one can be focused to a diffraction limited spot but the entire collection can't be squeezed together without the divergence becoming excessive. The usual solutions to produce sub-mm size spots involve either fiber bundles or lens ducts (light pipes) which don't need to obey that law - or the law of low cost options for real people either. :)
1,240 nm
E = 1.602*10-19 J * -----------
lambda
Where:
Then, photon flux = P/E where P is the beam power.
For example, a 1 mW, 620 nm source will produce about:
1*10-3
------------------- = 3*1015 photons/second.
1.60210*10-19 * 2
For simplicity, let's assume that we are comparing a xenon HID lamp and a mixed-gas (argon/krypton) white light ion laser. Some issues:
Another way of looking at it (no pun....) would be to determine the efficiency of your source in converting electrical watts to light watts.
As an approximation, a 100 W incandescent lamp produces about 1700 lumens or perhaps 6 W of light. So, if you could manage to collect most of it and collimate it very well you would have the equivalent of a 5 W mixed gas laser in terms of intensity. However, to do this would require a combination of non-imaging optics and fiber optic bundles to collect the light, and then conventional optics to focus and direct it. With a short arc discharge lamp, you could get closer to decent collimation with simpler optics but never anything like a laser!
See the section: Radiometry Primer: What is Lumen, Lux, Nit, Candela?
(From Don Klipstein (don@Misty.com).)
Lumens out of a xenon lamp per watt into it? I hear enough figures of 40 for this, optimistically 50 according to various sources. But xenon lamps have electrode and thermal conduction losses, and a majority of what actually does get radiated is UV and IR including some strong near-IR lines around 820 to 1,000 nm. One watt of the visible spectrum output (400 to 700 nm) of a xenon lamp has about 250 lumens, assuming this approximates a 5600 Kelvin blackbody.
Lumens in a watt of pure broadband visible light? Equal energy per nm band from 400 to 700 nm has about 242 lumens per watt. The 400 to 700 nm region of the spectrum of a 3900 Kelvin blackbody has about 262.6 lumens per watt. If you use single wavelengths or specific bands in the mid-blue, yellowish green, and orangish red you can get about 400 lumens per watt of white light.
As for lumens per watt in a 3-line white laser beam? Lumens in 5 watts of such? Depends on what wavelengths and amount of each and whether the mixture you desire or achieve is something you call white. This could be anywhere from 120 to 360 lumens per watt using the usual argon and krypton laser lines.
For the 30 W multiline mixed gas ion laser discussed in the section: More Comments on Argon/Krypton Spectral Lines, the results of combining the contributions of all the wavelengths listed was 238 lumens per watt.
At 250 lumens per watt, a 5 watt beam would have 1,250 lumens, or slightly more light than a typical 75 watt light bulb produces. Using 150 lumens per watt, the total of 750 lumens is less than the output of a 60 W light bulb. With the optimistic figure of 360 lumens per watt, you would get 1800 lumens which is slightly more light than from a typical 100 watt light bulb.
The bottom line: If you just want lumens, a laser isn't a good choice. :-)
(From: Dane (zanekurz@sansnetcom.com).)
One way to estimate this is to use one rule of thumb for the magnitude of a star that a well dark adapted eye (scotopic vision) can see in a very dark sky. That would be a 6th magnitude star. (Some people claim better than this and some worse.)
The irradiance of a 1st magnitude star is about 8*10-11 lumens/cm2 at the top of the atmosphere. Since the lumens per watt for scotopic vision is about 1,000 at 0.5 um, this is about 8*10-14 watts/cm2. A 6th magnitude star is about 100 times dimmer than a 1st magnitude star, so its irradiance is about 8*10-16 watts/cm2 (!!!).
Amazing! This is on the order of 2,500 photons per cm2 per second or perhaps 750 photons per second into the eye and about 25 photons over a 1/30 second integration period. This checks well with the common statement in many books that only a few photons from a point source are necessary for detection.
There's at least one thing which would make these numbers not too accurate for looking at the magnitude for 1 photon (but it errs on the high side). I used the lumens per watt (about 1,000) for a monochromatic laser wavelength of 0.53 um, which is near the eye's sensitivity peak. Since the light from a star is similar to a solar spectrum, the number of lumens per watt for the extended spectrum would be significantly less and the number of photons from the star would need to be considerably higher than a laser at the visibility threshold.
(From: Anthony Cook (a.l.cook@larc.nasa.gov).)
This question was intriguing to me so I performed a quick experiment with a red HeNe laser in my spare time:
With all lights out in the lab, I sent a red HeNe laser through an 18 mm focal length aspheric lens. This produced a beam divergent with about 4 to 5 degrees full angle. Put both discreet and variable ND filters in the beam path. Went out to where the beam was 30 cm in diameter and then attenuated the beam until the source spot was just barely visible to the eye. Measured the attenuated power at the source. Here are the results:
Note: This assumes an even distribution of power. However, the beam is Gaussian, so the when viewing the center of the beam, this number will be slightly higher. Maybe someone else can calculate the exact value of the power density in the center of the beam, considering the gaussian nature of the beam).
(From: OpticsNotes.Com (bruce_nichols@my-deja.com).)
Were you dark adapted? You may be able to go lower if you wait five minutes or so. You can go even lower if you use averted vision after your eyes are allowed a longer period of dark-adaptation. Your fovea improves with dark adaption, but 10 degrees from your fovea has a significant improvement (up to 1,000 times lower threshold). Averted vision dark adaptation takes about 10 minutes, and continues to improve to 30 minutes or more. Deep sky object gazers use this trick. To see a faint object, you look just to the side of it. It's pretty cool.
(From: Anthony.)
Good point. I was definitely not dark adapted. Neither did I have my glasses on (I'm not terribly bad of sight, but my glasses help me see things at a distance a bit better).
After reading the other posts, along with some other notes and refs at Can a Human See a Single Photon?, I now see that I could have achieved greater sensitivities with my crude experiment.
(From: Leonard Migliore (lm@laserk.com).)
Central irradiance for a TEM00 beam is twice the average irradiance based on total power divided by the area of the 1/e2 diameter. So, you were picking up 8.5 pW/cm2. That ain't much beam.
(From: Hao Fong (fonghao@polymer.uakron.edu).)
To estimate the beam profile, slide a knife edge into the beam, to reduce its power on a power meter. First reduce the initial power by 13%, then to 82% of initial power. You have just found the edges of the peak part of the Gaussian distribution where most of the power is. By watching your spot in the distance when you do this, you can see what parts of it to mask off to get a reasonably uniform spot afterwards.
BTW, many HeNe lasers with multiple modes going produce more of a top-hat distribution. You may need a tube longer then say 12 cm (which only supports two modes). I haven't tried this, but it should work.
Note that measuring the output voltage of the green or yellow LED with a multimeter will be inaccurate if your laser is pulsed or quasi-CW as it will read the average voltage which may be much lower than the forward voltage drop of the red LED. The peak power output of the LED will be proportional to the peak power of the incident laser beam. Thus, a pulsed laser is more likely to work here than a CW one. Your mileage may vary.
The principle behind this stunt is that the green or yellow LED acts like a solar cell (or should we say "laser cell") for the laser and generates an output which is a function of the incident optical power and its band-gap voltage. Shorter wavelength LEDs should be able to power longer wavelength LEDs but not the other way around (unless two are wired in series with two lasers used for optical input). Thus, it should be possible to power an IR LED from a red LED and HeNe laser but that would be so boring.
Don't expect rigs like this to be used an alternative power sources any time soon. The efficiency is less than a whopping 0.001 percent (electrical power of 0.5 W into the green DPSS laser for 1 microwatt or less optical output power from the red LED). :)
(From: Leonard Migliore (lm@laserk.com).)
It depends on the laser's power and also how tightly the beam is focused. From Hecht's Optics, the radiation pressure for an irradiance S is S/c where c is the speed of light. If I got the units right, an irradiance of 106 W/cm2 has a pressure of 33 Pa.
You need to focus a kW of power into a 360 micron spot to get this irradiance; the light pressure is the last thing you need to worry about.
(From: DeVon Griffin (DeVon.Griffin@lerc.nasa.gov).)
For laser tweezers with a focused laser beam, it is on the order of a few tens of picoNewtons.
You can get a rough idea of the intensity distribution by just looking at the laser beam projected on a screen or piece of white cardboard. However, unless it is a very low power laser, its brightness will have to be cut way down to be able to make anything out. To get more quantitative information, projecting the attenuated beam onto a cheap CCD camera with its lens removed will give you an image which can be viewed safely or digitized for analysis. The only problem I've found with this approach is that since the $50 CCD cameras have a sensitivity that can't be controlled manually (automatic level control), they may get confused by the small laser spot.
(From: Leonard Migliore (lm@laserk.com).)
This is, in fact, a pretty good way of looking at laser beams. Spiracon, Inc. and Coherent, Inc. make some neat software to process these images and generate 3-D mode images on your computer. I've never looked at the raw image, but I guess you can tell if the beam is round or if it has hot spots.
The sensitivity depends on the wavelength. CCD sensitivity drops like a rock past 1 micron, but if there's one thing lasers are good for, it's putting out a lot of light. The peak sensitivity (in the visible) is (for saturation) is about 0.2 to 1.0 microwatts/cm2 at visible wavelengths. You would need about 100 times that at 1,064 nm, but that's still not much. For pulsed Nd:YAG, you will saturate a CCD with 10 nJ/cm2.
For even small lasers, you'll likely need to cut the beam intensity way down with neutral density filters or other means. For a laser with a peak irradiance of 30 mW/cm2, you'll need to cut the beam down 3,000,000 times, which is a density of 4.4. You may want to use a reflective 4.0 filter with an absorptive 0.4 behind it. If the laser operates at a near-IR wavelength, the CCD will be much less sensitive as noted above so less filtering will be needed.
(From: Thomas R. Nelson (tnelson@uic.edu).)
I've done this at 745 nm, to look at both a 400 mW (average power) beam, and an amplified beam (peak power approximately 10 GW!). I would recommend using window reflections to attenuate, rather than any transmissive attenuators. For high power beams, thermal blooming in a ND can distort the beam, and at any power level, the slightest blemish or spec of dust on one of the filters can show up. Chances are you'd need to take only one or two reflections at most to avoid saturating the CCD. Once you have the image file, you can use a variety of graphics packages to look at the profile. You don't necessarily need to buy some special package for looking at laser beams.
(From: Paul Pax (phpax@azstarnet.com).)
We've gotten a Kodak DVC323 for exactly that purpose. Popped the lens off and sent the beam right to the chip (through about ND 5, for ~20 mW at 532 nm). Works fine for qualitative measurements, and even reasonably well for quantitative ones, if you watch out to get in a linear regime. Kodak says there is significant processing in the camera itself, and that the resulting image is not linear. By the way, Kodak makes the software controls for the camera available on its web site (VisualC and VisualBasic). I've written a basic beam analysis program with it.
(From: Johnathan Leppert (service@qth.net).)
Get a USB camera, like the one which is used often and is very popular with the amateur astronomer crowd. There is a certain camera (think it's a Panasonic) which has a lens which can be screwed off, revealing the CCD. This camera is around $50 to $125.
Then download the Spiracon, Inc. demo software.
All you need to do is have the beam centered on the CCD, and you can get a complete real-time beam profile (which includes a wealth of data including your spot size (FWHM) minus the $2000 bloat of a professional beam analyzer, which is good for most applications (CCD USB webcam resolution about 500 to 600 lines, plenty for high resolution profiles).
Beams of light do not interact in a linear medium like a vacuum, or air or glass at reasonable power densities). So, even at the intersection, only the original frequencies/wavelengths are present unless the power density is so high that the physical medium behaves non-linearly (but never in a perfect vacuum).
However, if the beams are both incident in the same location (and some polarization overlap) on a photodiode (a non-linear device having a square-law response) with sufficient bandwidth, the difference frequency between them will be seen. (The sum frequency is also produced but no know photodiode will respond that fast.) However, these frequencies do not really exist in the spectrum of the light beams until they have been detected by the photodiode.
In a non-linear medium like LiNbO3 or KTP, or optical fiber and many other materials at high enough power , there can be new frequencies generated including the sum, difference, doubling of either of the original frequencies, or other combinations.
So, no light sabers, but many other even stranger phenomena.
And photographing the beam scatter of even a high power laser from the side, even *almost* head-on is generally safe as long as the actual beam doesn't enter any of the optics (including our eyes!). Add some dust, smoke, or fog to make it stand out.
But, you've seen those photos apparently shot directly into a laser beam. My recommendation is to NOT try to reproduce them with a digital camera unless you won't mind ruining it. The CCD or CMOS sensor is the heart of your camera. Any damage to even a small number of sensor elements (pixels) will render the camera useless for most purposes.
A direct hit from a laser of less than 1 mW may damage the sensor since it can focus to a micron-size spot there. Using a fast shutter speed won't necessarily help since digital cameras don't have real shutters - the sensor is always exposed and a narrow laser beam may get through even a stopped down aperture in its entirety. Some guidelines:
Film cameras aren't as susceptible to damage from the laser beam but limiting the power to 1 mW is still a good idea.
WARNING: If your camera has an optical viewfinder, take special care that your vision isn't damaged should the beam enter it directly!
Unfortunately, low power laser beams don't look like Star Wars light sabers so some assistance is needed to make decent photographs.
(From: Joe Smiley (cadcoke3@yahoo.com).)
One technique to help catch the beam is to use two exposures, and combine them in something like Photoshop. One of the exposures, is done in complete darkness (except for the laser) and is timed to capture the beam itself, and the glow it has on the surrounding areas. Then, the next is done is subdued light (you can still have the laser on) to get the surroundings.
Another approach (which I've never tried) is to use a flash and an exposure time longer than the 1/60 second the flash requires. The flash itself will occur as soon as the shutter opens, but the longer exposure time will keep the shutter open after that and allow the light from the laser beam to accumulate.
Of course, if you want to see the beam, you must have something in the air to catch the beam, like smoke or dust.
If it is the intense light where the beam is hitting, I've not tried that. But, I figure the double exposure idea could be used there as well. However, in this case, the exposure for the laser is fast with a small aperture. Then the laser is turned off, and a second pictured done to catch the surrounding areas.
Here and elsewhere, the intracavity photon flux may also be referred to as "circulating power" or "intracavity power" and is measured in watts. However, the only way to actually tap into it would be to redirect the intracavity beam out of the laser with a super fast optical switch and then, the power would only be available for a duration of at most the time for 1 round trip between the mirrors. This is one reason why there can be a higher photon flux inside the cavity than there is input power to the laser. For example, a 100 mW diode pumped solid state laser typically uses less than 1 W of pump power to excite the lasing crystal. With 98% reflectivity OC mirror, the intracavity power will be 5 W. No, lasers are not free energy devices but they are energy storage devices. :)
The analogy comparing an electrical tuned circuit to a laser resonator is often used but isn't perfect. In a tuned circuit, the voltage and current inside can indeed be many times that of the driving source, by the ratio of the Q factor of the circuit. However, the true or real power is very low since the voltage and current are largely out of phase. As with the laser, the power can be extracted only by somehow diverting the energy into a load where it becomes true power and then only for a short time.
Also see the sections starting with: Gain, Stability, Efficiency, Life, FB versus DFB Laser.
There are several ways to design a device that will determine the power in a beam of light. Here are two:
Silicon PIN photodiodes all tend to have about the same spectral response curve unless they are specially processed or have a filter added to the detector assembly. They peak around 900 nm at about 0.4 to 0.6 A/W. At visible red expect around 0.3 to 0.4 A/W. See Typical Silicon Photodiode Spectral Response.
For all of these approaches, changes in beam diameter (with distance) or its position should not make much difference in readings as long as the entire beam falls on the sensor. However, if the surfaces are not AR coated (which is quite likely with the salvaged sensor in a home-built power meter), angle with respect to the beam will affect the reading by several percent or more due to the varying reflectivity. The sensitivity increases as the Brewster angle is approached for the portion of the light with the appropriate polarization orientation. The reflectivity of randomly polarized light also varies slightly with angle. Thus, it is important to have the sensor perpendicular to the input beam if possible. In addition, for non-AR coated sensors, the response may be much lower than expected (as much as 20 percent or more) due to reflections at several surfaces requiring increased gain or conversion factor to get accurate readings.
Here are some comments on these approaches:
(From: Jonathan E. Hardis (jhardis@tcs.wap.org).)
Here are a few effects that may not have been considered for photodiode based detectors:
Both of these methods are well documented in the technical literature.
(From: Bill Sloman (sloman@sci.kun.nl).)
The important thing to note is that a photodiode actually detects photons, not power. Up to about 850 nm, each photon actually reaching the diode junction generates one pair of charge carriers. A 425 nm photon, carrying twice the energy of an 850 nm photon generates the same pair of charge carriers, so the same current represents the absorption of twice the power.
Since the 425 nm photon has rather less chance than the 850 nm photon of actually surviving the trip down to the diode junction, so the actual ratio is closer to 2.5:1.
Above 850 nm, the photons haven't got quite enough energy to separate a pair of charge carriers, and can only separate those that are already somewhat excited. The proportion that are sufficiently excited depends on temperature. A electric field also helps, so biasing the diode increases it sensitivity to long wavelength photons. As the wavelength rises above 850nm the extra energy required to separate the charge carriers also rises, so the proportion of 'sufficiently excited' carriers declines quite rapidly.
In principle one could build a wavelength correction into the power meter, but you would need to add a wavelength sensor to the power meter to make it a useful feature.
The Centronics data book gives a typical spectral response for the 5T series diodes, which effectively gives you the inverse of the wavelength correction function, albeit with rather low precision.
The alternative approach is to use a sensor which responds to the heating effect of the laser beam. These exist, but what you win on wavelength independent calibration, you lose on sensitivity and zero stability - in effect you have built a thermometer to measure the heating effect of your laser beam on a more or less thermally insulated target. Unless someone has done something very neat in this line, it doesn't strike me as a practical proposition for your application, granting your limited budget.
(From: Mike Hancock (mhancock@utmb.edu).)
Sharp describes a power meter in their "Laser Diode Uuser's Manual". It uses a Sharp SPD102 reverse biased. They claim +/- 15% accuracy. The SPD102 has a flat response and their peak sensitivity matches the wavelength of "laser diodes", (whatever that means --- sam).
(From: A. E. Siegman (siegman@stanford.edu).)
Many simple low-cost large-area silicon PIN photodiodes (e.g., several mm to a cm in diameter) will have close to unity quantum efficiency, (meaning close to one electron out for one photon in) across much of the visible range and out to close to 1 micron. The manufacturer may also supply a curve showing how the actual quantum efficiency varies with wavelength.
This quantum efficiency doesn't vary much with the reverse bias that's applied over the normal range of operation, or with temperature, and these photodiodes are also fairly rugged devices whose properties tend to be fairly stable with time and use or abuse.
So, if you allow for the varying energy of a photon with wavelength and the manufacturer's claimed variation of quantum efficiency with wavelength, you can make a simple. rugged, large-area, auto-calibrated, and fairly accurate power meter using just one of these diodes, a small battery, and some simple electronics to measure the DC current from the photodiode.
Data on these diodes can be found on the web, and building a power meter like this should be a simple and interesting exercise for one of your electronically talented students.
Source: Handbook of Modern Electronics and Electrical Engineering, C. Belove, ed., John Wiley and Sons, second edition, 1986, pp. 433-434.
pn photodiode: Photons with an energy greater than the band-gap falling generates electrons in the p-type region and holes in the n-type region. If these are within the diffusion length of the junction, they move toward it and are swept across by the field. Light falling in the junction region generates electron-hole pairs which are separated by the field. In both cases, electron charge is contributed to the external circuit. The pn photodiode may be operated with reverse bias and then acts as a current source. They may be operated with no bias and will then generate a voltage and current (photovoltaic effect) with the p-type material being the positive terminal.
pin photodiode: The carriers generated in the junction region experience the highest field and get separated most rapidly and provide the fastest response. The pin photodiode has an intermediate thick intrinsic layer. This is where it is designed to absorb light thus minimizing the effects of the contributions of the slower p and n regions.
Avalanche photodiode: If the reverse bias on a photodiode is set close to the its breakdown voltage, carriers will be accelerated in the depletion region and will have enough energy to excite other electrons into the conduction band resulting in a multiplication effect (avalanche gain). Values of 50 are typical though the gain of some devices may exceed 2,500. Avalanche photodiodes are designed to have uniform junction regions to handle the high electric fields.
Solar cell: This is basically a large area pn silicon photodiode designed to absorb broadband solar radiation.
Phototransistor: A bipolar transistor where the collector-base junction is exposed to light and takes advantage of the gain of the device.
Photo-FET: A field effect transistor where the gain region is exposed to light thus changing the gate voltage.
Sensor manufacturers often have technical information and even sample circuits in their catalogs and on their Web sites. For example, see Hammamatsu Corporation, Thorlabs, and UDT Sensors.
Some specific technical information includes:
A resistance heater may be built into these types of sensors so they can be calibrated without using a laser. The procedure is straightforward, though not quite as simple as inputting a known power (I*V) and adjusting the appropriate pot so the meter reading matches the power since there is some difference in the sensitivity/losses/whatever between light input and electrical input which is lumped into a "calibration constant" for the sensor.
I know of two basic types of thermal sensors (but there are no doubt others): Those that use what are basically Peltier devices (Thermo Electric Coolers or TECs) and those that have an array of up to 50 or more really really tiny thermocouple junctions glued to a thin heat absorber/spreader plate. The response of the latter which are often called "thermopile" sensors should be much faster since there is almost no thermal mass involved. The TEC-based sensors have a slower response but are more robust.
CAUTION: Thermopile sensors are extremely: fragile. To minimize thermal mass, the plate is made very thin and is easily broken. And, it's suspended by the superfine wires going to the thermocouple junctions glued to its rear surface and these will break almost simply by looking at them the wrong way. Even gentle pressure from a cotton swab may ruin the sensor may fracturing the plate and/or tearing the wires. Been there, done that. :( Don't be tempted to do anything beyond using compressed air or dusting the surface off with a camel's hair brush. If it's ugly from previous laser shots, so be it. Ugly is good. :)
Except for minor details, the description below is similar to the TEC-based sensors for use with the instruments described in the section: Scientech Thermal Laser Power and Energy Meters.
(From: Steve Roberts (osteven@akrobiz.com).)
If you need to measure optical power above about 50 mW, thermal becomes a good choice. Having dissected one of mine, it consisted of a 3/4" diameter adsorber disk painted with carbon black in a binder. You can get the carbon black from some drugstores as powdered charcoal for adsorbing poisons in the stomach (at least that's what the pharmacist told me it was used for). A 100 ohm length of thin nichrome wire is wound in a grove around the exterior of the absorber disk and was used as a thermal reference to calibrate the device. The adsorber disk is clamped against a Peltier element with about 100 junctions and this is attached to the outside of the sensor, which acts as a heatsink. The sensor is mounted in a black body cavity (which both adsorbs and radiates heat with high efficiency). This is made of 3" aluminum drilled to hold the sensor. The aluminum is black anodized and then coated with a black oxide coating to make it really black. Other versions I have use a water cooled block with the same Peltier type junction, which when used in reverse generates current (Seebeck Effect). The output voltage from the peltier is very low and has an offset, so this gets ran into a opamp gain stage to clean things up and run the meter movement.
A sensor of this type is relatively easy to make if you have access to a decent set of shop tools, but your calibration would be +/- 10% at best.
Here are some more details on detectors:
I've used flat black black Krylon on some pyroelectric based adsorbers as a emergency fix. No difference in reading. The black from the factory on older thermal adsorbers was sprayed on with carbon dust in it. A few cheapies I've seen have just been black anodized plate with a thick dye layer. Now it's a vacuum deposited film on the new ones. I've had great success with the finely powdered charcoal sold by drug stores as a poison control treatment, mixed with a thin but strong nitrocellulose type binder, I've used clear model airplane dope, with just a few drops of thinned binder to a large amount of powder so it doesn't gloss and keep the applied layer thin. Results have always been a small error due to coating thickness, not enough to matter with most lasers
Some of these detectors have a disk of thin black glass as the absorber It is often something like a Schott RG series, try searching for a company called "Newport industrial glass", they do small quantities. RG has also been known to act as a Q-switch for YAG.
The pyro detector I blew was rated for a 50 joule laser, a 2 joule oscillator amplifier shot with a 2 mm or so beam blew a hole deep into the detector face on the first shot, seems the manufacturer claimed you needed to spread the beam over the whole face. I was doing a freebie consult for the local hospital on their pulsed holographic ruby laser used for breast cancer research. I ordered the detector, having asked the salesman if it could take a direct shot. "Oh sure, no problem, we have a model optimized for short pulse ruby." Bang! We tried to get a refund, but they refused, so we had the credit card company stop payment on it, I ended up stuffing a little carbon in the crack and a coating of black Krylon hand painted on. you couldn't see the hit. It ended up the detector worked great with a Tektronix digital scope and so the megadollar controller went back and the damaged detector is still in use to this day. The ruby was pretty stable from trace to trace and so the subsequent shots on the repaired detector.
(From: Lostgallifreyan.)
Activated charcoal powder. Various sources: Brewers supplies (comes in sachets with wine kits for fining). Incense burners (small disks, can be ground of with a fine file). Medical suppliers (in small packs that can be swallowed to absorb poisons).
The easiest and cheapest way might be to get the address of a brewer's supplier and ask them if they're willing to send you a sachet, the stuff is ideal.
I made a black paint out of 3 parts white spirit to 1 part yacht varnish. (I'd tried matt finish aeroplane kit glue, it was useless. I couldn't get any butyl acetate as thinner, and other solvents made it coagulate). The varnish is gloss, but the high viscosity and adhesion allow a heavy loading of carbon powder (activated charcoal, politely blagged from a brewers supplier). I can't quantify the amount of powder, as it won't suspend evenly in the liquid. I treated it as if it was very wet sand, painted on the ceramic surface of the thermopile, such that vibration could make it shiny as the particles settled after painting it as flat as I could get it. I then shook it, keeping it on a plane surface, to even out the thickness and consistency. I dried it with forced air from a 12 V 80 mm fan at very close range. The forced evaporation (and the high-frequency agitation in the fan airflow) made sure the carbon could not settle in time to allow a shiny surface to develop.
The result is a deep black, almost as good as soot deposition. It looks like very fine velvet, like that paper which photographers use for extreme light absorption. It's damage threshold is high, I had to focus 158 mW to within 0.5 mm diameter before I could get any smoke out of it, and to within 0.25 mm diameter before any blanching of the surface occurred. Response time on the thermopile is good (I didn't get numbers for this though), and the accuracy is good too, about 1% down in sensitivity off- centre to edge, symmetrical around that centre. I've made a very basic gain stage with a dual op-amp (LF412), with the first half making a new ground about 2.5 V above negative so I can get accurate through-zero offset tweak, and headroom to measure up to 30 watts on a voltmeter's 32 volt range. I don't know how much the carbon coating's varnish binder might vary with wavelength, but probably very little given that it has very low reflection now, and I think this system could be good for 1% accuracy providing the beam is centred on the detector plate and spread just wide enough to be below the damage threshold.
(From: Bill Sloman (sloman@sci.kun.nl).)
A lot depends on whether you are interested in the power averaged over the length of the pulse, or the time-resolved power within the pulse.
If you want nanosecond time resolution, you need a photo-multiplier tube (PMT) of some sort - you need lots of gain-bandwidth and the PMT is about the only way to to get it. Unfortunately the gain of a PMT depends on the 10th power (depends on the number of dynodes or whatever) of the voltage across the tube, plus a number of other less easily measurable parameters, so you need a fancy calibration scheme to let you compare your laser with a source of known brightness, which is going to involved quite a lot of predictable attenuation - in short, a can of worms.
If you just want to open a window around the time the laser is on, then a photodiode driving into a Burr-Brown OPA-655 may be enough. The photodiode output isn't as unpredictable as a photomultiplier's, but it depends on the temperature of the photodiode at the junction (which can rise significantly while the laser pulse is being absorbed - a thin junction hasn't got much thermal mass), and the wavelength of incident light, so you still end up with a calibration problem, but at least you haven't paid $1,000 for a photomultiplier before you start buying in the attenuators and so forth.
At least the calorimeter and pyro-electric approaches measure power directly. You can always use precision attenuators to reduce the power at the detector to something manageable.
I tossed this together using a 4 segment photodiode chip from a dead and abandoned Mouse Systems optical mouse (the old type which uses a pair of these chips - one for each axis). The active area of each segment is about 1 mm x 1.4 mm (total about 1 mm x 5.6 mm) which isn't great but is adequate to capture the entire beam of a typical collimated laser diode or HeNe laser.
There is no need for you to use this photodiode! There are better choices, probably already in your junk box. :) A larger area photodiode would be better. To ease this a bit, I tied all 4 segments in parallel so one dimension is no problem at all. There are microscopic gaps between the segments but I estimate it to be less than 5 percent of the area so the loss should not be a big problem.
An 'instrument' (this term is being used very generously!) of this type will not replace a $1,000 commercial laser power meter but may be sufficient for many applications where relative power measurements are acceptable and/or where the user is willing to do a little more of the computation. :-) One cannot complain about the cost: $0.00. :) If you're willing to splurge, go for a $2 photodiode from DigiKey.
The basic circuit is as follows:
S1 R1 1 A 2 7 6
Vcc o-----o/ o----/\/\-----+----|<|----+ _____|_______|_
Power 560 | 4 C 3 | | | | | |
+----|<|----+ U1 | A | B | C | D |
| 5 B 6 | AE1004 |___|___|___|___|
+----|<|----+ | |
| 8 D 7 | 2 3
M1 +----|<|----+
+---------+ | Arrangement of Segments
- | 0-10 mA | + | in Photodiode Array
Gnd o------| \ |-----------------+ (Pin 1,4,5,8 are Common
| o | <- I Cathode and Substrate)
+---------+
For the value of R1 shown above, Vcc should be at least 4 VDC for a photodiode current up to about 6 or 7 mA using a 9 V battery.
Unfortunately, with the small area of the photodetector, using this with intact CD laser optics may not be that easy.
I finally got around to comparing the response of the PD in my homemade power meter with a Coherent Lasercheck. While the shape of the response curve is similar, the actual falloff in sensitivity is much steeper going toward shorter wavelengths. However, this may be more due to the slightly orange tinted plastic of the PD rather than the actual response of the semiconductor. Here are some data points which compare the sensitivity of the photodiode in my home-built power meter (PD1) with the "Standard Response" from the graph, above. The values shown are relative to the red HeNe laser wavelength of 633 nm measured at low to medium power (under 20 mW). Note that for the small area phootodiode, linearity suffers above about 5 mW but the relative responses listed below shouldn't be very far off.
Wavelength PD1 Si Resp
----------------------------------
808 nm 1.38 1.27
670 nm 1.08 1.03
633 nm 1.00 1.00
612 nm 0.93 0.94
604 nm 0.89 0.92
594 nm 0.84 0.89
543 nm 0.67 0.77
532 nm 0.61 0.73
514 nm 0.51 0.66
488 nm 0.38 0.52
- | |+ R1 PC S1
+---||||----/\/\-------o PD1
| | | 560 PV \o------|<|-----o Out
| B1 +------o
| |
+---------------+-----------------------o Gnd
The switch can select PhotoConductive mode (PC) which is better for higher optical power and frequency response, or PhotoVoltaic mode (PV) which doesn't require the battery. This is all mounted in a little plastic box with an internal 9 V battery and BNC connector. R1 is simply for current limiting protection. A capacitor could be put across it to improve the high frequency response. Normally, there would be a load resistor across the output between 50 ohms and a few k ohms depending on the average optical power.
The original intended application was for SGPP1 to be used with an RS232 or USB data acquisition system for recording of the important parameters of various types of lasers. For example, the polarized modes of the output beam of a Zeeman split two-frequency helium-neon laser as it goes through mode sweep during warmup. These are typically low speed signals so the bandwidth is limited 1 or 2 kHz. I had been using a hand-wired passive front end but this has serious limitations with maximum gain and offset that could not be easily adjusted. And replicating that circuit was probably more work than stuffing a few of these PCBs!
SGPP1 Specifications
These assume the component values shown in the schematic:
SGPP1 Schematics
Please see: Sam's Photodiode Preamp 1.
SGPP1 PCB
A PCB layout is available, as well as blank PCBs from Forge Open Source. Go to: "Fusion PCB Pool" (Coming soon).
+------/\/\------o X1
| R3 11.1K X10 S1 Range Select
+------/\/\----o <---o--+
| R4 100K |
+------/\/\---+--o X100 |
| Cc * | |
+------||-----+ | R6 1K R7 5K Calibrate
| | | +---/\/\---/\/\---+
I-> | |\ | | | | |
PD o-----+---|- \ | | R5 1K | |\ +----+
| >----+---------+---/\/\---+---|- \ |
+---|+ / | >--------+----o +
_|_ |/ U2 +---|+ / Vout
- _|_ |/ U3 +--o -
- _|_
-
This circuit provides 3 ranges. R7 (calibrate) allows the sensitivity to be
adjusted for your particular photodiode and laser wavelength. For the
photodiode described above, the ranges will be .01 mW, .1 mW, and 1 mW per V
of Vout at 632.8 nm, with R7 set to 1.22 K. Vout can also be monitored with
a scope or connected to an audio amplifier to detect an amplitude modulated
laser beam.
For the Range Select switch (S1), make-before-break contacts are recommended to prevent high amplitude glitches when changing ranges.
For my photodiode array, the dark current was insignificant. Should this not be the case with your device a potentiometer tied to a negative reference can be used to null it out by injecting an equal and opposite current at the (-) input to U2. Cc compensates for the photodiode's capacitance to ground, see below.
Many variations and enhancements to this circuit are possible.
About the compensation capacitor, Cc:
(From: Gerhard Heinzel (ghh@mpq.mpg.de).)
The photodiode has a capacitance to ground. Thus, the circuit's frequency response will be that of a two-pole lowpass filter with a pole frequency of:
f(pole) = sqrt(F1 * f2)
Where:
The solution is easy: Put another capacitor in parallel with the feedback resistor. Its value (for maximally flat response, which usually also eliminates the instability):
sqrt(2 * R * C * w2)
C = ----------------------
R * w2
There are 4 power ranges calibrated for the HeNe laser 632.8 nm wavelength: 19.99 uW, 199.9 uW, 1.999 mW, and 19.99 mW full scale. A separate switch selects between HeNe laser power and straight mA readings. In addition, since I just had to use the other 2 positions of the 6 position switch for something, I included 199.9 mV and 1.999 V ranges as well. A couple of diodes across the meter inputs protects it against excessive voltage.
The precision resistors were each made up from a pair of 1% resistors to approximate the needed value to 0.1 %. A pot and resistor could also have been used.
The computer mouse photodiode array based sensor attaches via a cord with an RCA plug so it can easily be replaced with a 'real' laser power meter probe in the future.
I had to build power supply to for the panel meter which required both +5 and -5 VDC - a few parts from my various junk drawers took care of that. A power transformer wouldn't fit inside the case so I used an orphaned wall adapter instead.
It is best to use a single cell, not a series or parallel connected array. Places like Radio Shack and Edmund Scientific should have something suitable. A single op-amp is used as a current-to-voltage converter similar to the one above but since the Photocell generates current, no bias is needed.
The following design is similar to one presented in: "Homemade Holograms: The Complete Guide to Inexpensive, Do-It-Yourself Holography" by John Iovine, Tab Books, 1990, ISBN: 0-830-63460-6. Additional information can be found there.
R2 360
+-----/\/\------o 50 mW
| R3 1.8K
+-----/\/\------o 10 mW
| R4 3.6K
+-----/\/\------o 5 mW
| R5 18K 1 mW S1
+-----/\/\------o <------+ Range Select
| R6 36K | (Full Scale)
+-----/\/\------o .5 mW |
| R7 180K |
+-----/\/\------o .1 mW |
| R8 360K |
+-----/\/\------o 50 uW |
| |
| +Vcc +-----------+
Photocell | o |
- +--+ + | 2|\ |7 | Calibrate
+--|PC|---+----------+---|- \ 6 | R8 4K R9 2K - +-------------+ +
_|_ +--+ | R1 100 3| >---+---/\/\---+-/\/\-----| Panel Meter |---+
- +---/\/\---+---|+ / | | +-------------+ _|_
_|_ |/ |4 U1 uA741 +---+ 1 mA Full Scale -
- o
-Vcc
This circuit provides 7 ranges. I have optimistically extended the upper
and lower limits a bit (untested but the op-amp should remain happy). A
make-before-break type switch should be used to minimize transients when
changing ranges. The duel power supply can be anything in the range +/- 9 V
to +/-15 V. Use a pair of 9 V Alkaline batteries for portability. The
photocell itself can be mounted in a little box on the end of a shielded cable
if desired.
The feedback resistor values shown are based on a Radio Shack photocell that is probably no longer available (276-124) and even if it is, who knows how its specifications compare with what they sold a few years ago! For that matter, compared to what they sold you 10 minutes ago! :) Since the sensitivity of your photocell will probably be different, I recommend constructing everything except the feedback network. Then, using a laser of known power output (e.g., a 1 mW HeNe), with the Calibrate pot (R9) centered, select a feedback resistor which results in the proper power reading on the meter. (The resistor values shown are probably close but R9 may not have enough range to compensate for the sensitivity of your photocell using them.) Finally, adjust R9 so that the feedback resistors can be standard 1% values, calculate their values, and wire up the rest of the circuit.
I use a home-built power meter to measure green lasers, Diodes and HeNe lasers with power up to 400 mW. The diode (0.5A/W) has a 5 x 5 mm aperture and I use a 1% neutral density filter (OD=2). The range of measuring can be switched 1 to 20 mW, 10 to 200 mW, 20 to 400 mW. I calibrated the thing with a very expensive Coherent meter and the error is approx. 5% over the full range. The nonlinearity is only a problem at the ends of the signal curve of the diode, at too low power and at too high power. In my application, a real power between 50 microwatts and 5 mW at the diode gives no linearity problem. You should take care, that your signal is part of the linear ramp of the current/brightness graph of the diode. If you want to measure power of 0.1 mW and 5 W with the same meter, you should design the thing for low power (10 mW max) and add neutral density filters. Naturally, you cannot measure microwatts if the meter is designed for Watts. Because you need a high gain at low power in this case, noise and offsets will make error. The dark current of the diode will cause an error at the low end. I have a permanent offset of 0.8 mW on my display. If I want to measure power below some milliwatts, I should construct an extra meter for this low power. The biggest problem is, that you cannot measure a multiline laser with Photodiodes. And for different wavelengths I use a switch with several positions, switching several gain values. Every gain stage must be calibrated with a professional meter. It would be nice to have exactly data about spectral sensitivity from the manufacturer but I have not found any.
(From: Lou Boyd (boyd@fairborn.dakotacom.net).)
Diode detectors are a pain to calibrate unless you have a light source of known energy at the same wavelength you're trying to measure. A method which resolves (mostly) the calibration problem is to use a small thermistor. Epoxy a 1/4 watt resistor to one side and coat the other surface with lamp black. Put thermal insulation around all of it except the smoked side. Apply about 1/4 watt of power to the resistor and let it come to equilibrium and measure the resistance of the thermistor. Then focus the beam of the laser on the smoked thermistor and reduce the power to the resistor to keep the thermistor resistance at the same value. The laser power should be equal to how much the resistor power was reduced. It's very cheap, fairly accurate, uses your DMM for the readings, and will measure CW or average power of small pulsed lasers.
Photodiodes and other sensors are not perfect. Photodiodes will start saturating and becoming non-linear at lower power as the beam size decreases. Thermal detectors may not have quite the same sensitivity from center to edge. Even with high priced commercial instruments, a few percent variation can be expected as the beam size changes due to focus or distance even if it's known that the entire beam falls on the active area in all cases.
The specifications probably list the maximum power density for accurate readings, but few people take it seriously. But if you stay below that, then the change will be minimized. And, in general, there will be less effect at lower power density. If a neutral density filter is supplied with the meter, it may be best to use it even if the power level isn't very near the upper limit listed in the manual. Yeah, like you have read the manual! :)
Changes due to angle of incidence can be caused by the increase in power reflected from a cover glass or sensor surface. Periodic variations in the reading with respect to angle may be due to interference (etalon) effects within the sensor's cover glass. The most accurate reading will normally be for near-normal incidence, where the reflected beam would just miss the laser's output aperture. (Reflecting back into the laser is bad for most lasers and also may result in a reflection coming back from an optical surface in the laser and affecting the power reading.)
Sensors that have seen a hard life may show scars in the form of areas of differing surface characteristics which will further complicate things. My Coherent LaserCheck looks like it's been in combat. :)
The sample I tested seemed accurate enough as it agreed with my home-built power meter to better than 1% up to about 20 mW. :) (I assume the Lasercheck is more accurate for higher power.) It's convenient for making quick measurements of a laser without having to make space for a detector head. My main gripe is that the readout should have been mounted at a 90 degree angle (or on a swivel) to the sensor so it can be more easily seen while taking a reading. Even though the peak measured value is held for 10 seconds after releasing the "capture" button, I would still like to be able to see it being taken. The angle of beam incidence is also fairly critica and should be as close to normal as possible without reflections off the sensor hitting the laser output mirror and bouncing back into the sensor. Since the Lasercheck displays the peak power, even a momentary reflection will result in an excessively high reading. Speaking of which, I do not know how well the Lasercheck deals with quasi-CW sources as there are no specifications in the "user manual" (a 1/4 page insert) that came with it. My tests were inconclusive but readings of a green laser pointer producing a ~500 Hz squarewave (not Q-switched) output appear to be slightly high.
CAUTION: Although the Lasercheck is capable of measuring power up to 1 W, take precautions to spread it out over the area of the detector. The attenuating filter is made of plastic and will melt as I found out. Please contact me via the Sci.Electronics.Repair FAQ Email Links Page if you know where to get a replacement inexpensively. It still works fine but looks ugly. Not mention the melted areas of the plastic case near the detector. :( This from testing some high power fiber-coupled laser diodes.
To obtain consistent readings from the LaserCheck:
NOTE: The LaserCheck seems to be easily confused where multiple wavelengths are present. I was testing a green DPSS laser which for some reason lacked an IR-blocking filter. Without a filter, there was enough IR leakage, mostly at 1,064 nm, to totally confuse the LaserCheck. It was reading several hundred mW at 532 nm for a beam that was obviously only a few mW of green. In fact, the total optical power including pump and laser together was much less. When set at 1,064 nm, it showed a few mW of IR which was probably close to being correct. I'm still not sure why the LaserCheck was so totally confused when set at 532 nm. Assuming it uses a silicon photodiode, the sensitivity at 532 and 1,064 nm shouldn't be that different. (The specs say it is a "silicon sensor" but not explicity photodiode.) I would have expected some error since both wavelengths are contributing to the reading (perhaps a factor of 2 or 3) but not a couple orders of magnitude! Thus, it definitely CANNOT be used to measure the power of multiline lasers unless a filter is used for each wavelength.
My only complaint is that the mechanical design must have been done by a masochist. :) Removing a pair of screws inside the battery compartment allows the two halves to be separated. But this exposes the very delicate and fragile analog meter movement. So one must proceed with extreme caution in attempting any sort of repair. For example, on the one I have, a few segments of the display were somewhat flakey, most likely due to dirty "zebra stripe" connectors attaching the LCD to the mainboard. However, to clean these required removing and unsoldering the analog meter movement to gain access to the back of the LCD panel. While straightforward, there is always the chance of bending the needle, getting ferrous particles into the magnet, or worse. In addition to cleaning the connectors, I had to add a bit of electrical tape around the periphery of the LCD assembly to increase pressure on the contacts. So far, it seems realiable.
I have an LM2 bead (50 mW max, 400 to 1,100 nm) but am in search of other sensors for this unit. If you have a compatible sensor (or other FieldMaster related items like one in need of repair or a parts unit), in almost any condition gathering dust that needs a new homw, please contact me via the Sci.Electronics.Repair FAQ Email Links Page.
I have tested one so at least if you run across a system surplus, perhaps this will help. The meter has two input channels (one of them accepts temperature probes as well), an SD card slot for on-board data logging; digital, pseudo-analog bar and graphic displays; USB remote control with data acquisition to LabVIEW (included) on Windows (Win2000 and above), Mac, and Linux; and programmable gain analog outputs that track each of the input channels. The update rate is greater than 4 samples per second, except when the laser power increases by a large amount requiring a range change, in which case there is a small delay. A straightforward menu system enables measurement parameters to be easily checked or changed.
The backlit 320x240 LCD display provides both a digital readout and plotting capability right on the unit. So, for example, the mode sweep behavior of a HeNe laser can be viewed (and stored for later analysis) directly by the MPE-2500 without having to drag out a PC with a data acquisition card. I've really become quite fond of this feature, though a few more scale factors for the autoscaled vertical axis and an option for changing the horizontal timebase would be nice. The bargraph - useful for laser alignment - is not quite as good as a direct responding analog meter needle, but comes close.
I had the MPE-2500 with a pyroelectric and semiconductor probe on loan and there are a few improvements I would like to see (besides a lower price!), mostly related to the menu navigation, number of wavelength presets and ease of switching among them or changing wavelength directly, and graphing options on the LCD. All of these could be accomplished largely by a straightforward firmware upgrade. My main remaining complaint had to do with the angle sensitivity of the semiconductor probe, which I concluded was due to optical interference (etalon) effects between the two surfaces of the cover glass on the photodiode. Ironically, a lower cost Epoxy encapsulated device would have cured this, a suggestion I made to Spiricon, probably about the time they ceased to exist.
Otherwise, the MPE-2500 is an all around well engineered general purpose laser measuring system. A few more revisions of the firmware and minor changes to the sensors, and it would have been perfect. Too bad.
The probe for the 820 can be almost any old photodiode since there are separate calibration pots for 632.8 nm (red HeNe laser), and 514 and 488 nm (major green and blue lines of argon ion laser). It's old but solidly built and simple inside so there is very little to go wrong. The photodiode feeds into a virtual ground so no power is needed for the sensor head. My only gripe with it is that the ranges all go by powers of 10 rather than the more desirable 1,3,10,30... sequence. Without overlap, this is a less convenient arrangement and becomes somewhat annoying around the transitions.
However, there's a partial solution to this that is fairly painless. Since I mainly would use the 820 for 632.8 nm red HeNe lasers, I adjusted the calibration of the argon ion 514.5 nm and 488 nm ranges to be 2X and 3X of the 632.8 nm range using the pots accessible from the bottom of the 820's case. A 1-2-5 sequence would be better but that would require increasing the overall gain somehow, and then readjusting the pots since the 488 nm gain is maxed out with its pot at 0 ohms. However, a 1-2-3 (or just 1-3) sequence can be done with adjustments alone.
I found an 820 on eBay without probe for $30 including shipping and have been using a $2 photodiode as a sensor. I may upgrade that eventually. :) The only problem with the unit was a set of 3 very dead 8.4 V mercury batteries. These are probably not available anymore, would be very expensive if they were, and likely died because someone accidentally left the meter on for a few months. I thought about using three 9 V Alkaline batteries (the meter only uses about 5 mA) with a regulator but these would still have the accidental draining problem. Since I don't really care about portability, I installed a 25 V power supply fed by the wall adapter from an old modem (2,400 baud, totally obsolete, but probably much younger than this meter!). The 12 VAC output of the wall adapter feeds a doubler with an LT1084 adjustable regulator. The "Battery Test" button still functions to confirm that the power supply is working correctly - like this will change during the life of the Universe! :)
There is also apparently a version that has a 115 VAC power supply built in though the model numbers are identical. It lacks the battery holder clips but still has the battery test button.
The 820 really adds class to what passes for my laser lab. :)
I've since gotten 2 more, one for only $10, as well as a mating Newport 882 silicon photodiode low power sensor head for $10! The readouts are now showing up quite regularly on eBay.
The sensor head was missing on the unit I had and it would probably be much too sensitive anyhow so I used the photodiode from a barcode scanner to build a replacement. With a bit of experimentation, I determined that what it is measuring is a current on its input (convenient) so I built the following circuit to allow use of a silicon PN or PIN diode wit adjustable external calibration:
9V
+| | - Sensor Power Photodiode 43K 25K
+----||||--------o/ o----------|>|---------+---/\/\---+-/\/\-----> Input
| | | S1 PD1 | R2 | ^ R3
| BT1 ~0.43mA/mW R1 / | | Cal.
| 220 \ +---+
| /
| |
+------------------------------------------+---------------------> Return
The value for R1 was selected as being safe current limiting for the photodiode and it could possibly be reduced to increase the maximum input power that will register on the readout. The values for R2 and R3 were then selected so the calibration matched that of my super simple laser power meter. (There is an internal adjustment for calibration but I thought it best to leave this alone, just in case a proper sensor head ever showed up.) Later, I confirmed that my Coherent LaserCheck agreed with it. :) The negative polarity was required so the readout would be positive - I hate when these things indicate negative light levels! :) (I have no idea why a light meter would even support negative readings unless UDT just relabeled another type of meter, or more likely, used a standard LCD digital panel meter.)
A photo of the complete rig is shown in UDT 351 Based Laser Power Meter. The sensor is on the adjustable arm and can be instantly adjusted for the height of almost any laser. Believe it or not, despite owning several complete commercial laser power meters, this is my workhorse for evaluating low to medium power HeNe, ion, and DPSS lasers.
The six ranges are labeled 2, 20, 200, 2K, 20K, 200K which now read out directly in uW. So, 20K is 20,000 uW or 20 mW full scale. Given the component values, the maximum input power is limited to about 50 mW so only part of the 200K range is useful. And since the dark current of a typical photodiode is equivalent to a couple of uW, the 2 uW scale isn't terribly useful either.
Note that if it wasn't necessary to scale the current into the meter, the sensor could have just been a silicon photodiode because running in photovoltaic mode (directly connected) since I believe the input feeds into a virtual ground. However, reverse biasing the photodiode results in a higher power input before non-linearity becomes an issue (at the expense of dark current).
After calibrating the meter, to make it easy to check in the future, put a 10K resistor across the photodiode terminals and note the reading, X. Measure the voltage of BT1, Vb. The calibration constant is then just Vb/X and should not change. It can be checked at any time using the same resistor.
CAUTION: There is a rechargeable 9 V battery inside which powers the meter when the wall adapter is not used. However, it is connected directly to the charging jack - thus the original wall adapter must be used since (I assume) it limits the charging current to a safe value for the battery. If your sample didn't come with the original wall adapter, make sure what you use is current limited to prevent damage to the battery. One alternative is to discard the rechargeable battery and replace it with a 9 V Alkaline battery with a blocking diode in series with one lead so that the wall adapter can't attempt to charge it.
I have several older models. The 361 and 364 use analog (meter) readouts while the 365 has a 3-1/2 digital LED display. The 361 measures power only, in ranges from 1 mW to 10 W. The 364 does both power and energy measurements in ranges from 300 mW to 20 W. And the 365 also measures power and energy with ranges from 20 mW to 20 W and also has a "tune" mode which basically displays the derivative of the input, presumably useful laser alignment.
They all use sensors similar to the type described in the section: Thermal Laser Power and Energy Meters. The electronics are very simple: Just an op-amp to amplify the very low level voltage from the sensor along with some some frequency compensation to help improve the response speed. For power measurements, the readout is based on a combination of the rate of change of the input voltage from the sensor and the steady state value to account for the thermal time constant of the sensor. For energy measurements, the display is based on the difference between the input voltage before and after the laser pulse. (Normally, the display would be zeroed just prior to the pulse.) For the 365 tune mode, it displays the derivative of the power reading.
See the Scientech Web site for information on modern Scientech laser and power energy measuring instruments. There is also an article on thermal measurement in general under "Laser Power Meter Application Notes".
A home-built version of this type of laser power meter could be constructed relatively easily inexpensively. A meat thermometer might not be suitable for modest power lasers but more sensitive dial thermometers are readily available. A chunk of aluminum coated in lamp black (e.g., smoke from a candle) would suffice for the mass. Knowing its weight and the specific heat of aluminum, calibration could be done "off-line" - without any laser. :)
These can also use electronic IR or contact thermometers with home-built targets. With care, these can measure down to 5 mW or even lower. See Simple Laser Power Meter Using IR Thermometer.
It has ranges from 10-2 to 10-8 watts, selection of a number of common laser lines (intended to be determined by the sensor, since there is no switch for this purpose), and a zero adjust. The presense of the zero control suggests that one of the intended sensors might have been a thermal type. There is also a current range so photodiode sensors were probably available as well. In either case, it should be possible to use your own sensor with at most minor modifications to the very simple dual op-amp circuit, or just some simple additions.
But just figure that what you got for your money (assuming you spent anything on this) is a nice (but old) 3-1/2 digit Digital Panel Meter (DPM, and Analog Devices AD2006), and selectable range preamp. If you want to make use of the wavelength LEDs, install a selector switch to adjust the gain based your sensor and which wavelength is selected. It might be best to simply ignor them since the wavelengths don't include all those you're likely to want. The 460-1A wavelengths are: 441.6 nm (HeCd blue line), (488 nm and 514.5 nm (argon ion strongest blue and green lines), 632.8 nm (HeNe red line), and 904 nm (who knows). There is also an LED for a current range (Amperes) with the same range multipliers.
The connector labeled "Detector/Pulse Integrator" for the sensor appears intimidating with almost all of the pins used but that's an illusion. Over half the signals are there simply to select which LED is lit by connecting to the ground pin or by the output of a logic gate (the supply for the LEDs is +5 VDC). A coax-type pin (in the connector) is the sensor input. Only 5 wires need further attention - their functions are listed below but in essense, enable the circuit to be a used as a voltage or current amplifier with the appropriate gain constant. It should be possible to adapt this unit to almost any sensor that outputs a voltage or current (what else is there?).
The 460 also has a recorder output BNC which is exactly the same signal going to the DPM with a full scale range of 2 V (plus or minus). There is another BNC labeled "Variable Time Constant" which probably takes a capacitor to modify the speed of response.
The only active components are a pair of op-amps in socketed TO5 cans labeled "545KH", probably equivalent to the AD545 (Analog Devices FET input op-amp). One is used as an inverting with gain determined by the range selector switch and external components attached to the Detector/Pulse Integrator connector. The other is simply a buffer for the DPM with an internal gain adjust pot. On the unit I have, its gain was set at about 4.5. This makes sense if used with a silicon photodiode since all that is then needed is to add a voltage divider to reduce the gain depending on which wavelength is selected.
The DPM takes its power from the AC line and provides DC power to the rest of the system. The op-amps run on +/-15 VDC while +5 VDC is provided to the LEDs and external detector circuitry.
Since the mate to the detector connector isn't something that you're likely to find in your junk drawer, and most of the pins won't be used anyhow, consider adding a separate BNC for the sensor input, and possibly replacing it with a DB9 (which should fit in the space) for any other signals that might be needed. Or, just build any additional circuitry inside the case and just have a BNC for your sensor.
Note that the center of the Variable Time Constant BNC is the same as the input but its shield goes to the amplifier output, not ground (it's insulated from the chassis). So, without rewiring, this connector cannot be used for the input signal.
Detector/Pulse Integrator connector pinout:
Pin Wire Color Function ---------------------------------------------------------------------- A Violet 750 ohms to ground B Black-Coax Sensor input (center), ground (shield) C Brown 514.5 nm (green argon ion laser) LED cathode D White/green +5 VDC (logic or analog power) E White Amperes LED cathode F Brown/white 632.8 nm (red HeNe laser) LED cathode H Blue Input to DPM/Recorder buffer amplifier (HiZ) J Green 904.0 nm (who knows laser) LED cathode K -- No connection L White/red Output of selectable gain amplifier M Gray 441.6 nm (HeCd laser) LED cathode N Black Ground P Red Range switch common (to feedback network) R Yellow 488.0 nm (blue argon ion laser) LED cathode
Notes for specific signals:
Wiring for various uses:
Here are suggestions on various sets of connections and circuits to use with the 460:
LED Input Voltage
Function Connect Connect Divider Units
--------------------------------------------------------------------
Current E-N B 1/4.5 A
Laser Power (632.8 nm) F-N B 1/2 W
Laser Power (514.5 nm) C-N B 1/3 W
Voltage NC B via 10K 1/4.5 V*100
Notes:
I have a bunch of UDT model PIN-6955-4 pulled from some sort of gas analyser. This device is a custom part made for the Wyatt Corporation, but appears basically similar to the UDT-455 with an active detector area of slightly over 2x2 mm. It is in a 4 pin hermetic TO5 package with a glass window and is powered from +/-15 VDC (and common). The remaining pin is the output (0 to over 12 V). Unlike the UDT-455 which comes in an 8 pin package, since there are no other connections accessible, the sensitivity cannot be adjusted - and it is very high. I measured about 60 nanowatts (at 633 nm) for full scale output! I had to use a stack of ND filters in front of a 2 mW HeNe laser in a darkened room to get the output to not be maxed out. :) Assuming the circuit is similar to that of the UDT-455 and the op-amp is not running open-loop, the internal feedback resistor would be about 500M ohms!
While designed for CW lasers, it can also be used with quasi-CW lasers and low energy repetitive Q-switched lasers.
The pyroelectric sensor has a diameter of 1 cm with a maximum power density rating of 4,000 W/cm2. That means a 2 mm diameter 100 W beam won't melt it, supposedly! :)
A pyroelectrically-active material produces a voltage as a result of changes in temperature. So, it can't normally be used to measure the output power of CW lasers. However, the SP-405 has an internal mechanical chopper - a metal disk with a single narrow slot driven by a motor. (For that 100 W beam, perhaps 1 percent or less of it will reach the sensor - the rest is mostly reflected to heat the finned enclosure.)
The pyroelectric sensor has a faster response than most thermal sensors capable of handling a similar maximum power. Since the sensor really isn't exposed to the high power, there is probably less drift and need to adjust the zero setting compared to a thermal sensor.
The SP-405 has a "Prot" mode that may be enabled to close a mechanical shutter automatically if it detects a power level that is too high (if it isn't already too late).
While the SP-405 responds to sub-mW power levels or power changes, it is quite noisy on the high sensitivity ranges. The spec'd RMS noise of 50 uW or 2 percent of full scale (whichever is greater), means the display is jumping up and down by over 100 uW p-p. This is rather substantial on the 1 and 3 mW ranges! I wish there were an SP-405-Junior with a maximum power of 1 W but 100 times less noise! :-)
The system is shown in Spectra-Physics Model 405 Pyroelectric Laser Power Meter on the 1 mW Range and Spectra-Physics Model 405 Pyroelectric Laser Power Meter on the 100 WATT Range. (For the first photo, zero was adjusted to produce the reading shown with no input.)
IR indicator cards can have either an amber or a green phosphor (same as in old monochrome monitors). :) The ones sold by Radio Shack contain an amber phosphor which would glow (demonstrating Stokes law) under long-wave UV excitation. Phosphors normally would have persistence (phosphorescence). However the phosphor used in the cards contain a crystalline doping material added to suppress the spontaneous emission of light (the phosphorescence). Thus the excited atoms remain excited until you come along with your IR source and break them free. :) This is an example of stimulated emission, same as in a laser. Once the cards are pumped with UV light, they have a short lifespan before they spontaneously decay, again, just like a laser.
The use of a Neutral Density (ND) filter is one of the most commonly used approaches but it might be hard to find an optics store open at 3 AM on a Sunday morning to buy one that you need NOW. :)
Putting several pieces of paper or frosted glass or plastic in front of the photodetector is an often used technique to cut the sensitivity. Depending on the number of layers and color, the attenuation can be varied over a wide range. However, I bet the manufacturers call it something other than "a few pieces of paper" in their bill of materials. :)
Using a partially reflecting mirror is another possibility. An Output Coupler (OC) mirror for the same type of laser being tested might have a transmission of a few percent. Just put it at a slight angle to the beam so the reflected spot goes somewhere such that it doesn't interfere with the laser or the photodetector.
At a single wavelength laser or one having a fixed output mix of wavelengths (like a multiline argon ion laser) with a power level of up to a few mW, you can also try some bits of colored glass or plastic, even if they aren't intended to be used as filters. The fact that they aren't neutral density won't matter.
However, many dyes - even those used in some supposedly neutral density filters - are photochromic - they change their absorption (up or down) depending on the power density of the light passing through them and thus become non-linear. This may show up as a drift in the power reading after the beam intensity or position on the sensor changes. Spreading the beam may reduce this effect. I have some amber glass filters that do this when the incident power at 532 nm (green) exceeded a few 10s of mW. I was using a pair of them in series as an attenuation filter for a laser power meter so that a small silicon photodiode would work up to 200 mW. It took awhile to figure out that the slowly declining reading leading to a 2 or 3 percent error at 100 mW was caused by the filters and not some obscure circuit problem. The power reading would start out at one value and then gradually go down as time progressed, finally stabilizing at a lower value. Replacing the amber glass with a piece of an ND2 neutral density filter resulted in similar behavior but in the opposite direction - the dye was becoming slightly bleached by the high intensity light and would drift upward by 1 or 2 percent over the course of a few seconds. Since laser power meters usually aren't spec'd to have an accuracy much better than +/-5 percent, such behavior really isn't that significant, just annoying. And, since this particular power meter is part of my Coherent C315M laser test jig, calibrating it to be accurate at around 100 mW results in negligible error since that's the power at which most lasers are tested and adjusted. :)
Mount any polished filters at a slight angle so reflections from their non-AR coated surfaces won't affect the laser (from back-reflections) or the reading (from multiple reflections). Always orient the meter so reflections are slightly off to one side, but close to the laser's output aperture so that the reflection losses don't change much due to angle.
Determine the calibration factor for the power meter by measuring a low laser with and without the filter in place.
Assuming your laser power meter can be used at the wavelength of your new BIG laser, it can easily be adapted to read high power as long as the polarization of the laser is fixed (see below). Send the laser beam through a pair of 45 degree plain glass beamsplitters (e.g., microscope slides) in series with the reflected beam from beamsplitter 1 going to beamsplitter 2 and sending only the reflected beam from beamsplitter 2 to your laser power meter's sensor. Each beamsplitter will reflect about 8 percent and pass 92 percent. So, after two reflections, you get about 0.64 percent. The reading on the laser power meter will then be about 0.64 percent of the true power or roughly 64 mW for a 10 W laser. It can be calibrated more accurately by using a laser of known power to test it. The laser doesn't need to be high power as long as 0.64 percent of its power can be measured with enough resolution on your laser power meter.
There are at least two advantages to this approach over that of using neutral density filters to cut down the beam intensity. The main one is that there is no problem with the beam passing through plain glass while a neutral density filter could easily be damaged by an intense beam. The other one is that the cost is negligible!
Where the polarization of the source isn't constant (e.g., it is from a randomly polarized ion laser or from a multimode fiber), it is essential that the beamsplitter be polarization insensitive. The plain glass at 45 degrees does not satisfy this requirement since its getting close to the Brewster angle. For example, using the plain glass beamsplitter with a high power laser diode fed through a multimode fiber may result in a power reading that varies by a factor of two or more by just moving the fiber as the polarizations of the various modes move and their polarizations change. Furthermore, since the distribution of power in the various modes tend to change with power, the reading may not be linear with respect to power even if the fiber isn't touched. For a random polarized HeNe laser, the power reading may change by 10:1 due to mode sweep as the tube warms up. If the angle of incidence is arranged to be close to 90 degrees (normal incidence) rather than 45 degrees, the error will be small, but this is generally difficult and may not be possible at all.
Commercial beamsplitters are also available which are relatively polarization insensitive. But many are far from perfect and a residual error of 5 to 10 percent is often present. This will depend on design and is generally somewhat wavelength dependent. The manufacturer will generally supply a plot of the S and P polarization versus wavelength.
However, a polarization-insensitive beam sampler can be made by using two identical beam reflecting plates in series oriented so that the orthogonal polarizations are reflected at the same two angles of incidence (but in opposite order). So, for example, orient the first plate at 45 degree incidence so the vertical polarization has a high reflectance while the horizontal polarization has a low reflectance. Orient the second plate so the opposite occurs for the beam reflected by the first plate. If done with care, the result will be a beam sampler that is totally independent of polarization.
The extension to even higher power or for a laser power meter with a lower maximum power rating should be obvious. :)
WARNING: Make sure that the non-reflected beams terminate in something that can take the power and not burst into flames!!! And don't forget the laser safety goggles!!!
These are the type that are aimed either at the scene to be photographed or in the direction of the illumination. There have been many types manufactured over the years and all *are* basically measuring light intensity one way or another. However, measuring the power in a laser beam is not quite the same thing. In particular, the reading should be independent of the spot size to the greatest extent possible. And, of course, there are those trivial issues of wavelength. :)
As a test, I tried using an old General Electric exposure meter based on a selenium cell that requires no batteries. This thing is so old that there isn't even a model number. The readout is in Foot Candles. For measuring laser power, some arbitrary conversion factor would be needed for each wavelength. There is a frosted plate over the actual sensor and the response doesn't matter much where the laser is aimed. Similar exposure meters that have a fly's eye or honeycomb lens in front of the sensor are very sensitive to spot position and useless without further work.
However, the spot size definitely affects the sensitivity, possibly by more than 2:1. So, unless you can standardize on spot size, any readings would be quite questionable. For example, shining the laser on an oblique angle produces a much *higher* reading, as does reflecting the beam from a mirror 5 feet away (due to the larger spot, even though there is a loss hitting the mirror).
What might work more consistently is to add a diffuser in front of the sensor. This would spread the light over the entire sensor. But diffuser design could be tricky.
But this approach would work for comparing the output power of lasers with similar spot sizes such as, for example, selecting a green pointer.
Note that the configuration of the cavity and the mirrors determines the mode structure - they have to reproduce themselves in a round trip. The geometric shape of the gain medium only determines which modes see the most gain.
There are many more but these will keep you busy for a while designing a laser!
A particular resonator configuration will be selected based on many factors including diffraction loss, mode volume, ease of alignment - and cost.
In the following summary, r1 and r2 are the radius of curvature of the two mirrors and L is the distance between mirrors. Refer to: Common Laser Resonator Configurations while reading the descriptions of the 8 types below:
Highest mode volume and highest diffraction loss. Does not focus beam inside lasing medium minimizing possibility of damage in high power pulsed lasers. Most difficult configuration to align and maintain alignment over time. While this is what most people think of when discussing lasers, it is seldom used for other types of lasers.
Lowest mode volume lowest diffraction loss. Focuses beam to diffraction limited spot inside lasing medium making it unsuitable for even modest power pulsed solid state lasers due to likelihood of damage to lasing medium. However, this is an advantage for dye lasers requiring the peak intensity at the focal spot to achieve threshold. Easiest to align.
Note: The point of precise equality (r1 = r2 = L/2) is actually a singularity and unstable. Even the slightest increase in L or descrease in r1 or r2 will result in an unstable resonator and inability to lase. Very slight variations in mirror curvature or distance (e.g., due to manufacturing tolerances or thermal effects) will result in widely varying mode volume, spot sizes at the mirrors, lasing threshold, and output power. However, a cavity slightly shorter than the exact spherical configuration (1 or 2 percent) is quite stable with the desirable properties described above. Thus, this is what will actually be found in a laser spec'd as having a spherical resonator.
Improved mode volume at the expense of a more difficult alignment and slightly greater diffraction loss than that of the confocal configuration. Suitable for CW lasers but not widely used.
Compromise between the plane-parallel and spherical cavities combining the ease of alignment and low diffraction loss of the spherical cavity with the increased mode volume of the plane-parallel cavity. Confocal cavities can be used with almost any CW laser.
Note: The point of precise equality (r1 = r2 = L) is actually a singularity and unstable. Very slight variations in mirror curvature or distance (e.g., due to manufacturing tolerances or thermal effects) can produce large diffraction losses resulting in high threshold and fluctuations in output power. However, cavities slightly longer or shorter than the exact confocal configuration (1 or 2 percent) are quite stable with the desirable properties described above. Thus, one of these is what will actually be found in a laser spec'd as having a confocal resonator.
Essentially 1/2 of the spherical cavity with similar properties. The main advantage is in requiring only one curved mirror. Used with many low power HeNe lasers because of the low diffraction loss, ease of alignment, and the lower cost.
Note: The point of precise equality (r1 = L) is actually a singularity and unstable. Even the slightest increase in L or descrease in r1 will result in an unstable resonator and inability to lase. Very slight variations in mirror curvature or distance (e.g., due to manufacturing tolerances or thermal effects) will result in widely varying mode volume, spot sizes at the mirrors, lasing threshold, and output power. However, a cavity slightly shorter than the exact hemispherical configuration (1 or 2 percent) is quite stable with the desirable properties described above. Thus, this is what will actually be found in laser spec'd as having a hemispherical resonator.
This combines the cost advantage of the hemispherical cavity with the improved mode volume of the long-radius cavity. Most CW lasers (except low-power HeNe lasers) employ this type of cavity. In most cases, r1 > 2*L.
Normally used only with high power CW CO2 lasers where the diameter of r2 is smaller than that of r1 and the beam exits in that outer area as a doughnut shape. Thus, this configuration is unique in not requiring an OC mirror with less than 100 percent reflectance - a challenge for high power CO2 lasers.
However, I have also come across HeNe laser output mirrors with a very slight *negative* RoC - they are convex rather than concave with respect to inside the cavity. At first I thought these were a mistake, coating the wrong sides of the mirror glass or something like that. But these do indeed result in a stable resonator configuration and actually have a slightly lower divergence than a similar concave mirror (in the usual concave-concave or planar-concave configuration).
For non-symmetric resonators, r1 and r2 can of course be interchanged.
And here is another one that is nice for experimental lasers:
Essentially the special case of a long radius hemispherical cavity where r1=2*L. It is equivalent to 1/2 of a confocal cavity of length 2*L and has similar properties. However, in addition, this configuration requires less (or no) retuning when an optic like an etalon or Brewster window is introduced into the beam near the planar mirror. If the inserted piece (at any angle) has parallel faces no readjustment is required. The other hemispherical cavities also exhibit this desirable behavior to some extent.
A typical HeNe laser may have a LMG of only 1.01 to 1.05 depending on its length (1 to 5 percent). All optics must be as near to perfection as possible to get anything out of a short tube. For these, the following approximate equation for Laser Medium Gain (LRG) can be used:
LMG (approximate) = L * G
Where:
Where the gain is significant as in a solid state laser, the exact equation for LMG should be used:
LMG (exact) = ea*L
Where:
LRG = R(HR) * [T(B-HR) * LMG * T(B-OC)]2 * R(OC)
Where:
While the LRG determines whether a given configuration will lase or not, the available power that can be drawn from each spectral line will affect the actual output power from the laser. In other words, where all other factors are equal, a low gain line may actually produce a higher proportion of the output power than a high gain line at higher power input. For example, the 514.5 nm green line of an argon ion laser has only about 25% of the gain as the 488.0 nm blue-green line. However, at higher tube currents, the green line may predominate. (See the section: More Comments on Argon/Krypton Spectral Lines.)
Note that what we discuss above has nothing to do with anything external to the laser resonator (beyond the reflective surfaces of the mirrors), only what is part of the oscillation process itself. Also see the section: Laser System Efficiency.
The key equation determining whether a given configuration of mirrors will result in a stable resonator is:
0 < g1 * g2 < 1
With:
L L
g1 = 1 - ---- and g2 = 1 - ----
r1 r2
Where:
The short and the long of it (no pun...) is:
In practice, lasing may not continue quite to the limits but should come close.
Values for some of the common resonator configurations are:
The LR, LH, and CC resonators are just typical - the radii of one or both mirrors may differ from the examples. And in all cases, r1 and r2 may of course be interchanged without affecting internal resonator behavior though the external beam characteristics will depend on which mirror is the OC.
However, the CC configuration may be used as an unstable resonator for high power CO2 lasers with the actual curvatures selected to put g1,g2 just on the unstable side of the shaded area of the diagram. The useful beam is then a toroid (doughnut) exiting around the outside the smaller mirror. Thus both mirrors can have high reflectivity (which are probably easier and cheaper to fabricate for high power lasers).
(Portions from: Flavio Spedalieri (fspedalieri@nightlase.com.au).)
A stable resonator extracts the laser energy from around the optical axis of the laser medium, the resultant beam is a peak intensity in the center region of the beam (cross-section) and gradually decreasing in intensity as it moves out from the center axis of the beam to the edge. A laser that operates in the TEM00 mode is a good example of this - if you look at a spot produced on the wall, the beam is at its brightest at the center, as you move away from the center, the intensity decreases - a gaussian beam.
An unstable resonator on the other hand extracts the laer energy from the volume of the laser energy within the cavity. An Unstable resonator will produce a beam that has a 'doughnut' cross-section - thus it has a dark center region, and a peak brightness in a ring around the center (or vice-versa).
Such lasers can still be efficient (as such things go) and their construction is simpler in one respect: Both mirrors can be coated to be 100 percent reflective - much easier than providing a specific percentage of reflectance as would normally be required for the output coupler, particularly if more than one wavelength is involved.
The design of a resonator and the laser medium itself has nothing to do with the physical shape of the optics (well it does, for certain physical limitations obviously, but I'll explain in a second). A laser using an output mirror with a hole in the middle instead of a partially reflecting coating may be very inefficient, but it is not necessarily because of the fact the optic have a hole in it. High power copper vapor lasers often use unstable (unstable in this case refers to a resonator, that is designed such that if a photon starts traveling parallel to the tube centerline, it will eventually leave the resonator, either through a whole in the middle of the output coupler, or around the edges of the output coupler, where there is no reflective coating (i.e., it reflects in the center, but there is no mirror coating around the edges). The Spectra-Physics DCR and GCR laser product lines have output couplers that have radially varying reflectivity, a somewhat 'sexier' way of putting a hole in the center of the optic.
Short cavities, by their nature aren't capable of putting out a lot of TEM00 power - you COULD just put an aperture into the cavity to get a well focused beam, but doing so would reduce the output power tremendously. By lengthening the cavity, you can recoup much of that power loss.
The 'Q' factor of a laser resonator is analogous to the Q factor of a tuned circuit. It is a measure of the energy stored in the cavity versus the losses as the light bounces back and forth between the mirrors.
Some definitions of the Q factor of a laser resonator are:
E
Q = 2 * pi * ---------
delta-E
Where:
E
Q = 2 * pi * fmnq * ------
dE/dt
fmnq
Q = 2 * pi * ------------
delta-fmnq
Where:
Note that the Q factor of a laser resonator doesn't have any direct relation to M-square which is a measure of the beam profile. A laser with a mediocre Q can be perfect in the M-square department and vice-versa. See the section: What is M-Square?.
The "finesse" of a laser resonator is similar to Q but depends on the relation between the Free Spectral Range (FSR = longitudinal mode spacing = c/2*L) instead of the frequency, and line width:
FSR c
F = Finesse = --------- = -----------------
delta-f delta-f * 2 * L
For a Fabry-Perot resonator with mirrors of equal reflectance, R, the "reflectance finesse" is equal to:
pi*sqrt(R)
F = ------------
1-R
Or, for R close to 1:
pi
F = -----
1-R
While other factors affect the actual finesse, this is often the dominant one in an instrument like a scanning Fabry-Perot interferometer.
So, while the Q shows how good a resonator is with respect to the operating frequency/wavelength, F is an indication of how good it is with respect to the frequency/wavelength difference between adjacent longitudinal modes.
(From: Bob.)
The 'Q' of a laser is talking about the actual cavity and basically says how good the cavity is at keeping light in it. The more loss your cavity has, the less efficiently it will operate (speaking in very general terms).
In a Q-switched laser, the Q is initially made too low to lase by blocking or misaligning one mirror. While the Q is very low, light energy builds up in the laser medium. When the Q is restored, the laser starts lasing, and the result is a large high power pulse.
Most lasers are not what you would call efficient and even those that are would not be anything to write home about when discussing electrical generation, transportation, HVAC, or other energy conversion systems. Thus, the idea of a laser based cigarette lighter or the use of a laser beam to toast a rock to provide local heating is just plain silly - the power source could provide the energy directly with much greater efficiency. Clearly, the technology of Star Trek must have found a way around this but this won't be available under the 22nd or 23rd century.
Anyhow, MTBF basically tells you how long to expect between failures when the device is run within its rated specifications (or at a particular mode and power which may not be listed) AND after the initial "infant mortality" or burn-in period has passed AND before end-of-life where parts are just failing from old age. In other words, along the bottom of the "bathtub" curve. Obviously, with anything statistical, your mileage will vary.
With an expensive laser, it may be cost effective to overhaul, rebuild, or refurb (all basically the same thing) all or part of the system and thus return it to like-new condition.
This lifetime is also likely to be dependent on how close to its maximum ratings the laser is running. This is especially relevant for lasers that have a user control on output power. With HeNe lasers, for the most part, output power) is fixed. Varying tube current only has a slight (maybe a 20 percent range) effect on beam power and this capability is only rarely used for modulation purpose. However, a small air-cooled argon ion laser (like the ALC 60X) might go 25,000 hours or more when idling at minimum power (tube current of 4 A), 1,500 hours at full rated power (10 A), and less than 500 hours when run at 14 A (which IS listed in the table for the 60X in the section: Argon/Krypton Ion Laser Tube Life. After this - on average - it may fail entirely, become hard-to-start, won't start at all, or have reduced output power. Of course, being statistical in nature, some tubes will fail at 1/10 the expected MTBF and others will go on virtually forever.
Laser life could also mean the time until the output decays gradually to some percentage (e.g., 50 percent) of the original or specified power level, or how long they will remain at or above the rated power. As above, this will also likely be a strong function of how hard it is driven. This is a common way of characterizing diode lasers and diode pumped solid state lasers. A laser diode may have a specified life of 10,000 hours to the half-power point. See the section: Laser Diode Life. Gas lasers often produce much more than rated power when new and it is common for the life to be determined by how long its output takes to drop below rated power.
Or, for warranty purposes, a combination: "Guaranteed to produce 1 watt for 2000 hours minimum (there will often be a running time meter inside) or 3 years, whichever comes first". (Like the warranty on your automobile.)
Note that many factors affect laser life and singular events (especially for laser diodes) can blow the specifications right out the window!
(From: Dr. Mark W. Lund (lundm@acousb).)
A Fabry-Perot cavity is the standard run of the mill cavity with two highly reflecting mirrors bouncing the light back and forth, forming a standing wave. This cavity is not very frequency selective, theoretically you could have 1 mm wavelength light and 0.001 micron wavelength light in the same cavity, as long as the mirrors are the right distance apart to form a standing wave (and higher order modes make this easier than you might think).
A distributed feedback laser replaces the back mirror with a grating along the cavity axis. Instead of being reflected abruptly like a metal mirror would, the grating reflects a little over each part of the grating until at the back of the grating the light has petered out. Of course, since the light is being reflected by the grating the reflected light is always in the correct phase no matter if it was reflected from the front or back of the grating. The distributed nature of the reflection sharpens the cavity resonance and distributed feedback lasers are typically of much narrower bandwidth than the same laser with mirrors. Mostly seen in laser diodes, distributed feedback can also be done with non-linear optics, volume gratings, and other more esoteric optical elements.
(From: Bret Cannon (bd_cannon@pnl.gov).)
Fabry-Perot lasers are made with a gain region and a pair of mirrors on the facets, but the only wavelength selectivity is from the wavelength dependence of the gain and the requirement for an integral number of wavelengths in a cavity round trip.
DFB (Distributed FeedBack) lasers have the a periodic, spatially-modulated gain, which gives a strong selectivity for the wavelength that matches the period of the gain modulation. DFB lasers lase in the same single longitudinal mode from threshold up to the maximum operating power while Fabry-Perot lasers hop from one longitudinal mode to another as the current and/or temperature change. Most Fabry-Perot lasers lase on several longitudinal modes simultaneously though with some of these lasers you can find currents and temperatures where they lase on only a single mode.
The are also DBR (Distributed Bragg Reflector) lasers that have a Bragg reflector as a volume grating as the reflector at one end of the cavity to provide wavelength selective feedback. These lasers lase on a single longitudinal mode but the lasing hops from longitudinal mode to longitudinal mode to stay near the peak of the reflectivity of the Bragg reflector as temperature and current are changed.
(From: A. E. Siegman (siegman@stanford.edu).)
To extend this a bit, some lasers replace one or both of the end mirrors with a distributed Bragg grating, a.k.a. a distributed Bragg reflector (DBR). This is done particularly in some semiconductor lasers, and some fiber lasers.
Since the DBRs at one or both ends act essentially like mirrors, this could be called a sort of "Fabry-Perot" laser, especially if the central gain region of the laser is long and the DBR sections short. It's more common to call it a DBR laser, however, and reserve the term "Fabry-Perot for "real" mirrors.
Since a Bragg grating with many grating periods can have a fairly narrow reflection band, as well as high midband reflectivity, this can be a convenient way to provide a narrowband high-reflectivity mirror, which can serve to control the oscillation frequency range of the laser. DBRs are also relatively easy to fabricate in mass production, at least in fibers and diode lasers.
If you bring the two DBRs closer and closer together until they essentially touch, and distribute the gain throughout the grating sections rather than only in between them, you evolve from a distributed Bragg reflector (DBR) laser to a distributed feedback (DFB) laser, which can be a particularly convenient structure for stripe-type diode lasers.
One tricky point, however, is that for reasons having to do with inherent reflection phases in gratings, you need to provide an extra quarter wave or odd multiple of quarter wave discontinuity in the DFB grating somewhere in the center of the structure. DFB lasers can be made to operate without this, but not nearly as well.
Some DFB lasers have also be made to operate using periodic variation in the laser gain itself -- a "gain grating" -- to provide the distributed grating, rather than any kind of periodic index variation.
Perhaps, you've heard of the "ring laser gyro", a replacement for the spinning gyroscope used in navigation which has no moving parts (other than photons and electrons). (See the sections starting with: Ring Laser Gyros.) This is a one particular application for the ring configuration but has little bearing on the use of this geometry for a laser which is a source of light. In fact, one of the characteristics that is used to advantage in a ring laser gyro - a pair of counter-rotating beams - is usually suppressed in a laser using a ring cavity as we shall see below.
The ring configuration:
For the purposes of discussion, it is probably best to visualize a cavity in the shape of a regular polygon with with mirrors at the vertices. However, the "ring" can really be any shape as long as the light doesn't retrace its path inside the gain medium (and thus force a standing wave). The positions of the mirrors is also unimportant - they don't impose any boundary conditions as with the FP cavity. So, it can be planar or non-planar, an arbitrary sided regular or irregular polygon, a zig-zag, etc. In fact, the entire laser can be a closed loop of optical-fiber! The light paths can even cross (as with the Coherent Verdi, below). Ring laser cavities range in size from microchips a few mm on a side to many meters on a side. The typical size for commercial DPSS ring lasers is from a few cm to a few 10s of cm total round trip length.
Operation and benefits of the ring cavity:
While the actual details can vary quite a bit - often to the point of making the optical path unrecognizable without labels - the most important difference between the FP and ring cavity are standing wave and traveling wave lasers, respectively. In the FP cavity, light bounces back and forth between mirrors. For the resonance condition to be satisfied and laser oscillation to take place, a standing wave must be set up inside the gain medium. This requires that an integer number of half wavelengths fit between the mirrors and thus determines the mode spacing: c/2*L.
The equivalent condition for a standing wave to be set up in a ring cavity configuration is that an integer number of half wavelengths fit in the total round trip distance of the cavity. And, if both the clockwise and counterclockwise traveling waves which make up the standing wave are allowed to propagate, a ring cavity would behave much like an FP cavity except for the difference in what determines the mode spacing (2*L versus round trip distance). (This in itself has benefits as there is basically twice as much linear distance available to add intracavity optics but that's usually a minor consideration.)
However, it is possible to suppress the wave traveling in one direction around the ring using an optical isolator (sort of a diode for light) or Faraday rotation of the polarization within the cavity (the optical isolator simply packages everything inside a compact expensive part!). The Faraday effect is used to force a unidirectional ring as follows: A polarizing element like a Brewster plate or Brewster-cut end on the lasing crystal favors a linearly polarized beam at that point in the cavity. This passes through a 1/2 wave plate with its axis at an angle Beta to the beam's polarization orientation. A 1/2 wave plate has the characteristic that it rotates the polarization by an angle 2*Beta (same sign) for the beams traveling in either direction. A magnetically active crystal or glass rod is also in the beam path located inside a powerful axial magnetic field. By the Faraday effect, this rotates the polarization by a small angle Beta' but in opposite sign for the two beams. When Beta' equals Beta, one of the beams sees the same polarization orientation on each trip around the ring and thus maximum amplification. The beam going in the opposite direction sees a polarization rotation of 2*Beta and lots less gain - and is effectively suppressed. It turns out that YAG can be used both as the lasing crystal and Faraday rotator so this reduces complexity and cost. An example of a laser using this approach is the Coherent 532-200 mentioned below.
Allowing the light inside the cavity to travel in only one direction results in a traveling wave laser. The resonance condition turns out to be the same because the wave must be in phase after each trip around the ring. (If it were out of phase, the result would be reduced light or no light at all!) However, the unidirectional ring cavity highly favors single longitudinal mode operation. The reason is fairly simple: In a standing wave (FP) laser, the gain medium is only fully depopulated in the area of the peaks of the standing wave. This is called "spatial hole burning" and results in areas in the gain medium where additional longitudinal modes can build up (away from the peaks). Normally, any given laser when just above threshold will operate in a single longitudinal mode. As the excitation is increased, gain for other modes will become great enough for them to start oscillating and the laser will eventually operate with multiple longitudinal modes.
While these can be suppressed by making the laser cavity very short (so other modes fall outside the gain bandwidth of the lasing medium), this may not be a viable option. The tendency for multimode operation can also reduced by placing the gain medium against one of the mirrors since the adjacent modes are more highly correlated and the spatial hole burning effect is reduced, but this won't get rid of them entirely.
A traveling wave laser doesn't suffer from spatial hole burning at all since the wave is circulating around the cavity so all of the gain medium can be used uniformly. This results in much more robust single longitudinal mode operation - the laser can be operated at much higher power before other modes develop. And, with full utilization of the gain medium, efficiency will be increased as well. Another advantage for lasers using SHG (and other frequency multiplication crystals) is that being unidirectional, all the converted (e.g., green) light can be extracted at one optic - there is no backward traveling beam to deal with.
For these reasons, many commercial solid state lasers use the ring cavity configuration even if not an advertised benefit. This includes the highly popular Coherent, Inc. Compass (some models) and Verdi series of IR and green DPSS lasers. (Go to "Products", "Lasers", "Diode Pumped Solid State Lasers", "CW DPSS Lasers".) See Ring Cavity Resonator of Coherent, Inc. Verdi Green DPSS Laser.
Photos of the interior of an actual Coherent Compass 532-200, a lower power green DPSS laser than the Verdi also using a ring cavity can be found in the Laser Equipment Gallery (Version 1.86 or higher) under "Coherent Diode Pumped Solid State Lasers". The 532-200 is rated 200 mW, but can produce at least 400 mW by increasing current to the pump diode (at the expense of diode life expectancy). The last photo in the sequence is a closeup of the cavity and output optics showing the actual beam path.
So why aren't ring lasers used everywhere? One reason is that the complexity and cost tend to be much higher compared to FP lasers and there are many applications where single longitudinal mode operation isn't needed.
Consider a single longitudinal mode: Inside the lasing medium (e.g., HeNe gas or Nd:YAG crystal), the peaks will fully utilize the available gain but at the centers of the valleys or null points, the gain will not be used at all. In between, only a portion of the available gain will be used. This behavior is called "spatial hole burning". In essence, periodic areas ("holes") have been depleted ("burnt") of gain, leaving other areas which can still contribute to lasing action if there were something to stimulate it in those areas. Since the standing waves for other longitudinal modes will not have their peaks and valleys in exactly the same locations, they will see some gain. The result is that while the longitudinal mode with the highest overall gain will appear first (e.g., the one nearest the center of the gain curve), others will pop up as the pump excitation is increased.
However, there is a very elegant solution that virtually totally eliminates laser oscillation on more than one longitudinal mode: The unidirectional ring laser. Unlike the Fabry-Perot laser, a unidirectional ring laser is a traveling wave laser where the intracavity beam goes in only one direction through the gain medium. See the section: Ring Lasers.
Also see the sections: Performing the Single Pass Gain Test and Determining which Spectral Lines will Lase.
(From: Daniel Ames (dlames3@msn.com).)
Obviously, you could just call the manufacturer if you know who that is and give them as much information as possible including model number, dimensions of the tube, reflected spectra of any optics that are present, etc. Or, you can test it yourself:
If the pump laser is linearly polarized, the Brewster windows would have to be on the same plane, but then again, you knew that :)
This should prove to be much easier than actually building, or modifying an actual resonator, several times over and re-aligning the optics, just to verify, possible wavelengths.
As far as testing as to what lasing or amplification lines are compatible with a laser tube such as this one (HeNe with two Brewster windows), the easiest way, might be to just use different colored "pumping" HeNe lasers as if you were doing a single pass gain test. This means accurately measuring the input and output beams and computing the gain or loss from input to output.
I would suggest using a pinhole aperture to minimize non coherent radiation, from both of these tubes, plus I would assume that there could be some margin for error in the second (combined output test) simply due to the non-coherent light produced inside the optical cavity of the amplifying (tube ws/2 Brewster windows).
If I were to perform this (single pass gain) test, I would take (3) optical power measurements:
Then, repeat steps, (1 to 3) using using different colored pump lasers. Compare all the results and this should give you a pretty good idea of which wavelengths are candidates for lasing in the tube with (two) Brewster windows.
P.S. Don't forget to eat and sleep at sometime, oh yes, and please let the dog out when it needs to you-know-what. :)
There are most likely are other ways to determine the possible lasing wavelengths that a mirrorless laser tube is capable of, but that's for another topic.
(From: Sam.)
For the case where the laser being evaluated has a built-in (broadband) HR mirror, the test needs to be modified to pass the beam from the testing laser up and back reflecting off the HR. This will probably require a beamsplitter to permit the outgoing and return beams to take the same path inside the (narrow bore) laser cavity. There will be some losses in the optics but as long as the comparisons are made without moving anything, just turning power on and off or varying the voltage and/or current, the results will be valid for the relative gain (double pass through the lasing medium in this case). However, in order to determine the absolute gain, the tube would have to be removed and replaced with an HR mirror of the same curvature - a complication to be avoided if possible. See the section: The Single Pass Gain Test for additional explanations of these terms and test procedures.
In either case, whether a given line will actually lase will depend on the excitation and cavity configuration, competition from other possibly stronger lines, and many other factors apparently including the phase of the moon. :)
If you really want to search for new lasing lines, see the CRC Handbook of Laser Wavelengths (not sure of the exact title). Or, to browse over 46000 lines in 99 elements and maybe find a new lasing line in a few centuries, try the Strasbourg astronomical Data Center (CDS): Line Spectra of the Elements.
(From: A. E. Siegman (siegman@stanford.edu).)
If you look at an interstellar gas cloud (or Martian atmosphere) and see a VERY unusual distribution of the relative intensities of different lines -- notably that some lines known to come from a certain molecule are VERY much brighter than other lines known to come from the same molecule -- and if that correlates with your understanding of which upper levels are likely to be more heavily populated and have a strong transition strength, then you can have some confidence in saying that some transitions have been "inverted" by the UV pumping and are producing laser gain and ASE ("amplified spontaneous emission") on those specific lines. If these strong lines are also somewhat narrowed -- not like a coherent laser oscillator, but in conformity with ASE laser theory -- that just helps to make the case more certain.
If you look at the laser from the side, you see the intensity of the sideways spontaneous emission from that upper level to *any* other lower level more or less also "clamp" in amplitude at the level corresponding to the threshold point. This is not to hard to see in a He-Ne or other gas laser, and also in solid-state and semiconductor lasers -- though if you look at the laser wavelength itself you have to be careful not to pick up scattered light from the much stronger laser radiation.
If you have a good polarizer, you can even look at the output from the cleaved end face of a semiconductor diode laser and observe the TE and TM polarizations separately, and see that the ASE in the non-lasing polarization clamps at the point where the lasing polarization goes above threshold.
None of these experiments may show perfect clamping at threshold, for a variety of reasons -- but clear cut clamping effects are not difficult to see in most cases.
Without getting into messy details, one way to characterize radiation density is by the "number of photons per unit cell in phase space", where "phase space" refers to both spatial and spectral dimensions and "unit cell" means more or less the same as "single spatial and temporal mode".
The idea is very simple: Pass a 'probe beam' from another laser operating at the wavelength in question through the gain medium of the laser being tested. Compare the intensity of the input and output beams, with and without the gain medium being active. (Note that the term "intensity" is synonymous with "power" used elsewhere, not the amplitude of the E-filed or something equally obscure!) This results in four measurements (not necessarily in this order):
+---------+ | +--------+
| T-Laser |--> : )--| I(i) |
+---------+ Laser Under Test | +--------+
(On) (Removed) Pinhole Light Meter
+---------+ | +--------+
| T-Laser |--> /===============\ : )--| I(o,0) |
+---------+ Laser Under Test | +--------+
(On) (Unpowered) Pinhole Light Meter
+---------+ | +--------+
| T-Laser |--> /===============\ : )--| I(o,1) |
+---------+ Laser Under Test | +--------+
(On) (Powered) Pinhole Light Meter
+---------+ | +--------+
| T-Laser |--> /===============\ : )--| I(g) |
+---------+ Laser Under Test | +--------+
(Off) (Powered) Pinhole Light Meter
Make sure no extraneous light falls on the light meter's sensor. Also, cover the light sensor and zero the meter or subtract this 'dark current' value from the other readings.
At least three results can be computed from these measurements:
The result that really matters in the end is G(a), the absolute single pass gain. (It may also be the most difficult due to unavoidable problems in alignment of the test setup.) In conjunction with the mirror reflectances, G(a) will determine whether the complete laser has a chance of working. However, G(a) isn't definitive as other factors like the curvature of the mirrors can affect the shape of the gain medium that is active so the actual gain when everything is assembled into a laser resonator may be slightly less than G(a). And, there is always the issue of dust, dirt, and grime on external optics! :(
Finding G(r) is often much easier since it is only the ratio of the two measurements that matters - losses are the same in both cases. However, while G(r) will tell how much gain is present inside the cavity at the wavelength(s) in question, without knowing how much loss there is through the Brewster windows, there is no way to be sure of whether the complete assembly has a chance of working. If it lases, you'll know that G(a) was adequate; if it doesn't, you won't know why except by the process of elimination.
For a laser tube with an internal HR mirror, (one-Brewster or perpendicular window tube) this turns into a Double Pass Gain Test (DPGT) but the basic procedures are similar, though somewhat more complex, requiring a beamsplitter in the optical path. If a non-polarizing beamsplitter is used, the power in the measurement beam will be reduced by approximately 75 percent. This is generally of no consequence. (If for some reason, every photon is important, a polarizing beamsplitter can be used followed by a quarterwave plate. There will be minimal losses in the incident beam and nearly 100 percent of the return beam will be directed to the sensor.) An additional HR mirror will be needed for the G(a) measurement to substitute for the internal HR. However, they are obvious extensions of the SPGT discussed above. Details are left as an exercise for the student. :)
I don't know of any way to do an absolute SPGT for a laser with two internal mirrors and nothing else inside the cavity - or any valid or sane reason to want to! The relative SGPT will be just as good since there should be no losses inside the cavity and the mirror reflectivities can be determined from outside the cavity (care to guess how?) or after (destructive) disassembly. However, if there were, say, an etalon or polarizing Brewster plate in there, it might be possible to come up with an excuse to do such tests given enough time!
Both lasers are mounted on a solid optical bench and carefully aligned so that the T-Laser's beam passes cleanly through the TUT's bore oriented to minimize losses through the Brewster windows. Getting the beam of a HeNe laser cleanly through the very narrow bore of the typical HeNe TUT can be quite a challenge - maybe even impossible. External optics may be necessary to narrow the converge the raw beam - and even then the diffraction limit may get in the way for a long narrow bore!
The light sensor can be a photodiode with a pinhole aperture since all we care about is the intensity, not the total laser power. The pinhole will help to assure that what is being measured is only the center of the beam which is least likely to be affected by stray reflections from the tube walls.
After allowing the T-Laser to stabilize for at least 1/2 hour (to minimize intensity fluctuations), I(o,0), I(o,1), and I(g) are measured, the TUT is removed without changing anything else, and I(i) is measured. The numbers are then crunched. Hopefully, the outcome is positive. :)
I acquired a slightly strange helium-neon tube designed to be used with external mirrors and decided that before even thinking about finding suitable mirrors, a SPGT would be prudent to determine what I was up against. This tube is also funny in another way - the gas fill is not your normal 4Ne and 20Ne but rather 3He and 22Ne (probably someone's thesis project but that's another story). I expected that the spectral lines wouldn't be affected significantly by these isotope differences (see the section: Spectral Differences Based on Isotope) but confirming gain at the normal 632.8 nm wavelength would be desirable.
The tube looks like an ordinary one in all respects except that instead of normal mirror mounts and internal mirrors, it has a pair of Brewster windows. It is otherwise similar to a 2 to 3 mW Melles Griot design, about 9" long and 1-3/8" in diameter. I constructed a resonator frame along with adjustable mirror mounts especially for it. (I will describe this in detail once I find some mirrors to use and either succeed or fail at getting the thing to actually lase.)
For the SPGT, I set up a normal HeNe laser on an adjustable platform and aligned it with the bore of the Tube Under Test (TUT) so that a clean beam was exiting the other end. I used Sam's Super Cheap and Dirty Laser Power Meter to monitor beam power. At first, the Test Laser (T-Laser) was a randomly polarized Siemens LGR-7631A 2 mW HeNe tube but the mode cycling was causing a significant and unpredictable variation in beam power reading due to the polarization preference of the Brewster windows on the TUT (or so I thought). So, I substituted a linearly polarized 0.5 mW Aerotech tube instead - which helped a little but there was still too much variation to enable any reliable determination of a change using a slow responding multimeter (my trusty Radio Shack DMM) when the TUT was powered up. Of course, perhaps if I had waited the recommended 1/2 hour for the T-Laser to warm up, the situation would have improved.... Nah, that would have been too easy!
What I needed was to be able to cycle the TUT's power on and off and look at the change in reading. To do this, I connected an oscilloscope across the resistor in series with the photodiode and set it for AC coupling. To get the TUT's power to cycle conveniently, I turned down the current adjust on the power supply brick until the discharge became unstable (below about 4.5 mA for this tube designed to run at 6.5 mA). This results in the discharge flashing on and off at about a 10 Hz rate. Repeated starting isn't good for either the HeNe tube or the power supply but I was only going to be doing this for a few seconds. With the TUT flashing, a nice (more or less) squarewave showed up on the scope. By measuring its amplitude, I could determine the change in transmitted beam power and thus the percent gain of the TUT's bore. To assure that it the variation indicated on the scope was really due to the actual gain of the TUT and not just the glow of the TUT's discharge or electrical noise, I made the same measurement with the T-Laser off and the TUT power cycling, with and without the photodiode covered. There was no detectable response in either case.
The results:
Thus, based on these measurements, the increase in power output by stimulated emission is about 2 percent - which isn't bad for a HeNe tube with a bore length of only about 6.5". This also confirms that the isotope difference is probably of negligible consequence and if anything, the gain will be higher at its optimal wavelength - if that is shifted at all.
However, what I could not really measure was the absolute gain since there were too many variables affecting the actual amount of the T-Laser's beam that made it through the TUT's bore. With the TUT removed from the beam path, the photodiode current averaged about 0.37 mA but the discrepancy is very likely due to factors which won't matter or will be taken care of when the tube is part of a resonator like: misalignment of the polarization of the T-Laser and Brewster windows, dust on the Brewster windows, and scattering from the side walls. With infinite time, a beam reducer and nice stable optical bench (which I don't have), more precise measurements could be made. But for now, these will have to do.
The absolute single pass gain, of course, is really what matters. Based on the expected transmission of properly made Brewster windows, the losses should be quite small - probably a lot less than 1 percent. Thus, there should be ample margin for the 2 percent relative gain measured above - I hope! See the section: Sam's DIY External Mirror HeNe Laser - Some Assembly Required! for the continuing saga of getting this funny tube to lase.
For example, solid state lasers like Nd:YAG or Nd:YVO4 typically have relaxation oscillation frequencies from 40 or 50 kHz for large lasers to several MHz for microchip lasers with short cavities. It's easy to view this on an oscilloscope by diverting a portion of the output of a fundamental mode (i.e., not doubled) Nd:YAG or Nd:YVO4 laser to a fast photodiode. (Lasers with non-linear elements like KTP frequency doublers add another level of complexity to the laser dynamics which might obscure the more basic relaxation oscillations.)
Diode lasers also exhibit relaxation oscillations in the GHz range.
Gas lasers usually do not have this behavior (see below).
(From: A. E. Siegman (siegman@stanford.edu).)
Some general comments:
If gain is momentarily too high (greater than loss), signal level starts to grow above the steady-state value (rapidly in some kinds of lasers); but if gain is momentarily too low (compared to loss), signal level drops.
But also, if signal is too high, it pushes gain down (rather slowly, in solid state lasers); and again v.v. if signal is to low.
Essentially the same phenomena also occur, however, in lots of other kinds of oscillators as well - e.g., in the very first HP audio oscillators. Here is some info from a copy of the HP Journal from some decades back in which Barney Oliver (of "Chirp Radar" fame) studied and analyzed the phenomena.
As I read this, the slow thermal change of the tungsten filament lamp's resistance resulting from changes in the amplitude of the audio oscillation changed the magnitude of the feedback in the oscillator, and thus the round-trip gain in the feedback loop, in a manner pretty much exactly akin to slow gain saturation in a laser oscillator.
Signal-induced changes in the feedback through the lamp thus played essentially the same role as gain saturation in a laser, and stabilized the steady-state amplitude of the audio oscillation. The time constants of this "feedback saturation" and of the oscillation build-up rate for the ac voltage signal at a given feedback level were quite different, however, leading to the result that _all_ of these audio oscillators should have "spiked" badly in response to large perturbations, and all of them should have exhibited laser-like damped relaxation oscillations back to steady state in response to small perturbations about steady state.
The experimental fact was that in general the majority of them did _not_ spike in this way, except that every once in a while a unit would come off the production line at random which _did_ spike badly and which would also exhibit damped relaxation oscillations with envelope amplitude variations which look exactly like YAG laser spiking. Changing any one of the tubes in the amplifier section at random would almost always eliminate this behavior.
The eventual explanation was that there were also weak but fast-acting signal nonlinearities in the tube amplifier section, essentially a weak compression at the peak of the ac sine waves, and this additional weak but fast nonlinearity normally acted to suppress the spiking and RO that would otherwise have occurred. Every once in a while, however, a unit would come off the line with a set of tubes whose individual nonlinearities combined in such as way as to produce a highly linear overall response, so that this weak but fast nonlinearity was suppressed or possibly even changed sign. Changing any one tube destroyed this and restored the normal n on-RO operation.
I believe this represents a very interesting audio analog to the same kind of spiking and relaxation oscillation behavior that occurs in lasers (as those terms are interpreted in the laser field).
(From: Repeating Rifle (salmonegg@sbcglobal.net).)
The way I understood the HP oscillator was that it was a Wien bridge oscillator in which the lamp acted as a variable resistor to adjust the loop gain to unity. Feedback from the amplifier output was through the frequency selective bridge. It used an class A amplifier that was about as linear as you could conveniently get in those days. It is impossible to get exact unity loop gain. As in threshold lasing, oscillation is only possible near the bridge's frequency transmission peak. There would have to be amplitude fluctuation or some distortion to keep a class A oscillator working. That is where the lamp came in. Increased oscillator output heated the lamp and increased its resistance. This reduced the amount of feedback. The result was a feedback amplifier running very close to unit loop gain with very little distortion and amplitude fluctuation.
In contrast, a typical vacuum (or transistor) LC oscillator is usually very nonlinear running Class C. Peaks of the rf on the grid would pulse the tube for a small fraction of a cycle. The plate (or collector) current pulses would drive the LC tank circuit that smoothed out the pulses into sine waves. Q's of at least 10 were typically used for that, meaning that energy circulating in the tank was about an order of magnitude greater than was delivered to the tank each cycle.
The nonlinearity for a typical oscillator circuit was controlled by a grid leak. If the grid leak was not correctly set, the oscillator could block causing a squegging relaxation oscillation.
Laser operation has many analogies to how electronic oscillators work but are different in detail.
The term *relaxation oscillation* has rather broad application and is certainly not limited to optical oscillation. Electronic circuitry is probably where the essence of relaxation oscillation has had wide application as well as loathing.
> The key, in my mind is that frequency is not set by ordinary resonant phenomena and that highly nonlinear phenomena, such as on-off switching, can be key.
Perhaps the simplest relaxation oscillator is a neon tube discharge oscillator (or a corresponding solid state version). A battery or dc supply is used to charge a capacitor connected across a neon lamp through a current limiting resistor. When the breakdown voltage of the lamp is reached, it discharges the capacitor and the cycle repeats. Blocking oscillators and multivibrators are other example.
A mechanical example is a squeaky door with successive sticking an releasing of a rubbing surface.
(From: A. E, Siegman.)
I agree with all of the above (except maybe the very last paragraph). The same term is indeed used to describe electronic relaxation oscillators that involve strong nonlinearities such as switching or breakdown or "triggering" phenomena, often leading to square or discontinuous or otherwise non-sinusoidal waveforms with large jumps in each cycle of the relaxation oscillator; and then also used in the quite different relaxation oscillation behavior of certain oscillators such as lasers, that have "soft" or slow nonlinearities that build up over many cycles of the oscillator carrier frequency, leading to slow damped sinusoidal oscillations of the envelope of the basic oscillator.
(From: Repeating Rifle.)
There are relaxation oscillations in which resonance does play a role. A good example no longer found in practice is the damped oscillations of a spark transmitter. The center frequency is set by a resonant circuit. Resonant tuning was used to provide some receiving selectivity. The repetition rate, however, had little to do with the radio frequency itself.
Regenerative detectors could be made super-regenerative with proper grid leak selection. That caused squegging akin to blocking oscillators.
In lasers, there are all kinds of funny oscillations. Multiple Q-switched pulses could be obtained. For example, a dilute Q-switching dye can produce a string of pulses (not mode-locked). Even with EO Q-switching, it is possible to get multiple pulses. After the first pulse is generated, another one with lower gain can build up.
What is the objection to calling squeaking from a door or shoe a relaxation oscillation? I have no problem calling the normal lasing from a pulsed laser a relaxation oscillation.
(From: Phil Hobbs.)
The term "relaxation oscillation" is used in somewhat different vague senses in electronics and laser engineering. The underdamped ringing following some externally-applied disturbance would be called a settling transient in electronics. Sustained laser spiking, e.g. in an N2 laser, is more what a circuits guy would understand by "relaxation oscillation". The connection is close - it's all in whether the damping goes to 0 or not - but the terminology is a little different. A spark transmitter isn't a relaxation oscillator unless the spark is being produced by a mechanical buzzer, say. A self-quenching super-regen is a better example, as you point out.
Circuits guys have their own loose terminology - Terman's "Radio Engineer's Handbook" (1943 ed.) says that a relaxation oscillator is one "in which the frequency is controlled by the charge or discharge of a condenser or inductor through a resistance." This would make an LC oscillator whose inductance was synthesized by a gyrator qualify as a relaxation oscillator, which isn't quite what one might want to say.
I don't know that I have a definition for "relaxation oscillation" that would fit on a bumper sticker. "Relaxation" is more like a unipolar exponential decay, where "resonance" would be an exponentially damped sinusoid. Something that rings is just more like a resonance than a relaxation.
Units:
With a normal pulsed laser, the pumping source raises the active atoms of the lasing medium to an upper energy state. Almost immediately (even during the pumping) some will decay, emitting a photon in the processes. This is called spontaneous emission.
If enough of the atoms are in the upper energy state (population inversion) and one of these photons happens to be emitted in the direction so that it will reflect back and forth between the mirrors of the resonator cavity, laser action will commence as it triggers other similar energy transitions and additional photons to be emitted (stimulated emission). However, the resulting laser pulse will be somewhat broad and of random shape from pulse to pulse.
The idea of a Q-switched laser is that the resonator is prevented from being effective until after the pumping pulse and most of the atoms are in the upper energy state (the population inversion in as complete as possible). Its so-called Q is spoiled by in effect disabling one of the mirrors. This can be accomplished mechanically by simply rotating the mirror or an optical element like a prism between the mirror and the lasing medium, or electro-optically using something like a Pockel's cell (a high speed electrically controlled optical shutter) in a similar location. With the cavity not able to resonate (mirror blocked or mirror at the wrong angle), there can be no buildup of stimulated radiation. There will still be the spontaneous emission but this is a small drain on the upper energy state.
At a point in time just after the pumping is complete, the Q is restored so that the resonator is once more intact - the mirror has rotated to be perpendicular to the optical axis, for example. At this instant, with a nearly total population inversion, laser action commences resulting in a short, intense, consistent laser pulse each time and the pump energy is used more efficiently. Peak optical output power can be much greater than it would be without the Q-Switch. Because of the short pulse duration - measured in nanoseconds or picoseconds (or even less), peak power of megawatts or gigawatts may be produced by even modest size lasers - with truly astounding peak power available from large lasers like those found at Lawrence Livermore National Laboratory.
With a motor driven Q-switch, a sensor is used to trigger the flash lamp (pump source) just before the mirror or other optical element rotates into position. For the Kerr cell type, a delay circuit is used to open the shutter a precise time after the flash lamp is triggered.
Q-Switched lasers are very often solid state optically pumped types (e.g., Nd:YAG, ruby, etc.) but this technique can be applied to many other (but not all) lasers as well.
WARNING: With their extremely high peak power, these may be Class IV lasers! Take extreme care if you are using or attempting the repair of one of these.
CAUTION: For some lasers which run near their power limits, if the cavity is not perfectly aligned, it may be possible to damage the optical components by attempting to run near full power in Q-Switched mode. Perform testing and alignment while free running - not Q-Switched (rotating mirror set up to be perpendicular or shutter open). Use a CCD or other profiling technique to adjust for a perfectly symmetric beam before enabling the Q-Switched mode.
(From: Leonard Migliore (lm@laserk.com).)
I had a very short description of ultrafast lasers and their potential uses in my November 1998 newsletter. That portion was:
Processing with Ultrashort-Pulse Lasers
Ultrashort pulses are generally considered to be 1 ps or less; 100 femtoseconds is typical. To provide some sense of scale, a Q-switched Nd:YAG pulse is generally around 100 nanoseconds or 0.0000001 second. Since light travels 1 foot per nanosecond (my favorite non-SI unit), these pulses are about 100 feet long. A 100 femtosecond pulse (0.0000000000001 second if I counted my zeroes right) is 30 microns long.
Lately, it has become possible to build relatively small lasers that deliver these short pulses, and several workers have been using them for material processing. Materials react quite differently at femtosecond time scales than at longer ones. In metals, the electrons do not have time to transfer heat to the lattice; processing is essentially athermal. In dielectrics, the electrons are ionized by multi-photon absorption and are ejected from their atoms. The ionized atoms are dragged along with them to maintain electrical neutrality in the plume. For both metals and dielectrics, material is removed without transferring heat to the substrate. Ultrashort-pulse lasers are consequently ideal material removal tools.
At least, they could be ideal if they ran decently. Present units are fiendishly complicated, rather touchy to align and hard to keep running. The currently favored laser material, titanium-sapphire, requires another laser to pump it. Work is being done on other laser materials that can be pumped with diodes; ultrashort-pulse lasers made with these have a chance to be much simpler and more reliable than current units.
Martyn Knowles of Oxford Lasers provided an excellent counterpoint in his paper: In metals, reducing pulse duration 1,000 times reduces the heat-affected zone by a factor of only 10. If you process metal with nanosecond pulses, you can get a 1 micron HAZ. Femtosecond pulses can give you 0.1 microns. In most real-life applications, a 1 micron HAZ is undetectably small, so it's not worth an enormous increase in complexity to make it smaller.
As I see it, ultrashort-pulse lasers will be extremely useful tools for material processing, but will not be widely adopted until they are much simpler and more reliable than the units that exist today. Until then, you can do more useful work with "long-pulse" nanosecond lasers because they run all the time.
(From: Thomas R. Nelson (tnelson@uic.edu).)
There are two main advantages to using femtosecond laser pulses. Firstly, the short pulse duration makes it easier to reach high peak powers while at relatively low energies. 100 mJ in 100 fs gives an average pulse power of 1 Terawatt (1 TW = 1012 watts). Using a 1 ns pulse would require 1,000 J of energy to reach the same average power, and would generally cost much more money to build and operate such a laser.
Second, the interaction of laser pulses with matter is much different on femtosecond time-scales than on picosecond or nanosecond time scales. The effects which can be produced and studied vary greatly, compared to what sort of science can be done using a nanosecond laser pulse.
Also, at this point in time, the technology is advanced enough that a high powered "turn-key" laser system can be purchased quite easily.
(From: Wei-Choon (wng@ux11.cso.uiuc.edu).)
Check out this paper:
Also, look out for papers in mode-locking and saturable absorbers by H. A. Haus.
(From: James Whitby (james.whitby@phim.unibe.ch).)
The main thing that matters is the irradiance of the beam (i.e. power per area). One way of making an estimate is to consider when the electric field strength in the laser beam is comparable to that experienced by an electron in a a molecule of 'air', or to reported values for the dielectric breakdown of air using DC fields. The presence of any particulate matter will have a big effect on the threshold.
For practical numbers with pulsed lasers see for example: "A numerical investigation of the dependence of the threshold irradiance on the wavelength in laser-induced breakdown in N2", Gamal YEED, Shafik MSED, Daoud JM JOURNAL OF PHYSICS D-APPLIED PHYSICS 32 (4): 423-429 Feb. 21, 1999.
For quick numbers, from another very short paper: Tambay et. al., Pramana 37(2) pp163-166, 1991. Using approximately 2 ns pulses in clean dry air at atmospheric pressure, the thresholds for breakdown were found to be about:
Wavelength Power Density
------------------------------
1064 nm 6 x 1011 W/cm^2
532 nm 3 x 1011 W/cm^2
355 nm 2 x 1012 W/cm^2
(Note the minimum value for the second harmonic, although this looks like an outlier in the data-set this behavior is highlighted in the text so was presumably reproducible.)
(From: Phil Hobbs.)
One thing to watch out for is that after the plasma forms, it grows very rapidly in the direction of the source. Many moons ago, I had a passively Q-switched YAG laser whose output was a 10-ns pulse, adjustable from 2 to 10 mJ. I excavated the front surface of a 40X microscope objective with about 5 shots. The plasma drilled right into it by about 1 mm--it was a great conversation piece.
(From: Sam.)
I found the following go/no-go test for correct operation in the user manual of a certain Q-switched 1064 nm YAG laser with a spot size of 25 um and a pulse width of 6 ns: "Air breakdown should occur at an energy setting of 5 mJ or more". The math works out such that 5 mJ is slightly higher than the value given above. To emphasize: This is only a 5 mJ pulse but oh what peak power! Left as an exercise for the reader. :)
(From: Sonicguru (cgraber@fwi.com).)
Have heard an amped Korad ruby pulse the air to plasma VERY hard with 40 to 50 joules per pulse and a bit of lens.
Also had a Continium short pulse pop the air relatively hard with average powers of well under a watt!
I concur with everyone else as to the energy/area ratio however It must be stated that it can happen with many different combinations of hardware such as 3.5 to 4 kW CW CO2 laser, 50 J per pulse ruby or Nd:Glass amplifier drill, or short pulse Q-switched YAG with a gazillion watts peak power and less than 1 watt average power!
Silly as it might sound:
A big CW CO2 laser "Breaking wind" sounds like an electrical capacitive discharged arc gap from a Tesla or other HV Frankenstein equipment.
A short pulse YAG "Breaking wind" sounds like a riffle shot at medium distance.
An amped hotrod Korad when in tweak sounds like a shotgun nearby. Even cooler was putting various materials at the focal point of that monster and watching the debris fly.
I remember talking to one guy who was in on an experimental weapons project with a (I believe) 3 stage ruby laser that would explode 2x4s like they were made of foam and had 100+ joules per pulse output and yet the optics rail was supposedly small enough for an average GI Joe to carry except that the power supply was a refrigerator and a half full of chargers and BIG capacitors! This was done in the early 1980s as I recall.
(From: Harvey N. Rutt (hnr@ecs.soton.ac.uk).)
Pulsed breakdown is dead easy; a very modest pulsed CO2 or q-switched YAG laser will do it with a decent low f number positive lens.
A 5 kW CW near diffraction limited CO2 laser can *just*, and only just, maintain a continuous air breakdown; from memory the focus was more like F#6 or so. You have to initiate the plasma by waving something in the focus to provide some initial ionization; I guess a spark might do to. Sometimes happens when two bits of metal being welded run out from under the beam.
A 10 kW laser did it quite easily.
It's quite spectacular - a blue, glowing shifting 'egg' hanging in the air. At 5 kW it could be 'blown out' quite easily. We used to do it as a visitor demo (in a safety enclosure!)
(From: Manuel (cfn@cfn.ist.utl.pt).)
I was using a pulsed Nd:YAG laser to make air breakdown. The minimum that I have found was 1 joule in 10 ns with a 25 mm diameter beam and a lens 1 m focal length.
Mirrors used inside the laser resonator are almost always of the so-called dielectric variety using multiple layers of transparent insulating materials rather than metal films. (These may also be called dichroic.)
Here are some typical reflectivities of metal coated and dielectric mirrors (form various optics catalogs and other sources):
Type/Coating Reflectance
-------------------------------------
Bare aluminum 91 %
Enhanced aluminum 96 %
Protected silver 98 %
Laser line 99.7 %
Laser high reflector >99.9 %
There are many types of dielectric mirrors but the most common are:
The basic highly reflective narrowband dielectric mirror is coated with a stack of 50 or more alternating layers of two transparent dielectric (insulating non-metallic) materials with slightly different indices of refraction. You ask: "How can a bunch of transparent layers result in a mirror with up to 99.99% or more reflectivity?". Good question! :) The way this works is that the layers are carefully laid down so that the thickness of each is exactly 1/4 of the desired wavelength of light in each material (taking into consideration its index of refraction). The small discontinuity at each layer boundary results in a small reflection at that point. But due to the 1/4 wavelength coating thickness, the reflections all occur in phase at the surface and reinforce each-other. With enough layers, the result can be a mirror much better than one made using a metal coating.
Depending on whether the desired result is a High Reflector (HR) mirror which is as close to 100 percent reflecting as possible or an Output Coupler (OC) which has a specified reflectance less than 100 percent, depends on the number, type, and quality of the layers. However, even a commercial HR mirror isn't perfect - there will be some transmitted light. Typically, the transmission coefficient (very nearly equal to 100 minus R) is 0.1 percent or less, possibly much less but not zero. (Some high quality HR mirrors may be better than 99.995 percent reflective - T less than 0.005 percent - over a specified range of wavelengths!) For all but the most demanding applications, the loss is insignificant and not worth the additional expense to reduce it further. What this does mean is that there will be a weak beam exiting the HR-end of a laser (assuming the mirror isn't covered) representing the internal light flux in the resonator times T. It may look like a lot, but don't worry, you aren't losing that many photons! :)
Note that where the wavelength of the incident light doesn't match the design wavelength of the mirror, the reflected waves from the multiple layers will no longer return in phase. For a typical narrow band mirror, move 10 or 20 nm away and the reflectance will no longer be even as good as a shaving mirror; move 50 nm away and the "mirror" will be essentially transparent.
Broadband dielectric mirrors use basically the same principles but with many more layers of varying thickness and possibly varying materials. As noted below, they are correspondingly much more expensive as well!
Most lasers use a pair of mirrors - one at each end of the resonator - so the optical axis makes an angle of very close to 90 degrees or normal incidence with respect to the mirror's surface. When the incident and reflected beams are not at normal incidence, a shift in the reflectivity spectral response of the dielectric mirror will occur due to the fact that the planes of the dielectric coatings are now at an angle to the beam and have a different effective spacing to the light waves inside the coating stack. The peak of the reflectivity shifts to correspondingly. The shift is toward shorter wavelengths as the mirror is tilted. I'll leave the analysis as an exercise for the student but the result may appear somewhat counterintuitive as one might think that since any given ray needs to traverse a *longer* distance inside the stack, the shift should have been toward longer wavelengths. :)
I informally (e.g., eyeball) tested an argon optic marked: HR for 450-520 nm @ 45 Degrees. This was one of the beam folding mirrors for a dual tube large-frame argon ion laser. When viewed at a 45 degree angle the reflection was blueish while the transmitted light appeared yellow. On-axis, these changed to greenish and red-orange respectively.
A more quantitative test of some High Reflector (HR) mirrors intended for red (632.8 nm) HeNe lasers shows:
Angle T% (1-R%)
(Degrees) Mirror 1 Mirror 2
--------------------------------
0 0.1 0.1
10 0.1 0.1
20 0.1 0.1
30 0.3 0.1
40 0.7 0.6
45 2.0 2.6
50 8.1 6.1
Angle is measured from normal incidence. Thus, when used at up to 20 or 30 degrees, these particular mirrors will behave as expected. But, beyond 45 degrees, they may make decent beamsplitters, but not HR mirrors.
Some examples of equipment where mirrors are used off-axis include triangular cavity ring laser gyros, folding or redirecting optics in dual tube or split discharge lasers, and articulated beam delivery pipes. This effect is strong enough even for slight changes in angle to have a significant impact on high performance applications - like laser resonators - where the percentage of reflection or transmission is very critical. Therefore, those salvaged optics may not quite work as expected!
See Appearance of HeNe Laser Mirrors for typical colors in reflection and transmission at various wavelengths (for red and other color HeNe lasers). However, depending on the particular model/manufacturer and length of the laser (which affects the required reflectivity of the OC), there could be considerable variation in actual color. (For accurate rendition, your display should be set up for 24 bit color and your monitor should be adjusted for proper color balance.)
Dielectric mirrors are fabricated by coating the multiple layers one at a time in a vacuum chamber. Techniques include direct vapor phase deposition (essentially opening jars of various materials for specific lengths of time), and electron beam and ion beam sputtering.
Also see the sections: Ion Laser Dielectric Mirrors and Mirrors in Sealed HeNe Tubes.
(Portions from: Dan (dmassey3996@my-dejanews.com).)
The term "dichroic" has been in use as long as I can remember (since I was a Physics undergrad in the late 50's and early 60s). It always referred to a filter built up on clear glass from multiple thin films of materials of varying refractive index. I suppose that qualifies it for the term "dielectric" as well.
When light impinges on such a surface, some wavelengths are strongly reflected and the rest is transmitted. The rejection bandwidth and reflectance of the filter at different wavelengths within the rejection band can be controlled by varying the fine structure of the reflective coatings, which are basically physically stabilized Langmuir-Blodgett films.
The "dichroic/dielectric" filter is normally not absorbing. What is not selectively reflected is transmitted. Thus, the filter places a "notch" in the spectrum of the transmitted light. Of course, if such a filter were deposited on colored glass, the absorptive properties of the glass would be added to the transmitted or reflected spectrum (depending on which way you pass light through the filter--glass first or reflective film first).
Although I cannot be certain, it seems obvious to me that the term "dichroic" meaning "two-colored" stems from the fact that the reflected beam of light from such a filter is the spectral complement of the transmitted beam (assuming use of clear glass substrate). Non-dichroic filters based on absorption in the glass typically appear about the same color by reflected light as by transmitted light because some light is reflected from the rear surface back through filter material. However, it will be less saturated (e.g., more pink than red for a red filter) because there is a specular reflection of the (presumably white) light source from the front surface as well, which isn't affected by the color of the filter material. Their reflected color will also be affected by second-order scattering effects.
Printing inks may exhibit dichroic properties, but are usually designed to absorb specific wavelengths, modifying the reflectance of an otherwise bright white substrate so they are seen in the complementary color to what they absorb. Opaque paints are usually designed to absorb specific wavelengths and scatter the others.
Where this information is not available, try viewing the reflection at normal as close to incidence as you can manage of a reasonably well collimated white light source like a decent flashlight with the Instant Spectroscope for Viewing Lines in HeNe Discharge at a far enough distance from the mirror so that the reflection is a small spot (yes it works for other things than HeNe lasers). This should give you an idea of where the peak(s) of the reflectivity curve are located.
However, for anything more quantitative, it would be necessary to test them for reflectance/transmission over the band of interest, typically from the near UV to near IR.
Unfortunately, aside from some general guidelines, there is no consistency in the visual appearance even among coatings for the same laser line from the same manufacturer if they weren't made on using the same coating technology. This is especially true of invisible (e.g., IR and UV) coatings but also to some extent with visible ones. Short of proper instrumentation, the easiest test would be to measure the transmission (or reflectivity) at common laser wavelengths (e.g., HeNe 632.8 nm, argon ion 488 and 514 nm, and DPSS 532 and 1,064 nm). Any that show a reflectance percentage that is useful for a particular laser could then be tested further, including of course, the radius of curvature. This is what I do with unidentified mirrors.
Some of the general guidelines:
(From: Steve Roberts (osteven@akrobiz.com).)
Ah, welcome to ion optics, no spectrophotometer, no easy guess.
The pink is probably a 4700 to 5200 nM white-light OC, they usually are pink in transmission, unless they have the yellow lines, then they are silvery. Otherwise it is basically impossible to tell blue green optics from red optics without putting them in the laser or in a broadband argon beam, unless it's a single line optic. White-Light HRs usually have a silvery reflection.
The best way to ballpark it is to set up a flashlight for nearly zero degree incidence, then hold a 3x5 card along the side of the optic to get the nearly normal incidence reflection, you might see some more definitive colors.
Type Part Number RoC Trans. Wavelength Comments
-------------------------------------------------------------------------------
HeNe HR G3866-001 Planar -- 633 nm SP-120, 124, 125 prisms
(3.391 um suppressed)
HeNe HR G3801-001 ?? -- 633 nm Used in SP-120
HeNe HR G3818-003 ?? -- 1152 nm Used in SP-120
HeNe HR G3801-003 ?? -- 3391 nm Used in SP-120
HeNe OC G3816-001 ?? ?? 633 nm Used in SP-120
HeNe OC G3816-002 ?? ?? 1152 nm Used in SP-120
HeNe OC G3818-002 ?? ?? 3391 nm Used in SP-120
HeNe HR G3801-012 ?? -- 633 nm Used in SP-124
HeNe HR G3801-005 ?? -- 1152 nm Used in SP-124
HeNe HR G3801-003 ?? -- 3391 nm Used in SP-124
HeNe OC G3817-005 ?? ?? 633 nm Used in SP-124
(3.391 um suppressed)
HeNe OC G3817-002 ?? ?? 1152 nm Used in SP-124
HeNe OC G3817-003 ?? ?? 3391 nm Used in SP-124
HeNe HR G3802-001 Planar -- 633 nm 15 mm, used in SP-125
HeNe OC G3860-001 30 cm 2% 633 nm 12.5 mm
HeNe OC G3854-001 4.3 cm 0.5% 633 nm 7.5 mm diam., may be goof.
Ar OC G0297-001 ?? ?? ??? Internal mirror tube
Ar HR G0326-005 ?? ?? Part of HR prism assmbly.
Ar HR G3801-010 Planar -- 488-514 nm 7.75 mm, for prism assbly.
Ar HR G3802-009 Planar -- Broadband SP-171, 168
Ar HR G3802-016 Planar -- 333-364 nm UV set for SP-171
Ar OC G3808-018
Ar OC G3814-016 600 cm 12% 488-514 nm SP-171
Ar OC G3814-019 600 cm 3.5% 333-364 nm UV set for SP-171
Ar OC G3814-029 600 cm 20% 488-514 nm SP-171
Ar OC G3818-009 60 cm 1.7% 457-514 nm (May be SL 488 nm)
Ar OC G3861-001 400 cm 4.3% 488-514 nm SP-164, 165, 168
Kr HR G0001-002 400 cm -- 752-799 nm
Kr HR G0001-003 400 cm -- 488-514 nm
Kr HR G0001-004 400 cm -- 647-676 nm
Kr HR G0193-001 Planar -- Yellow/green 15 mm
Kr HR G3802-022 Planar -- 646-676 nm 15 mm
Kr HR G3802-026 Planar -- 520-568 nm 15 mm
Kr OC G3808-001 ?? ?? Broadband MM set for SP-168
Kr HR G3808-004 ?? ?? Broadband MM SP-168
Kr OC G3808-905
Kr HR G3812-011 300 cm -- 647-676 nm 15 mm, SP-164, 165
Kr HR G3812-013 300 cm -- 752-799 nm 15 mm, SP-164, 165
Kr HR G3814-021 600 cm -- 647-676 nm
Kr HR G3814-025 600 cm -- 647-676 nm 15 mm, Red set for SP-171
Kr OC G3814-026 600 cm 4.7% 647-676 nm 15 mm, Red set for SP-171
Kr HR G3861-007 400 cm -- 752-799 nm 15 mm
Ar/Kr HR G3814-040 ?? ?? 488-647 nm? RGB Braodband
YAG OC G3809-LPD860 ?? ?? 18% 1064 nm 15 mm
YAG HR G0101-002 60 cm -- 1064 nm
Dye OC G3845-002 5 cm 488 nm pump
Dye OC G3845-003 5 cm 7.5 mm, 488 nm pump
Dye OC G3845-004 5 cm Folding Mirror, R110 Dye
Dye PM G3845-008 5 cm 705-800 nm 725 nm peak
Dye PM G3845-011 5 cm 743-825 nm
Dye PM G3845-006 5 cm 647-676 nm
?? OC G0072-001 Planar? ?? 633 nm? 15x4 mm, for ring laser?
?? HR G0020-023 Planar? -- 633 nm? 25x4 mm
?? HR G0068-006 22.8 cm ?? 407-427 nm 15x4 mm
(From: Dave Corridon (dacorridon@aol.com).)
Historically, users have relied upon metallic coatings to reflect ultrafast pulses as they do not really distort the pulse length. Considering the electrodynamics of a perfect conductor, all incident radiation will reflect from the conductor's surface as the electric field inside the conductor equals zero.
There are advantages to using dielectric optical coatings for reflecting ultrafast laser light. However, since the light must penetrate individual layers of the coating for interference conditions to occur, that light which penetrates the coating will eventually reflect from one of the deeper layers and exit the coating.
That light which eventually reflects from the depths of the coating will have traveled further than the light which reflected from the first surface. This path difference results in a "stretched" pulse which is wider than the original.
To compensate for the pulse broadening (known as Group Velocity Dispersion or GVD) laser physicists implement prisms which bend the various wavelengths constituent to the laser line at different rates so that the redder need to travel a shorter distance with the blue.
Recently, however, optical coating designers have introduced designs which reduce the path difference by using fewer layers (high index difference between material layers) and coatings that apparently reverse the effects of GVD.
(From: Bob.)
Many coatings use thorium. Thorium fluoride or oxyfluoride is fairly common. I am not familiar with the current technique of depositing such films. Thorium oxide, such as used in gas mantles, is one of the highest, if not the highest, temperature melting oxides.
There are two major classes of optical filters:
Cost and immunity to minor surface damage are the major advantages of bulk absorbers. For a given batch of material, the characteristics of multiple filters is very consistent. The angle of incidence of the input beam has a relatively slight impact on behavior. However, since they do absorb what they don't pass, even a modest power laser beam may cause serious damage or destruction throughout the thickness of the material. Control of selectivity is poor.
Selectivity and the ability to handle high power density are major advantages of dielectric filters. What isn't passed is almost entirely reflected with less than 0.1 percent actually being absorbed in the coating and almost none in the substrate. Therefore, these types of filters can handle high power with specifications typically being MW per square centimeter or better. By adjusting the coating "recipe", the filters can be tailored to pass or block a very specific range of wavelengths. Multiple bands can be blocked by applying multiple coatings in succession. However, the cost is much higher than for bulk absorbers, being closer to that of planar dielectric mirrors. And, minor errors in the coating process can result in an unacceptable shift in the wavelength band(s). Even where the particular substrate happened to be located in the coating chamber can impact wavelength band location and transmission. The angle of the input beam away from 90 degree incidence can significantly change the wavelength band location toward shorter wavelengths by order of 1 or 2 nm/degree.
The Brewster angle, theta_b, is computed as:
theta_b = arctan(n2/n1)
where n2 and n1 are the index of refraction of the window material and the
medium outside the window (usually air), respectively. Since n1 for
air = 1, this reduces to:
theta_b = arctan(n2)
Theta_b is measured with respect to a line normal to the window's surface.
For an n2 of 1.5, typical of optical glass, this results in a Brewster angle of approximately 56 degrees. Other optical materials like fused quartz will have different Brewster angles. Since n depends on wavelength to some extent, the wavelength of the laser will also affect the calculation. See the next section.
A derivation of the Brewster angle equation can be found at: Brewster's Angle - from Eric Weisstein's World of Physics.
You will often see the terms: S and P polarization used in conjunction with these sorts of reflections. S derives from senkrecht (perpendicular, from the German) and P from parallel. The P vibrations have the E (electric) field parallel to the plane of incidence. Upon reflection at the Brewster angle, only the S rays remain, all the P rays are coupled into the glass.
If you care, the reason there is no reflection at the Brewster angle is due to the radiation pattern of the electric dipoles induced by the incident field within the material. The dipole axis coincides with the reflection direction and there is no emission along the dipole axis. (This is only true for an ideal non-absorbing material - which is close to the situation for many useful materials. For absorbers, it doesn't work out quite as nicely.) As a result, the internal rays in a Brewster window are at right angles to the external reflected rays.
The key to the benefits of using Brewster angle windows inside a laser resonator is that there are essentially no losses from reflection for light polarized at the correct angle. Whereas reflection from uncoated glass is typically 4 percent or more, reflection from a high quality Brewster window for light of this angle can be much less than 0.1 percent - it is almost as though the window isn't there at all as far as transmission is concerned (there will still be a slight shift in the beam position due to refraction but this has no effect on losses and shift can be completely compensated if necessary). The losses due to reflection are high enough at angles only a few degrees away from the preferred polarization that gain will be substantially reduced. Thus, laser oscillation will take place centered around the preferred polarization, the output will be highly polarized (which is another benefit and/or requirement for many applications), and virtually all of the stimulated emission will be exploited (due to the near-zero losses). Where every fraction of a percentage point counts in the gain of the lasing medium, minimizing losses in this way is critical to efficiency or getting the laser to lase at all!
The alternative - antireflection (AR) coated windows - still have some losses, perhaps 0.25 percent. But, that is significant for a low gain laser like a HeNe. However, some laser tubes are manufactured with perpendicular AR coated windows where the polarization must be controlled externally.
An angled Brewster plate may also be found inside the resonator of sealed helium-neon or other gas lasers. This results in the optical resonator favoring one polarization orientation (just like the laser with external mirrors) and the output beam will therefore also be linearly polarized. Without the Brewster plate, these gas lasers produce a beam with random polarization (it may jump from one polarization orientation to another at random times, slowly rotate as the tube heats up, or emit at more than one orientation simultaneously - or all of these)!
Note that due to refraction, the beam path shifts slightly in going through the angled Brewster window(s). If the tube bore is centered with respect to the mirrors, the actual beam will be off-center. Usually, centering is done by looking through the mirrors (or mirror mounts) from the ends so this is not a problem. However, a tube with an internal Brewster plate at one end may be more likely to have an offset beam at that end since. It's not a bug, it's a feature. :)
The polarization purity from a laser with external mirrors and Brewster windows or an internal Brewster plate is typically specified as 500:1 to 1,000:1. The problem in achieving perfection is that the laser cavity gain isn't an impulse function with respect to Brewster orientation but falls off gradually for either of these - or for a polarizing filter for that matter. So, some oscillation is still possible slightly off axis. There are probably (expensive) ways to improve this somewhat and a single frequency stabilized linear polarized laser is pretty darn good. True perfection, however, is in the eyes of the beholder!
Note that the Brewster condition only states that there will be no reflection of the P-polarized waves. It does NOT say that all of the (orthogonal) S-polarized waves will be reflected. In fact, only a small percent will be reflected (perhaps 10%) based on the index of refraction of the uncoated window material. So a simple Brewster window or plate isn't any good as a polarizing beamsplitter (see below). But, 10%/0% is still a very big number when it comes to determining the lasing orientation. :)
You can demonstrate the principle of the Brewster window easily in a couple of ways using a window pane, microscope slide, or other piece of clear uncoated (not mirrored) glass (Brewster angle around 57 degrees):
There are also things called "Brewster stacks". While transmission of the P-polarized rays through a Brewster window is nearly perfect, as noted above, what portion of S-polarized rays are transmitted/reflected depends on the index of refraction and for typical materials, is not nearly as perfect - in fact, most of these get through (perhaps 90 percent). By placing a series of Brewster windows in series, the reflection percentage can be increased. That's the theory anyhow. In practice, internal reflections, unavoidable losses, and other beam degradation effects complicate the situation so alternatives like polarizing beamsplitters are a better solution where it is desired to separate the S and P waves cleanly and efficiently.
(From: Steve Eckhardt (skeckhardt@mmm.com).)
According to Shurcliff's "Polarized Light", the "pile of plates" polarizer was invented by Arago in 1812. The reference is: Arago, F. J., Oeuvres completes, vol. 10, p. 36 (1812). I hope you have access to a good library and a working knowledge of French!
You could also look at Fresnel's equations for transmission and reflection at a dielectric interface. When the reflected and transmitted (refracted) beams are separated by 90 degrees, and tan(theta)=nt/ni, where:
Then none of the P-polarized (parallel to the plane of incidence) is reflected. Thus the reflected beam is completely polarized. However, about 92% of the S-polarized light is transmitted, so the transmitted beam is not completely polarized and the reflected beam is relatively weak. Stacking a bunch of microscope slides progressively weakens the s transmission, and thereby increases the degree of polarization of the transmitted beam.
A little bit more on Brewster windows. Here are the formulas for reflection:
sin2(alpha-beta) tan2(alpha-beta)
Rs= ----------------- and Rp = -----------------
sin2(alpha+beta) tan2(alpha+beta)
Where:
I used the above formula for Rp to get transmission (T=1-R) and for a Brewster window there are two surfaces so the transmission through the plate is T2.
In a resonant cavity a photon transits the cell many times, so I figured the resultant transmission for many passes. They are shown in Window Transmission versus Angle. The left graph covers the full range of 0 to 90 degrees while the right one expands the area around the Brewster angle. The top (red) curves are for one pass through a window. Note the boundary values of 92 percent for normal incidence and 0 percent for grazing incidence. The other curves are for 300 (green) and 1,000 (blue) passes, as indicated. This gives you an idea of how much tolerance there is in setting Brewster angle. It all depends on how much loss you can afford (though, of course, within this range of angles, the losses due to 4 reflections - most relevant in relation to the round trip gain of a laser cavity with two Brewster windows - are still very small). It's also a measure of a photon's lifetime inside the cavity, though perhaps not mathematically rigorous.
On another note, we have all said from time to time that Brewster windows need to be nice and flat, but have we really tested that assertion? A confocal laser will work just about as well if you substitute a mirror with twice the radius, or anything in between. That's a lot of tolerance. It seems to me that all you need (geometrically) for a mirror is something that will steer a beam back toward the center when it strays to the edge, but not with so much correction that it falls off the other side. From this point of view, a window only needs to be very transparent with minimal scattering. Of course, as you may have noticed in just about all of my writings, I'm talking about multimode lasers.
The following are from various vintage sources including "Procedures in Experimental Physics" by John Strong, Prentice-Hall (1941), various "CRC Handbooks" including one from 1930, and "Elements of Physics" by Smith (1938). Thanks to George Werner (glwerner@sprynet.com) for digging up most these numbers. Where there is a small range of index of refractions depending on orientation, an average value is used in this list.
So, when designing a laser, what you need is the index of refraction, n, for the Brewster window material at the wavelength or range of wavelengths that your laser is designed to produce. If n varies significantly, you can try for a compromise by using the average of the Brewster angle or mount them so a bit of adjustment is possible. For a tube that is not permanently sealed, this could be glass ball-and-socket joints but for a sealed tube, you would want something else like metal bellows. Or, better yet, select a different material with a more constant n! Note that for a laser with multiple Brewster surfaces, there isn't any fundamental benefit to facing them in opposite directions or the same way. However, with the orientations alternating, the beam doesn't shift away from the optical axis with an even number of equal thickness windows or plates.
For a gas laser, the beam passes through the Brewster window or Brewster plate which needs to be oriented with its normal at the Brewster angle with respect to the optical axis of the resonator. For example, using BK7, the index of refraction is 1.517 with a Brewster angle of 56.6 degrees. The Brewster window or Brewster plate must then be oriented at 56.6 degrees with respect to the optical axis - the rather steep angle seen in any external mirror gas laser.
However, for a solid state laser rod where the beam passes down the center of the rod, it's the angle inside that is critical. Knowing the Brewster angle, use the fact that the reflected and transmitted beams are at 90 degrees to each other to determine the angle the ray makes inside the rod for grinding its ends. From simple geometry, this means the rod ends should be ground so their surface normals are at (90 - Brewster angle) with respect to the optical axis. So, a larger Brewster angle will result in a smaller angle of the rod surface (compared to a normal 90 degree cut) but a larger angle of deviation between the beam axis outside the rod and the rod axis.
This can also be confirmed using Snell's Law:
n1*sin(theta1) = n2*sin(theta2)
Where:
And of course, the beam outside the crystal is at the Brewster angle so the mirrors must be aligned normal to that. For example, for a ruby rod, the index of refraction is 1.76 and the Brewster angle is 60.4 degrees. Thus, the rod ends should be ground at an angle of 29.6 degrees and the beams outside the rod will be at the 60.4 degree Brewster angle with respect to the rod ends but 30.8 degrees from the rod axis. Got that? A simple diagram will help, left as an exercise for the student. :)
Another example: The Brewster angle for Nd:YAG is 61.3 degrees. The rod ends will then be cut at 28.7 degrees with respect to normal, but the beam will enter the rod at 32.6 degrees from the rod axis [90-2*(90-B)]=[90-28.7-28.7].
The most common types of high quality polarizing optics are Brewster windows or plates, and polarizing beamsplitters (prisms, pellicles, mirrors). Also see the section: Polarization.
A wonderful interactive application that provides animations of polarized waves and the effects of a material (birefringent or not) in their path can be found at EMANIM Download or to just view some tutorials go to EMANIM Tutorials Index.
(From: Tim Coker (tim.coker@gecm.com).)
Sheet (or dichroic) polarisers generally use an oriented organic dye. These absorb one polarisation and not the other, the trouble is of course that the absorption is wavelength dependent, this is generally true for most if not all optical effects. You can optimise the dye for particular parts of the spectrum but it's difficult to get one that is truly flat across the whole visible.
Crystal polarisers work differently - they exploit the anisotropy of the crystal wherein the S and P polarisations behave differently as they propagate through the crystal. This acts to split the 2 polarisations (leading to double refraction, etc.). The problem is that the divergence is quite small so you need quite a lot of crystal to be able to separate the polarisations over an area. A slightly different effect is to exploit the different refractive indices of the 2 polarisations. A boundary with a material with an index between the 2 values will cause one polarisation to transmit and one to totally internally reflect. This makes for a very good polarising beamsplitter (e.g., Glan-Thompson). But they still need to be deep so you couldn't make sunglasses out of them, not practically anyway, certainly not cheaply). Because the polarising effect itself is not absorbing its very efficient and has very high extinction ratios.
The birefringent effect in crystals does have a very broad wavelength response, but it is still dispersive as an effect even if the observed effect may look wavelength independent in certain circumstances (e.g., over a restricted wavelength range and set of angles).
(From: William Buchman (billyfish@aol.com).)
I just want to point out that the difference between sheet and crystal polarizers is really not as great as the comments above may imply. The biggest difference would be the size of the crystal involved. Tourmaline is a dichroic crystal that has all the properties required of a crystal polarizer except that it also absorbs one of the two polarizations more strongly as it passes through. In principle, one could chop up pieces of tourmaline to produce microcrystals that are then oriented in a film to form a sheet polarizer.
The basis for a polarizer is anisotropy. It shows up as a difference of refractive index for two different polarizations. This difference can be used to make beamsplitting polarizers. The refractive indexes can also differ by having an imaginary component that differentially absorbs the polarization. In principle, it is possible to make a polarizer that is both double refractive and dichroic.
Most of the description below assumes a crystalline material though most of the principles are similar for both types.
Depending on the type of crystal, due to the crystal structure, there will be only 1 or 2 directions (called the optical axis or axes of the crystal) where the internal beams will have the same direction and travel at the same speed. These crystals are termed "uniaxial" and "biaxial", respectively.
If the faces of the crystal are plane-parallel, a beam entering from one side at an orientation which is not the same as the/an optical axis will divide inside the crystal into orthogonally polarized beams and will exit as separate beams (which may overlap) at the other face:
no and ne are only equal in the direction of an optical axis. The principle indices of refraction of the crystal are no and the maximum value of ne.
A common example of a birefringent material is calcite which is the reason that this crystal produces double images. Others include crystalline (not fused) quartz and the non-crystalline plastic used as the base for Scotch(tm) tape. :) Important laser, non-linear, and electro-optic crystals are also birefringent to some degree so it can't be ignored and can be used to advantage as well. Some of these materials are useful specifically because of their birefringence.
Birefringent crystals have all sorts of uses in implementing various optical components including polarizers and isolators. Since birefringence is also a fact of life, it must be taken into consideration when designing a laser configuration. For example, for a microchip laser consisting of a sandwich of Nd:YVO4 (neodymium doped vanadate) and MgO:LiNbO3 (magnesium oxide doped lithium niobate), the relative orientation of the two crystals will change the effective (optical) length of the cavity because of the variation in nE in the MgO:LiNbO3 with respect to the polarization orientation of the Nd:YVO4 (which is fixed). This can be critical where the round trip time needs to be accurately controlled as with a mode-locked laser. And, the variation in index of refraction resulting from birefringence is essential in enabling the phase matching required for frequency multiplication, OPOs, OPAs, and other non-linear optical processes.
Orthogonal polarizations remain orthogonal through any transformation that can be described by a unitary Jones matrix - i.e., any lossless polarization operation. That's how Faraday rotator mirrors work.
The best way to make two orthogonal linear polarizations interfere losslessly is to use a beam-splitting polarizer like a Wollaston, oriented at 45 degrees, detect each resulting beam, and *subtract* the detected photocurrents. This gets you the full interference term, without the 6 dB (electrical) signal loss that comes from the ordinary 45 degree polarizer trick. Another advantage is that the signal has a zero background, so that additive noise doesn't usually bury you. (You can also use a laser noise canceler in many cases, to get 50 to 70 dB of additive noise suppression.)
Wollaston beamsplitters don't have etalon fringes, which is a huge help in real applications. Note also that subtracting the photocurrents is considerably tougher with imaging detectors than with single photodiodes, but it's still possible.
The change in the reflection coefficient for S-polarized light as the angle of incidence is varied from 90 degrees to 0 degrees passing through the Brewster angle is another common example. The reflection coefficient for p-polarized light is unaffected.
Some green HeNe lasers are even designed to take advantage of the slight polarization preference of light reflected from a pair of dielectric HR mirrors (one at 45 degrees) to polarize the output without Brewster windows.
Reflection from a conducting mirror (e.g., aluminum or gold) should not affect polarization. However, these are not perfect conductors but of more significance for aluminum, there will either be a clear protective layer of SiO2 or some other passivation ("protected aluminum") or simply aluminum oxide which forms on the surface. These are dielectric materials and will result in a slight polarization preference even for metal coated mirrors.
(From: Louis Boyd.)
Many commercial first surface mirrors are overcoated with SiO2 (quartz) to protect the surface. Those will have some weak polarization if the reflection isn't perpendicular to the surface. Likewise "uncoated" aluminized mirrors will form a layer of aluminum oxide just by being in air. You may be able to design your instruments so the effects are equal in both polarization axis and effectively neutral. For example, in a Cassegrain telescope the net polarization close to zero as the angles are small and symmetrical about the optical axis. That assumes the mirror surfaces are uniformly reflective.
Certainly most spectroscope designs aren't polarization neutral. That's difficult to archive in either a grating or prism spectroscope unless the light source is actively rotated and integrated.
(From: Jargen.)
A lossless mirror cannot polarize, no matter whether it is a first-surface, a metallic, total internal reflection or a dielectric mirror. Any linear optical element only can do a unitary transformation between modes: Orthogonal modes always stay orthogonal. If the mirror is not lossless, of course the losses can be polarization dependent.
Note however that for a general reflection the s- and p-polarized modes may experience a different phase shift. So only linearly polarized light in these planes stays unaffected whereas in other directions the polarization angle can turn and even elliptic polarization may result.
(From: Phil Hobbs.)
Spectrometers are all polarization sensitive at some level. This is hardly avoidable since the p-to-s diffraction efficiency ratio of reflection gratings is massively wavelength-dependent.
Cheap first surface mirrors are usually 'protected aluminum', which is Al covered with a half-wavelength worth of SiO, which is a non stoichiometric, silicon-rich oxide whose index can range anywhere from that of SiO2 (1.46) to about 1.9, depending on the deposition conditions (which change the oxygen content of the film).
Aluminum-air surfaces are much better reflectors than aluminum-glass, so protected aluminum mirrors have quite low efficiencies except where thin film interference in the SiO helps. The thin film interference is polarization sensitive off axis, of course, which makes protected Al mirrors somewhat polarizing.
Better quality aluminum mirrors are usually 'enhanced aluminum', in which the single SiO layer is replaced with a dielectric stack. With more layers, the coating designer has more degrees of freedom, so the off-axis and polarizing performance of enhanced Al is harder to know from first principles.
(From: Coater.)
To cover a wide range of wavelengths, the best all around reflecting material is aluminum. Usually, a very thin layer of MgF2 or LiF is used to help slow oxidation, but the mirrors are still extremely fragile. Silver should NEVER be used to cover those wavelengths. Reflection drops off drastically in the UV. As a matter of fact, it's a dielectric somewhere down there (forget the wavelength right now.. think it's somewhere around 270nm).
As for enhanced aluminum mirrors, they are great for fairly narrow wavelength regions. But, in trying to cover very wide wavelengths, an extremely large number of layers would be required. Once you get that many layers on the substrate, you may as well not even bother with the aluminum.
But one way of implementing zeroth-order waveplates that doesn't require elaborate and expensive grinding and polishing operations is to use mica, a naturally occurring birefringent crystal that can be cleaved to precise very thin sections. Fine tuning of the retardation can be done by a slightly adjusting tilt. The mica may be protected by being cemented between optical glass plates. They are broadband, relatively low cost (as these things go), and are often used in imaging and low power (e.g., HeNe laser) applications. The HP/Agilent two-frequency HeNe metrology lasers have both 1/4 and 1/2 waveplates on separate tilt/rotation mounts. The 1/4 waveplate converts the Zeeman-split circular polarization from the HeNe laser tube to orthogonal linear polarization, and the 1/2 waveplate aligns them with the horizontal and vertical (XY) axes.
See Polarized Light Waveforms for a description and interactive Java Applet showing the effects of the phase shift of a waveplate on polarization. Finally, a good use for Java. :)
Input Output
---------------------------------------------------
Quarter Wave Plate
---------------------------------------------------
Linear, theta = +45° Right circular
Linear, theta = -45° Left circular
Right circular Linear, theta = -45°
Left circular Linear, theta = +45°
Linear, theta not +/-45° Elliptical
---------------------------------------------------
Half Wave Plate
---------------------------------------------------
Linear, theta = a° Linear, theta = -a°
Left circular Right circular
Right circular Left circular
---------------------------------------------------
Any Wave Plate
---------------------------------------------------
Linear, theta = 0 or 90° Unchanged
---------------------------------------------------
Note in particular the effect of a half wave plate on linearly polarized light. This is often given as "a rotation of theta degrees in the input results in a rotation of 2*theta degrees in the output", correct only if the waveplate is being rotated but not if the light beam is rotated. It's easy to see why the half wave plate operates this way. The vector component of the polarized input beam parallel to the fast axis of the waveplate sees a retardation, r. However, the vector component of the polarized input beam parallel to the slow axis see a retardation of r+pi, which in effect is a sign change. Thus, the angle flips around the fast axis.
One implication is that a beam of light possessing multiple linearly polarized components at different frequencies which are close enough to satisfying the half wave condition, can be rotated together to an arbitrary orientation with a half wave plate. (Though for more than two beams, since the result is actually a mirror image of the input, a reflection may be needed to achieve the same arrangement of the beams.) One useful application would be in orienting the output of a two frequency (two mode or Zeeman split) HeNe laser in an interferometer measuring system.
All sorts of other conversions are possible depending on the input polarization and the angle and type of the waveplate. For example, a 1/4 waveplate can convert elliptical to linear or circular depending on theta.
Like a normal Fabry-Perot cavity, the etalon imposes a set of longitudinal modes of its own on top of those of the overall resonator. The peaks of these correspond to the conditions where constructive interference occurs at both surfaces and this happens when the effective thickness of the etalon (i.e., the distance between its partially reflecting surfaces) is an integer multiple of 1/2 the wavelength of the light inside the etalon - just as in a normal laser resonator. Another way to this of this is that if the etalon has a thickness that is an integer number of 1/2 wavelengths, it will not affect the standing wave pattern inside the main resonator. (This basic description assumes that the beam inside the resonator is planar/parallel and single (transverse) mode. Where this is not the case (as with many common cavity configurations), matters will be somewhat more complex.)
The overall distance between surfaces compared to the total cavity length and their reflectances will affect the strength and selectivity of the etalon on the laser's behavior. Actual adjustment is done by slightly tilting the etalon. This changes its effective thickness (which varies as the cosine of the angle ignoring refraction). In a high quality laser, this tilt may be done using a precision micrometer screw.
Note that if you tried to construct a system with a single additional reflective surface (e.g., a plate with one of its surfaces AR coated), the result would be very unpredictable because although the 3 conditions above could still be met, essentially trivially, unless the distance between the reflective surface and one end of the cavity was small and stable, thermal expansion of the entire resonator would affect the lengths of both parts unequally and as the modes move with respect to each other, the operation would be erratic. See the section: External Mirror Laser Using HeNe Tube with Missing Mirror Coating for an amusing experiment.
Here's a laser stunt to impress your friends. We all know that laser windows (unless they are well AR coated) are set at the Brewster angle to the beam to minimize losses and low gain lasers (like the HeNe) will not work at all otherwise. That's the party line. Well, one day I set out to disprove it. I had a HeNe laser that produced a few milliwatts of power and a bunch of spare glass plates that we used for windows. They were rectangular, about 14 x 40 mm, with the corners cut off, bought from Edmund Salvage Company in the early '60s (now Edmund Scientific, I assume. --- Sam). I found out later that they were the same plates as used for a mirror in the Norden Bomb Sight. They had good flat surfaces and they would stand on edge. I positioned a larger glass baseplate (to be used as a common support) about 7 mm under the beam between the Brewster window and the output coupler. Here I placed one of these windows approximately perpendicular to the beam and found just the right orientation to get constructive interference and lasing restored. Then I set the next small plate in place. I repeated this until I had eight little windows lined up in the beam with the laser happily continuing to lase. Here's the evidence: Perpendicular Uncoated Windows Inside Cavity of HeNe Laser. The output coupler mirror can be seen at the left with the plasma tube's Brewster window visible on the right. The path of the beam can be clearly seen as a series of bright spots (along with their reflection on the baseplate). Sorry, it's only in black and white. :)
(From: Sam.)
I really like the perpendicular plate trick. I've done this in the past with a single plate without thinking much about the physics. But your achievement forced me to actually attempt to analyze what was going on. I'm still not sure I understand the behavior fully. It really is a cute bit of optics magic and a definite violation of Murphy's law. :)
If you have access to an external cavity HeNe laser, this stunt is easy to duplicate. Get yourself a very clean glass plate (an optical flat is best but a good quality microscope slide will suffice). Position the plate inside the cavity (watch out for the high voltage!) nearly perpendicular to the beam path. With a little care (you don't need a fancy adjustable mount - a steady hand will do unless you want to line up a bunch of them), you will be able to get the lasing to continue even though you would think there should be about 16 percent loss due to reflections from its uncoated surfaces (4 percent from each surface in both directions) which should kill lasing in almost any small to medium (or maybe even large) size HeNe laser due to its low gain. It works easily with a small one-Brewster HeNe laser head (approximately 8 inch long bore, 4 to 6 percent round trip gain).
This is actually just a (perhaps not so) simple case of interference - with the plate acting like an etalon in the laser cavity. When the thickness of the plate (or etalon) is a multiple of 1/2 the wavelength of the light inside the plate and the length of the resonator is also a multiple of 1/2 wavelength, it's almost as though the plate isn't there at all. See the section: What is an Etalon? for a more complete explanation.
Note that in general, the plate may not be perfectly aligned with the resonator mirrors, but slightly off-axis so the internal path length results in constructive interference at each surface at the lasing wavelength. However, as with a normal HeNe laser, the total length of the resonator is not critical as the lasing modes will shift under the gain curve to compensate. Any change in lasing wavelength that results due to mode cycling will not significantly affect the behavior of the thin plate as an etalon.
Note that a plate that is AR coated on only one surface will not exhibit this behavior but will do something else that is equally interesting inside a laser cavity. Why and what is it?
For a low gain laser, the plate must be nearly perpendicular (perhaps within a couple of degrees with 1 or 2 orientations on either side where there is lasing) because as the angle increases, the overlap of the incident and reflected beams at the front surface of the flat decreases. Their relative angle also increases. The net result are losses which quickly become enough to kill lasing. In addition, the beam path shifts slightly in the resonator (though this could be compensated by readjusting one of the mirrors). Where more gain is available (as with a large frame HeNe laser or a pair of One-Brewster HeNe laser heads as described in the section: One-Brewster HeNe Laser Heads in Tandem, the angle can be larger without killing lasing entirely, perhaps up to 10 or 15 degrees. There will be multiple peaks between null spots, every degree or so for a 1 mm thick plate.
As the plate is tilted, the very low intensity waste beams reflecting from it (due to the not quite perfect suppression of the surface reflections) will be visible on on the mirror mount and/or tube face. At small angles, one of these may even make its way through the output mirror appearing as a ghost beam.
Some of the magic (which I had a hard time explaining at first) was that for 3 of the 4 apparently identical slides I've tried as plates, the effect was present (and quite strong) only when nearly perfectly on-axis using my one-Brewster rig but occurs at multiple angles when using two one-Brewster tubes in tandem to double the gain. And for the 4th slide, there was a 'sweet' spot near one corner where I could easily get a half dozen or more peaks on either side of perpendicular at approximately 1 degree increments without even trying. It would now appear that except for the sweet spot, all these slides had significant wedge (A micrometer does show that the 4 slides differ slightly in thickness and from one side to the other.) I then selected a 5th slide based on the criteria that wedge be minimal - first using the micrometer and then the reflectance test, see below. This one behaved nicely in a fair size region lending some credibility to the minimal wedge requirement claim. :)
The axial position of the plate within the resonator also significantly changes behavior in terms of ease of alignment presumably due to how parallel the beam is at that point and this also affects the resulting transverse mode structure and power. In fact, the output of this multi (transverse) mode laser would appear to be generally forced to a TEM00 or TEM01 beam profile with the plate present. This would seem to correlate with the interference patterns resulting from thickness variations of the plate (see below with respect to wedge) and a very flat plate produces a TEM00 beam. There may also be stability problems if the plate is positioned very close to the mirror since that would limit the possible standing wave patterns that are possible between the plate and mirror.
However, if this were only a matter of standing waves, one would expect that all distances would need to be an integer number of 1/2 wavelengths - inside the plates, between them, as well as between the plates and the mirrors. This would seem to be an extremely critical relationship and I haven't yet seen any evidence to support it. My laser with a split resonator which has a single 4 percent uncoated intermediate surface is EXTREMELY critical in every respect - just barely touching the mirror mount will cause the output to come and go. But our friendly perpendicular plate setups don't behave this way. Positioning both the angle of each plate and its location with respect to its neighbor properly would be next to impossible if every distance had to be a multiple of 1/2 wavelength. It's as though the only thing that matters here is what's between the plates' surfaces.
I've now successfully placed two (2) very clean microscope slides inside the cavity of a one-Brewster HeNe laser using some really mediocre 'third hand' thingies as mounts. I only stopped with two because that's all of the mounts I had. :) (Because slides are so thin, they wouldn't stand up straight or stable enough without help.)
Although almost any reasonably clean plate may get you something, there are several things that will contribute to maximum success - especially if you want to beat the unofficial World's record of 8 plates in a row:
All these effects are striking demonstrations of how tiny a wavelength of visible light really is! If two distinct spots are always visible and rotate along with your plate, the wedge is huge - you're not even in the same ball park! :)
(From: Thomas R. Nelson (tnelson@uic.edu).)
Dust is attracted to a high power laser beam. The mechanism is the same as that which makes laser tweezers (used to manipulate microscopic objects like blood cells) possible work. The dust is polarizable, and when it's near the laser field it gets polarized. Since the laser field is typically non-uniform, the dust will follow the gradient of the field to the field's strongest point (typically the center). Those of us who work with high powered lasers regularly know that among other things, the place where your optics get the dirtiest is the place where you want the dust the least - namely where the beam hits them.
(From: David Van Baak (dvanbaak@calvin.edu).)
Laser beams *do* exert forces on polarizable materials, and the direction of force is toward the more intense part of the beam. Thus for a laser beam focussed to a Gaussian waist, a dust mote, such as a tiny piece of thread, will first be attracted from the fringes of the beam toward its center, and will then also feel a (weaker) force along the direction of the beam to the focal point. The result is a highly scattering particle of dust visibly trapped in the focus of the beam, with an active restoring force in all three dimensions to stabilize its position. The phenomenon is dramatic enough to be noticed by persons not attuned to the mechanism; I myself was startled to see it in a 1 W beam of an argon ion laser way back in 1979, and I'm sure I wasn't the first.
The basic idea is that for a dielectric mirror coated for a specific reflectance at a particular wavelength and 90 degree incidence, the actual reflectance and transmittance will change as a function of the angle with which the beam hits the mirror. The cause of the this change is a shift in the peak wavelength (toward shorter wavelengths) as the incidence angle moves away from 90 degrees. The precise behavior will depend on the details of the actual coating. For a mirror designed to peak at 632.8 nm (HeNe red) and 90 degree incidence, the reflectance will decrease and the peak wavelength will move toward the yellow and beyond. For a mirror coated for 45 degree incidence, the peak at 90 degrees will be more toward the deep red and IR.
Thus:
(From: George Werner (glwerner@sprynet.com).)
Note that another (simpler) way of implementing a similar function is to insert a variable angle Brewster plate inside the cavity. Adjusting its angle over a range which includes the Brewster angle will adjust the reflectance from near zero to a few percent at each of its surfaces. The sum of all reflections from the plate will then subtract from the reflectance of the resonator mirrors (which should both be HRs in this case). However, with this scheme there will be 4 output beams (not counting the leakage through the HR): a pair in each direction from the plate's two surfaces (unless one surface is AR coated). And, the angle of each pair will change as the angle of the plate is varied. A planar HR may be desirable to eliminate the need for realignment caused by the slight shift in internal beam position as the plate's angle is varied.
(From: Carl Grossman (cgrossman@swarthmore.edu).)
There is nothing subtle about the peak power in a 100 mJ, 5 ns doubled YAG pulse (especially if you accidentally put a finger in one); you are talking about 20 MW peak compared to 1 W. Though the heat energy is less, the huge fields in the Q-switched pulse can ionize atoms, vaporize solids and generally wreak a lot more damage than a 1 W CW beam. For example, the specs on pinholes should follow the peak power, not the average power (I've burned many a copper pinhole with my pulsed dye laser of nanojoule average power, the pump laser would blast its footprint through). Use ceramic pinholes instead (Lee Laser sells 'em). Be sure that your mirrors are designed for pulsed powers, especially the ones right outside the laser. Further down the beam-line, presumably at lower powers, standard broadband dielectrics are fine. Forget about metal mirrors unless we are in the 1 mJ range. WARNING: Wear goggles, block beams, and work carefully!
Brian Vanderkolk (skywise711@earthlink.net) has been putting together a free program that will display many of the common (and some not so common) laser lines via an interactive GUI: See: Skywise's Laser Line Software Page.
Some of the information in this table is from: Rockwell Laser International Laser Tutorials. The Chart of Laser Types and Applications also lists some typical applications for each laser type.
Brian Vanderkolk (skywise711@earthlink.net) has copies of Marvin Weber's "Handbook of Lasers" and Jeff Hecht's "The Laser Guidebook". He has gone over this list and added some of the more precise wavelengths, as well as pointing out some corrections/discrepancies as noted below. Most of his references are from Weber.
Also note the correct way to show solid state lasers with multiple dopants. It seems the first one listed is generally the lasing ion and any co-dopants are listed afterwards. The co-dopants either assist getting energy into the lasing ion or taking energy away after it relaxes to an intermediate state.
Wavelength (nm)
Laser Type Approx. Exact Notes
-----------------------------------------------------------------------------
Fluorine (F2, Excimer-UV) 157 157.48
Argon Fluoride (ArF, Excimer-UV) 193 193.3
Krypton Chloride (KrCl, Excimer-UV) 222 222
Helium-Silver Ion (HeAg+) 224 224.3
Krypton Fluoride (KrF, Excimer-UV) 248 248.4
Neon-Copper Ion (NeCu+) 249 248.6
Frequency Quadrupled Nd:YLF (UV) 262
Frequency Quadrupled Nd:YAG (UV) 266
Xenon Chloride (XeCl, Excimer-UV) 308 308.17
Helium-Cadmium (HeCd, UV) 325 325.029
Nitrogen (N2, UV) 337 337.1 Multiple
Xenon Fluoride (XeF, Excimer-UV) 351 351
Frequency Tripled Nd:YAG (NUV) 349
Frequency Tripled Nd:YLF (NUV) 351
Frequency Tripled Nd:YLF (NUV) 355
Calcium Vapor Ion (NUV) 374 373.690
Gallium Nitride (GaN, NUV to violet) 400-410 -
Gallium Nitride (GaN, violet-blue to blue) 430-445 -
Strontium Vapor Ion (violet) 431 430.544
Helium-Cadmium (HeCd, violet-blue) 442 441.565
Frequency Doubled Nd:YVO4 (blue) 457
Frequency Doubled Nd:YAG (blue) 473
Krypton Ion (Kr+, blue) 476 476.243
Argon Ion (Ar+, green-blue) 488 487.986
Xenon Ion (Xe+, green-blue) 499
Copper Vapor (Cu, green) 510 510.554
Argon Ion (Ar+, green) 514 514.532
Krypton Ion (Kr+, green) 520.8
Xenon Ion (Xe+, green) 526 526.012
Krypton Ion (Kr+, green) 530.8
Frequency Doubled Nd:YLF (green) 523
Frequency Doubled Nd:YLF (green) 527
Frequency Doubled Nd:YVO4 (green) 532
Frequency Doubled Nd:YAG (green) 532
Xenon Ion (Xe+, green) 542 541.915
Helium-Neon (HeNe, green) 543 543.5161
Frequency Doubled Nd:YAG (yellow-green) 561
Helium-Mercury (HeHg, green) 567 567.717
Krypton Ion (Kr+, yellow-green) 568 568.188
Copper Vapor (Cu, yellow) 578 578.213
Sum Frequency Nd:YVO4 (1342+1064, yellow) 593
Helium-Neon (HeNe, yellow) 594 594.09633
Helium-Neon (HeNe, orange) 612 611.97087
Helium-Mercury (HeHg, red-orange) 615 614.947
Gold Vapor (Au, orange-red) 627 627.8170
Helium-Neon (HeNe, orange-red) 633 632.81646
Krypton Ion (Kr+, red) 647 647.088
Alexandrite (red-NIR) 655-860 (8)
Gallium Aluminum Arsenide (GaAlAs, red to NIR) 670-830
Titanium:Sapphire (Ti:Sapphire, red to NIR) 675-1,100 -
Chromium:Sapphire (Ruby, Cr:AlO3, red) 694 694.3
Chromium:LiCaF (Cr:CaF, NIR) 720-840
Chromium:LiSAF (Cr:LiSrAlF6, NIR) 780-920
Chromium:LiSGaF (Cr:LiSGaF, NIR) 820
Gallium Arsenide (Gaas, NIR) 840
Neodymium:YVO4 (Nd:YV04, NIR) 914
Neodymium:YAG (Nd:YAG, NIR) 946 946
Ytterbium:KGW (Yb:KGW, NIR) 1,026-1,024 -
Ytterbium:YAG (Yb:YAG, NIR) 1,031 1,029.6
Neodymium:YLF (Nd:YLF, NIR) 1,047
Neodymium:YLF (Nd:YLF, NIR) 1,053 1,053
Neodymium,Chromium:GSGG (Nd,Cr:GSGG, NIR) 1,061 1,061
Neodymium:Glass (Nd:Glass, silica glass, NIR) 1,062
Neodymium:LSB (Nd:LSB, NIR) 1,062 1,062
Neodymium,Chromium:LSB (Nd,Cr:LSB, NIR) 1,062
Neodymium:YAG (Nd:YAG, NIR) 1,064 1,064
Neodymium:YVO4 (Nd:YV04, NIR) 1,064 1,064
Neodymium:KGW (Nd:KGW, NIR) 1,067 1,067.2
Neodymium:YAG (Nd:YAG, NIR) 1,122
Helium-Neon (HeNe, NIR) 1,152 1,152.5900
Neodymium:YLF (Nd:YLF, NIR) 1,313
Neodymium:YAG (Nd:YAG, NIR) 1,319 1,318.7
Neodymium:YLF (Nd:YLF, NIR) 1,321
Neodymium:YVO4 (Nd:YVO4, NIR) 1,342 1,342.5
Erbium:Glass (NIR) 1,540 1,540
Thulium:YAG (Tm:YAG, MIR) 1870-2160 -
Thulium,Chromium:YAG (Tm,Cr:YAG, MIR) 2,013 2,013.2
Thulium:LuAG (Tm:LuAG, MIR) 2,020-2,030 (9)
Holmium,Thulium:YLF (Ho,Th:YLF, MIR) 2,047-2,059 (10)
Holmium:YLF (Ho:YLF, MIR) 2,060 2,050.5
Holmium,Chromium,Thulium:YAG (Ho,Cr,Th:YAG, MIR) 2,090 2,091
Holmium:YAG (Ho:YAG, MIR) 2,100 2,098
Hydrogen Fluoride (HF, MIR) 2,700 2,700
Erbium:YAG (Er:YAG, MIR) 2,940 2,940.3
Helium-Neon (HeNe, MIR) 3,391 3,391.2224
Deuterium Fluoride (DF, MIR) 3,600-4,200 (11)
Carbon Dioxide (CO2, FIR) (12) 9,600 9,600 Multiple
Carbon Dioxide (CO2, FIR) (12) 10,600 10,600 Multiple
Notes:
Skywise's Lasers and Optics Reference Section (also at: LaserFX Archives and Downloads) has a nice spectrum chart (visible and beyond) with annotation showing many of the common laser lines as well as an even more extensive list of laser types and wavelengths.
PEW-nm Dye Name PEW-nm Dye Name PEW-nm Dye Name
-----------------------------------------------------------------------------
330 BM-Terphenyl 491 Coumarin 6H 775 NCI
340 PTP 500 Coumarin 307 780 Methyl-DOTCI
350 TMQ 501 Coumarin 50 795 Styryl 11
357 BMQ 504 Coumarin 314 800 Rhodamine 800
359 DMQ 510 Coumarin 51 840 Styryl 9
360 Butyl-PBD 515 Coumarin 3 841 Styryl 9 (M)
364 PBD 521 Coumarin 334 863 IR 125
365 TMI 522 Coumarin 522 876 DTTCI
369 QUI 535 Coumarin 7 880 IR 144
370 PPO 536 Bril. Sulfaflavine 881 Styryl 15
372 PPF 537 Coumarin 6 885 DNTTCI
374 PQP 540 Coumarin 153 930 DDCI-4
378 BBD 552 Uranin 945 Styryl 14
380 Polyphenyl 1 553 Fluorescein 27 950 IR 132
381 Polyphenyl 2 555 Fluorol 7GA 994 Styryl 2D
386 BiBuQ 570 Rhodamine 110 1060 IR 25
390 Quinolon 390 575 Rhodamine 19
393 TBS 590 Rhodamine 6G
395 alpha-NPO 590.1 Rhodamine 6G (Perchlorate)
399 Furan 2 610 Rhodamine B
400 PBBO 610.1 Rhodamine B (Perchlorate)
409 DPS 620 Sulforhodamine B
410 Stilbene 1 640 Rhodamine 101
415 BBO 650 DCM
420 Stilbene 3 650.1 DCM-special
422 Carbostyryl 7 660 Sulforhodamine 101
423 POPOP 670 Cresyl Violet
424 Coumarin 4 675 Phenoxazone 9
425 Bis-MSB 690 Nile Blue
430 BBOT 695 Oxazine 4
435 Carbostyryl 3 700 Rhodamine 700
440 Coumarin 120 710 Pyridine 1
450 Coumarin 2 721 Oxazine 170
466 Coumarin 466 725 Oxazine 1
470 Coumarin 47 727 Oxazine 750
480 Coumarin 102 730 Pyridine 2
481 Coumarin 152A 750 Styryl 6
485 Coumarin 152 755 Styryl 8
490 Coumarin 151 771 Pyridine 4
Consider the lasing medium - for example, such as the 7:1 mixture of helium and neon used in a HeNe laser. If the gas mixture is excited by an electrical discharge, it will produce a bright line spectrum similar to what is shown in Bright Line Spectra of Helium and Neon. Each of the colored lines represents a particular energy level transition in helium or neon (separate in this case, the combined mixture will differ slightly). One might think that the brightest and thus strongest spectral lines are the most likely to result in laser action. This is not necessarily the case. For the HeNe case, *none* of the lines in the helium spectra contribute to the production of coherent light directly - the helium is used only to excite the neon atoms because a set of their upper energy levels match and electrical excitation of the He atoms with subsequent coupling of the energy to the Ne is much more effective than exciting the Ne atoms directly. And, even in the case of neon, only a few of the spectral lines are useful for a laser. In fact, for the red HeNe laser, the one that is important resulting in an output at 632.8 nm is quite weak compared to many of the others.
In order for a laser to lase, the round-trip Laser Resonator Gain (LRG) must start out being greater than 1 (see the section: Resonator Gain and Losses). Oscillations will then build up until non-linearities and finite pumping input bring LRG down to exactly 1. Where LRG starts out being less than 1, at best a weak pulse of light will be emitted as oscillations die out.
The fundamental characteristics of the laser determine whether the LRG greater than 1 condition will be met:
Also see the chapters: Helium-Neon Lasers and Argon/Krypton Ion Lasers for specific information on wavelength selection. For more details, some possibilities are a nice heavy book on laser physics or the On-line Introduction to Lasers.
The following discusses the first two methods while the next section deals with monochronometers.
All it takes is a piece of diffraction grating projecting the spot from the collimated laser onto a screen. The position of the spot will determine the wavelength. The cheapest diffraction grating will be good enough where you can compare the position against one using a laser of a known wavelength. See the section: Diffraction Gratings for the required equations. Basically, the ratio of the angles is equal to the ratio of the wavelengths for the same order spots with the approximation that for small theta, sin(theta)=theta. See the section: Use of a CD, CDROM, CD-R, or DVD Disc as a Diffraction Grating for sources of free diffraction gratings.
As an example, consider the problem of estimating the wavelength of a diode laser module with a HeNe laser as a reference. I had to do this when I obtained a couple of laser diodes (with collimating lenses and drivers) used in cheap laser pointers (LD-1). The claim was that they were 650 nm units but I don't trust claims! I also had a diode laser module from a piece of medical equipment (LD-2) to test. So, I set up a HeNe laser and the diode lasers shooting through my Kellogg's special diffraction grating (3-D glasses from a box of cereal!), taking care that they were all parallel to each other and perpendicular to the screen:
Laser X Y X/Y theta lambda
----------------------------------------------------
HeNe 74" 9.60" .12973 7.3917 Deg 632.8 nm
LD-1 74" 9.98" .13486 7.6808 Deg 657.6 nm
LD-2 74" 9.65" .13040 7.4298 Deg 636.1 mm
Where:
So, the wavelength of 657.6 nm is not quite what was claimed in the product blurb for LD-1! Or, maybe they just rounded down. :( I already knew that LD-2 was very close to the HeNe wavelength just by its color so 636.1 nm was no surprise.
As an additional bonus, the spacing, s, of the diffraction grating grooves was found to be 4.919 um based on: S=lambda/sin(Theta) for the first order spots - not a spectacularly small spacing but what do you expect with your Cheerios!.
Now, for another insomnia cure, consider how to determine the wavelength of a laser with just a Stanley ruler (machinist's scale)! This apparently was one of A. L. Schawlow's demonstration tricks so you should at least be able to duplicate the work of a Nobel prize winner. :) Give up? Here's a link: Interference Experiment Using a Ruler.
Also see the section: Monochronometers.
It turns out that iodine is an excellent choice for use as a wavelength reference because it has literally thousands of lines between 500 and 900 nm. (A Google Image search for "iodine spectrum" will turn up a variety of examples in various wavelength ranges.) In addition, iodine has a usable vapor pressure near room temperature so that it's a simple matter to pass a beam through it and detect the absorption or fluorescence that results when an iodine spectral line is excited. Much research has been done to measure the precise locations of these lines and with the large number of lines present, there's a good chance that at least a few will fall within the gain bandwidth of a specific laser, or close enough so that an a high speed optical modulator to create a sideband offset from the lasing line that can be locked to an iodine line. Many other materials may be used in a gas cell but iodine has a unique combination of desirable properties which seems to make it one of the most common.
An iodine gas absorption cell is a sealed tube with a small quantity of iodine inside under vacuum or with a buffer gas, with optical windows at both ends (Brewster angle or AR coated). A resistance heater may be wrapped around the tube to adjust the temperature and thus vapor pressure of the iodine vapor. This affects both the sensitivity (depth of absorption) as well as the width of the individual spectral lines. A photodetector may be mounted on the side to measure any fluorescence that is produced.
An example of a device with Brewster windows intended to be used inside a laser cavity is shown in Iodine Absorption Cell Showing Fluorescence From Green HeNe Laser Beam. It was found in a resonator assembly that appears to be the remains of an iodine stabilized HeNe laser. The glow in the photo was the response from a 3 mW random polarized laser at 543.5 nm. Not being linearly polarized, there were noticeable reflections from the Brewster windows. The fluorescence being longer wavelength than the input, appears more yellow than the green input beam and its reflections. The fluorescence includes wavelengths from green to red, and possibly near IR. The connector visible at the bottom of the photo is for the side-mounted photodetector. A connector on the other side is for the heater and temperature sensor.
Iodine and other gas absorption cells are available from many suppliers including ISSI, Opthos Instruments, Newport, Sacher Lasertechnik, Triad Technologies, and others.
Constructing an iodine absorption cell is straightforward in principle, but there are issues with the handling of iodine and preventing backflow into the vacuum system.
For stabilizing a laser, the iodine cell may be installed inside the laser cavity or in the output beam. The advantages of an intracavity cell is the increase in sensitivity resulting from the high circulating optical power. But for very low gain lasers, this may not be practical. And, where an iodine line doesn't fall within the gain bandwidth of the laser, addition components like an AOM or EOM must also be present.
Iodine stabilized HeNe (632.8 nm, 543.5 nm), Argon ion (514.5 nm), DPSS (532 nm), and many other lasers are commercially available. Countless systems incorporating iodine stabilization have been built as part of basic and applied research programs.
References
The following comments were prompted by an external mirror HeNe tube (with Brewster windows) which was labeled: 3He, 22Ne, 2.8 (this I assume was the pressure in Torr but don't know for sure). The common isotopes of He and Ne are 4He and 20Ne respectively. My best guess as to the purpose of this otherwise unmarked tube was that it was manufacturered for someone's thesis project - probably with a title like: "Determination of How Lasing Spectral Characteristics are Affected by Gas Isotope". :)
However, there is a reference to using the isotope ratio to advantage in green HeNe laser tubes so perhaps that is what this was supposed to be. See the section: Steve's Comments on Other Color HeNe Lasers.
Also see the section: Comments on the Funny Two-Brewster HeNe Tube.
(From: Don Klipstein (Don@Misty.com).)
The spectral differences between isotopes are negligible. Even between 1H and 2H (heavy hydrogen, approximately twice the mass of normal hydrogen), the spectrums are quite similar!
How isotopes can make differences:
As for 22Ne? I don't know about that one. The wavelengths of the lines will be different by only a fraction of an angstrom. Maybe heavier Ne atoms have a slightly higher tendency to get excited instead of picking up kinetic energy when hit by excited He atoms. I wonder how much difference this makes or even if it is a gimmick.
I don't expect to see much intensity difference of lines in single-element lamps by using different isotopes. Unless you half/double the molecular weight in the case of hydrogen or maybe a little different between 3He and 4He. I think tubes of 20Ne and 22Ne should have negligible differences.
There is an effect in some fluorescent lamps that is worse with single-isotope than multi-isotope. One thing that happens is that Hg atoms absorb their own 253.7 nm UV. Typically, a 253.7 nm photon gets absorbed and re-emitted several times until it finally escapes the mercury vapor (or a mercury atom loses the energy in some way other than re-emitting that 253.7 nm photon). This phenomenon is known as "imprisonment". It gets worse of there is too much mercury vapor. Imprisonment of 253.7 nm is worse with single isotope mercury than multi isotope mercury (naturally occurring mercury). Different isotopes mostly absorb only their own radiation, so each isotope-specific line has only mercury atoms of its own isotope to imprison it instead of all the mercury atoms.
One thing I tried: Putting a magnet against a fluorescent tube. Zeeman splitting would smear the lines and any wavelength would have fewer mercury atoms in the way to absorb it. My personal results: Only sometimes seems to work. It seems to work less on compact fluorescents.
I recently was trying to explain to a friend who wanted to know why when discussing the topic of "light" we use the word wavelength versus frequency. I gave the fellow a number of answers why wavelength would be a better term... However, I decided that I didn't even like the way I phrased my own answers and am not even sure if there is an ironclad definitive reason...
Seems to be more a matter of tradition and maybe convenience than anything else.
(From: Brian Vanderkolk (skywise711@earthlink.net).)
I think it's more a matter of convenience. The frequency of light is pretty high. I think most of us find it easier to say 632.8 nanometers instead of 473755464601800 Hertz. Even if you wanted to round that out a bit and use scientific notation to use 4.7375546E14, you're introducing more error than what you have by using the actual wavelength. 632.9 nm would be 4.736006E14, a pretty significant change in frequency.
(From: H. Peter Anvin (hpa@transmeta.com).)
Actually, you can only use as many significant digits in the output as in the input. You're taking a number with four significant digits (wavelength) and putting out numbers with seven or eight -- if that was truly justified then you would have written 632.80000 nm. You could just as well say 473.8 THz (1 THz = 1012 Hz) as you would 632.8 nm; 632.9 nm would be 473.7 THz.
Not to mention that the frequency, unlike the wavelength, is independent of the propagation medium. Above I am assuming you're referring to wavelength in a vacuum (the speed of light in a vacuum is 299792458 m/s exactly.)
(Much of the following is from: Don Klipstein (don@misty.com).)
Note: In the table below, the entry under 'Color' attempts to describe the actual appearance while the color listed under 'Typical Source/Application' is what you are likely to see in a laser catalog.
(Portions of the following from: Don Klipstein (don@Misty.com).)
Wavelength Response Color Typical Source/Application
-------------------------------------------------------------------------------
350 nm .00001? UV
380 nm .0002 Near UV
400 nm .0028 Border UV Nichia violet GaN laser diode
410 nm .0074 " "
420 nm .0175 Violet
442 nm .0398 Violet-blue Violet-blue line of HeCd laser
450 nm .0468 Blue
457.5 nm .0556 " Blue frequency doubled Nd:YVO4
457.9 nm .0562 " Blue line of argon ion laser
473 nm .104 " Blue frequency doubled Nd:YAG
488 nm .191 Green-blue Green-blue line of argon ion laser
500 nm .323 Blue-green
510 nm .503 Green Emerald green line of copper vapor laser
514.5 nm .588 " Green line of argon ion laser
532 nm .885 " Green frequency doubled Nd:YAG or Nd:YVO4
543.5 nm .974 " Green HeNe laser
550 nm .995 Yellow-green
555 nm 1.000 " Reference (peak) wavelength
567 nm .969 " Green line of Helium-Mercury laser
568 nm .964 " Y-G line of some krypton ion lasers
578 nm .889 Yellow Gold line of copper vapor laser
580 nm .870 "
594.1 nm .706 Orange-yellow Yellow HeNe laser
600 nm .631 Orange
611.9 nm .479 Red-orange Orange HeNe laser
615 nm .441 " Orange line of Helium-Mercury laser
627 nm .298 " Orange line of Gold Vapor Laser
632.8 nm .237 Orange-red Red HeNe laser
635 nm .217 " Laser diode (DVD, newer laser pointers)
640 nm .175 " "
645 nm .138 " "
647.1 nm .125 Red Red line of krypton or Ar/Kr ion laser
650 nm .107 " Laser diode (DVD, newer laser pointers)
655 nm .082 " Laser diode
660 nm .061 " "
670 nm .032 " Laser diode (UPC scanners, old pointers)
680 nm .017 "
685 nm .0119 Deep red
690 nm .0082 "
694.3 nm .006 " Ruby laser
700 nm .0041 Border IR
750 nm .00012 Near IR
780 nm .000015 " CD player/CDROM/LaserDisc laser diode
800 nm 3.7*10-6 " Laser diodes for pumping Nd:YAG, Nd:YVO4
850 nm 1.1*10-7 "
900 nm 3.2*10-9 "
1,064 nm 3*10-14 " Nd lasers (including YAG)
1,523.1 nm 0.0000 " IR HeNe laser
3,390 nm 0.0000 Mid-IR IR HeNe laser
10,600 nm 0.0000 Far-IR CO2 laser
This is according to the 1988 C.I.E. Photopic Luminous Efficiency Function. A plot of these data may be found in Response of Human Eye Versus Wavelength. The C.I.E. (Committee Internationale d'Eclairage) may also be known by other initials indicating the English translation (ICI for "International Commission on Illumination").
A variety of information on color perception including many charts, tables, references, and links, can be found at the Color and Vision Research Laboratories of the University of California, San Diego. However, the corresponding table at this site is the older 1931 version. In 1988 C.I.E. updated the Photopic Luminous Efficiency Function because the 1931 function did not sufficiently weight the higher blue response of young people.
For all intents and purposes, wavelengths beyond 1,000 nm are absolutely and totally invisible - period! In other words, the only time you will see them is for about a microsecond before your eyeballs, your head, or you in the entirety is vaporized due to the high power required. However, the exact cutoff will depend on the specific model and revision level of your eyeballs. Consult factory for details. :) I (Sam) can see beyond 870 nm but it is very very faint and I can't detect anything at 980 nm.
Note that wavelengths from around 460 through the low 500's can be more visible in dim environments than indicated by the C.I.E. 'Y' function due to scotopic vision. Scotopic vision peaks in the 500 to 515 nm range, and the ratio of scotopic to photopic is maximized in these and somewhat lower wavelengths down through around 460.
In addition scotopic vision can be very significant even at brightnesses high enough to permit some color vision. Some preliminary data that I have indicate some significance of scotopic vision at up to 100 to 200 lux for viewing more than about 3 degrees off the axis of the eye. This is lower ranges of ordinary room lighting.
Also see the sections: Spectra of Visible and IR Laser Diodes and Visibility of Near-IR (NIR) Laser Diodes.
Faintly seeing a beam in the air in a dark room is something scotopic vision helps with. Scotopic vision is less important, usually downright insignificant in judging the brightness of bright spots on a wall.
Scotopic vision, A.K.A. "Night Vision" is more favored in dimmer environments, more favored in off-center vision and less favored in the central couple degrees of vision, and more favorable to shorter wavelengths than photopic vision is.
If a red laser and a green one made spots on a white wall that looked equally bright, the green one has a beam that is more visible from the side in a dark room than the red one makes.
Note: To assure that these spectra appear anywhere near correct on your system, make sure the monitor is adjusted properly for white highlights (bright areas). The actual number of available colors, and how close they are to what they should be, will also depend on the color depth setting of your video card (and the mapping in effect if less than 24 bit true color). For Windows 95/98, check and set by going to Display from the Control Panel or by right-clicking on the desktop, then to Properties. Under Settings, selecting True Color (24 bit) or higher for the Colors option will result in optimal appearance.
I am still looking for the 'perfect' rendering of the visible continuous spectrum. If you know of anything on-line, or have one to offer, or can get those programs to work, and believe yours is better, please send me mail via the Sci.Electronics.Repair FAQ Email Links Page.
The color as normally perceived by the Mark-I eyeball and brain appears to be reasonably accurate in this image. However, the brightness does not vary correctly with respect to wavelength. Nonetheless, this spectrum can be used to provide a general idea of how any given visible laser line should appear.
(From: Brian Vanderkolk (skywise711@earthlink.net).)
The idea of making an accurate image of the visible spectrum is something I've been trying to do for some time. Actually what I was wanting to do was come up with an algorithm for converting nm to rgb values. I've gotten a hold of CIE chromaticity lists and response curves, like the one referenced in the section: Relative Visibility of Light at Various Wavelengths FAQ for relative brightness of lasers. That taught me some stuff about color theory that just never occured to me.
I had even run across one Web site that had a small GIF format image of the spectrum that was calculated totally from chromaticity coordinates and supposedly corrected for monitor gamma. To put it simply, it was terrible. The red end tends towards pink before fading and the violet end is almost non-existent.
Of course, it's impossible to do this perfectly given the variability of phosphors - and eyeballs, but I think I came up with a pretty close rendition. The file spctrm2r.zip is a compressed BMP version of the original spectrum data used to make Visible Continuous Spectrum 2. It's 450 x 30, 24 bits, and has grey tick marks along the bottom denoting nanometers starting on the left at 350 nm and goes up to 800 nm on the right at 1 pixel/nm (in spctrm2r.bmp, 2 pixels/nm in the annotated image, spctrm2.jpg). Tick marks are on 2, 10, 50, and 100 nm points.
I had a lot of trouble with the cyan and especially violet parts. I was using a flashlight with a slitted cover and a diffraction grating to help me compare something real to what I was drawing. It was really noticable how deficient monitors are at making pure colors. Green is pretty close. The blue phosphors seem to be too broadbanded including greens and violets, and the red phosphor is really orange.
Anyway, the way I generated the image was using my favorite ray-tracing program (POVRay) because it has a really nice way of handling color maps. The program interpolates between specified points linearly but the way it's coded makes it a breeze to change values. So if you notice any colors that could use adjustment let me know how they should be changed and I can adjust the specified points or even add new ones.
I now have a spectrum chart (visible and beyond) with annotation showing many of the common laser lines at Lasers and Optics Reference Section of my Web site.
(From: Don Klipstein (don@misty.com).)
The file, spctrm3r.zip, is a compressed 600 x 64 x 24 bit BMP image going from 380 to 780 nm, or 2 nm per 3 pixels horizontally. I actually created it mathematically at first using the CIE X, Y, and Z curves, then added several modifications at a few different stages (mathematically and with a photo editor) to make it look as "correct" as I could.
(From: Sam.)
About the problem with purple. You say: "What problem with purple?". If you don't see a problem with purple in this spectrum image, don't worry about it. Or, if you do think there is not enough purple (which is what I had complained to Don about), we're working on it. :)
(From: Don.)
Now a strange bit of human vision...
The C.I.E. "standard observer" supposedly sees violet (400 nm region) as of being very close to the same hue as deep blue (440 to 450 nm region) if brightness is matched. I wonder if the tests done in color matching to generate these data were a bit flawed in the really short wavelengths?
I know that two of the three C.I.E. curves are known to not be really close to the red and green responses, but are supposedly linear combinations of red, green, and blue response. But I wonder if their "x" curve runs a few percent low below 425-430 nm?
Then again, my father seems to see as a "standard observer". He sees the 404.7 nm mercury line as being the same color as the 435.8 nm one if brightness is matched. The "standard observer" supposedly sees it this way. But everyone else in my family, including myself, see a big difference between these two lines even with brightness matched. At equally high apparent brightness, 435.8 nm looks an only slightly violet-ish blue to me and 404.7 nm is much purpler than that.
Now a little minor possibly interesting point: Purple refers to hues more red than anything in the short end of the visible spectrum and violet refers to hues that can be found in the short end of the spectrum. I wonder how the C.I.E. would handle that if violet is hardly different from blue?
Another little thing.... At times I have seen the 365-366 nm mercury line cluster. This needs a dilated pupil and isolation from the more visible wavelengths. The central part of the lens of the eye blocks UV more than the edges of the lens do. This wavelength looks more blue than violet to me, with a hue about matching 425, maybe 430 nm. Maximum purplishness seems to be in the 390's to around 400 nm.
Depending on what question is really being asked, their is probably no answer.
If you want to calculate what mixture of RGB light is necessary to give exactly the same colour as some single-frequency light of a particular wavelength, it's not possible, unless the colour you are trying to reproduce is identical to one of the three RGB primaries you are using.
Even if you start with pure single-frequency red, green, and blue (e.g. from lasers), any mixture of these three colours will not be as saturated as a pure spectral colour. For example, you can mix single-frequency red and single-frequency green to get a range of hues of yellow, but you cannot get the pure saturated yellow of a sodium flame.
If you're happy matching only the *hue* of the colours, while allowing the saturation to be less, then you can "match" most pure spectral colours in this sense. Even then, nobody can give you a table of the results, since the answer depends on exactly *what* red, green, and blue primary colours you are mixing.
The actual solution ends up being a rather simple bit of linear math, but you really should look at a book talking about simple colour theory in order to understand what's going on before you try it.
Laser diodes have only been able to produce red and infrared beams so far (at least commercially). There have been some research reports of green and possibly blue laser diodes but only operating in pulse mode, at reduced temperature, and/or with very limited lifetime. This will no doubt change as enormous incentives exist to develop shorter wavelength laser diodes numerous applications.
The green lasers you see are either argon or frequency-doubled Nd:YAG (neodymium doped yittrium-aluminum-garnet). The argon laser is a very large and complex device, almost always putting out hundreds of times the power of your pointer. A Nd:YAG laser is usually even more powerful, but is often pulsed. Diode lasers are not used in laser light shows because they are never powerful enough. I am sitting here typing this while allowing my 15 mW Helium-Neon laser to stabilize and warm up. Its wavelength is shorter, and it is 3 times more powerful than the pointer. When a red beam is needed in a laser light show, these are usually used because they are usually more powerful than diodes, and the beam is more visible per milliwatt because of it's shorter wavelength. Happy Lasing, and be sure to visit alt.lasers for any laser info you need!
No, it's not because of the inverse square law as then it would just gradually diminish in intensity) or the geometry of perspective. Nor is it due to differences in the major layers of the Earth's atmosphere.
But there is something called the "Planetary Boundary Layer" which is the lowest part of the Troposphere (where we live). The thickness of the Planetary Boundary Layer varies from a few hundred to a few thousand meters, which is very thin compared to the thickness of the whole Troposphere.
For more info on this topic, see RASC Calgary Centre - The Atmosphere, Astronomy and Green Lasers.
(Portions from: Mike Goodnight.)
Laser pointers do one thing only, but they do it very well. They point! Since the availability of inexpensive green Pointers, more and more astronomers are adding the device to their accessory case. Green pointers are especially useful due to their inherent brightness at low wattage to the human eye.
While trying to find DSO's (Deep Sky Objects) at a recent star party, I frequently asked a fellow viewer to point out an object for me to find with my telescope. The easiest way was with a laser pointer. He/she would aim their pointer to an object in the sky that was between two bright stars. Easy enough, just point the finder scope at the spot where he pointed the laser and look for two bright stars. Problem being, when you look through the finder scope, there are now twenty bright stars. Which two was he aiming for? I got into the habit of asking the person to aim their pointer while I used the finder scope to follow the laser down to the target area. Worked like a charm and I bagged 8 DSO's in the period of an hour. Simple things like the Ring Nebula, Owl Nebula, M31 and so on. The other issue is the person holding the pointer has their own list of objects they want to explore. Besides, you will find yourself stargazing a lot on your own.
I have good eye-hand coordination but pointing to an object field while looking through the finder scope is a lot to ask. Why not shine the pointer down the finder scope? That works really well as long as you do not need to move the scope at the same time.
So Sam comes up with this device that holds the pointer on the finder scope's eyepiece hands free. Version 1.0 is basically just a cheap green laser pointer modified with a thumb screw switch in the rear end-cap to enable continuous operation. (The push-button switch is taped in the ON position.) It is attached to the finder's eyepiece with a suitable set of Home-Depot plastic plumbing fittings and shims. For a right-angle finder, a press fit is probably adequate. For a straight finder, a hose clamp may be desirable to provide the snug fit.
The only problem is that since as a result of the way the finder's optics work, the pointer beam ends up being focused at the very center of the optical axis at the exact location where the cross-hairs intersect, it has to be positioned just a wee bit off axis to bypass this point. So, perhaps, the cross-hairs could be modified with a tiny ring leaving the very center open.
Version 1.1 will use a separate battery pack to reduce the mass and length of the entire assembly (which is prone to being accidentally knocked out of position.
I am now at liberty to move the scope while following the laser beam that is aligned with the OTA's (Optical Tube Assembly) finder scope. The device is easily slipped on and off of the finder scope's eyepiece. Tried this on Jupiter because it is bright and easily identifiable even in my light polluted surroundings. Aimed the laser beam at Jupiter and then removed the device from the finder. Bingo, Jupiter was near dead center in the crosshairs. Perfect.
If you are lucky enough to have access to a green laser pointer (or green or blue or UV laser), try shining it on various paints, glass, plastic, fluids, etc. The effects will be interesting. One example I've found that might not be expected is a piece of red plastic (from in front of the modem or VCR display or something). This *totally* blocks the beam from a green laser pointer (not a single green photon gets through) but also results in a very pretty red fluorescence glow.
For some other experiments, I used the HR mirror from a defunct green (543.5 nm) HeNe laser tube as a filter to view the fluorescence without the bright green light masking it. This mirror blocks better than 99.99 percent of the green light at 532 nm while passing light from yellow through red with only modest attenuation.
Based on informal experiments using a green laser pointer, most common materials do fluoresce from a 532 nm beam with a yellow-orange appearance. The power of the fluorescence is around 0.1 to 1 percent of incident power. For a material designed specifically with fluorescent properties, the effect is much more dramatic. In another experiment, I used a C315M-100 DPSS laser rather than a laser pointer because it is more stable and has higher power (same 532 nm wavelength but 100 mW) shining on a piece of cardboard with what looks like a red DayGlow(tm) coating though I have no idea what it actually is. The fluorescence from this material was perceived as an orange which I'd guess to be equivalent to around 620 nm. However, it was actually a band of wavelengths from yellow-green to red (as determined using an AOL CD as a diffraction grating). I estimate the power of the fluorescence to be between 10 and 25 percent of the power of the incident beam, based on appearance and monitoring the reflected power with a light meter. The reflected green light was probably down to below 25 percent of the incident power. Interestingly, the coating material, whatever it might be, was easily damaged from the 100 mW beam, much more readily than similar colored paper that didn't fluoresce as strongly. The initial effect was for it to darken but if left in the beam, the coating disappeared entirely revealing the white paper underneath.
If you shine the beam of, say, a 20 mW argon ion laser through various bottles of spirits - and other fluids - that are more or less yellow/orange in color, the beam shows up as a very dim YELLOW beam while going through the fluid - though any emerging beam is still green. Thus, this is not changing the wavelength but is a fluorescence phenomenon. Anti-freeze and actual laser dyes should work quite well
(From: Steve Roberts: (osteven@akrobiz.com).)
You're seeing side glow from good old fluorescence, try a few drops of merthiolate or the red dye used in maraschino cherries. Many of the same UV excited fluorescent materials will glow from your 532 nm green. Just don't expect to see that much activity from blue or green glowing materials, as the pump wavelength must be shorter then the emitted wavelength. Find a fluorescent orange warning sticker - you will be very impressed with your "white" dot. I used to cheat and use a fluorescent orange sheet as a projection screen for my 20 mW argon, before I had a bigger laser. It made a nice "poor man's whitelight" display.
(From: Frank Roberts (Frank_Roberts@klru.pbs.org).)
I have seen a similar effect with my ALC-68C argon ion laser when shooting the beam through a glass prism. Evidently, the glass in this particular prism is strongly fluorescent since the beam path through the glass shows as a strong reddish-orange line. The color of the exiting beam seems to be a bit "bluer" than the blue-green beam entering the glass. I would take this as a sign that some of the 488 nm blue line from the laser is being absorbed and causing the glass to fluoresce strongly in the red. I have also seen solutions of rhodamine fluoresce so strongly that the beam path through the solution appears white, obviously a mixture of the blue and green lines of the laser and the red fluorescence of the dye.
"I have one of those $300 green laser pointers. When shined at certain materials, especially fluorescent colored paper/cloth/plastic, the spot changes color from green to yellow, orange, red, or somewhere in between. It's a very drastic color change, and the light reflected off of the surface is this color as well."
This is a fluorescence phenomenon, basically the same as in the previous section. The output of those green laser pointers is quite monochromatic at 532 nm and the IR of the pump diode and Nd:YAG or Nd:YVO4 crystal should be blocked by a filter. (See the section: Diode Pumped Solid State Lasers for info on how these lasers work though this has no direct bearing on the effects being described - any laser with a similar output wavelength would do the same.) Put their beam through a diffraction grating or prism or reflect off a mirror or other non-fluorescent surface and only the original 532 nm green wavelength will be present.
So, your fluorescent colored paper or whatever is absorbing the 532 nm photons and reemitting photons at a lower energy. However, there is no actual beam being reflected, only a diffuse incoherent glow. When viewing that glow through a filter that blocks the original laser wavelength (e.g., 532 nm), your first reaction may be to think the color of the fluorescence is actually in the incident beam but that is not the case. It's only because the fluorescence and incident beam are shining on the same spot.
Next, someone will claim that you can get DayGlow(tm) paper to lase by sticking a piece between a couple of shaving mirrors. :)
(From: William Smith (frostybeard@hotmail.com).)
You can see a lot of this effect also using a blue LED. (Bright blue LED key chains are available everywhere.) Fluorescent (so-called neon) materials fluoresce quite brilliantly in the almost monochromatic blue light. It also causes phosphorescent items (key chains and such) to glow.
"I pointed a laser pointer at a glow in a dark EXIT sign. Where the light was a dark spot formed on the sign. Why is this?? It seems like the laser light stops the glow in the dark. This was your average EXIT sign above the door at work. We also shined a flashlight on the sign while we were doing this and were still able to see the dark spot only not as bright. I have tried it with other Glow In-The Dark items and I get the same thing.
Similar effects can be demonstrated with other fluorescent materials including the phosphors in some CRTs and fluorescent lamps. However, photons of sufficient energy are required for this effect - putting the sign in a microwave oven won't do it. :)
(From: Steve Roberts (steven@akrobiz.com).)
You're either depleting the trapped or stored electrons in the upper levels of the material that emits the light by causing it to speed up with the red stimulation or you're moving them to a point where they don't fall down and emit a visible photon but fall to another non radiating transition. Who makes the sign? I want one! :-)
(From: Stephen (stephmon@aol.com).)
The phosphorescent material absorbs light energy and releases it very slowly. The efficiency of absorption to emission varies with the wavelength (color) of the incoming light. If you shine blue light on it, you get a moderate amount back. If you shine green light on it, you get a stronger reaction. If you work your way through the spectrum and measure the reaction, you will be plotting a curve, that peaks near green. At the red end of the spectrum, you get minimal return, while accelerating the emission process.
In short, you are speeding the release of light energy from the phosphorescent material, while contributing almost nothing to the absorption of energy. This causes the area in your pointer beam to fall below the energy levels of the surrounding material and appear darker.
(From: Terry Greene (xray@cstel.net).)
Stimulated emission. At the risk of serious oversimplification: When the wave front or photon packet (however you prefer to look at it) passes an atom that is above ground state (as would be the case with a phosphorescing material) it can take the energy with it and leave the electrons in a lower (ground state) energy orbit. Same principle that makes lasers lase.
(From: Tim & Vironique (tvkas@prodigy.net).)
OK. I'll buy that. But what is it about the red light that speeds the release of energy??? I can see that the red light would not be at a frequency that contributes energy. But if the sign is already glowing and you shine the laser on it, where the laser spot was, the glowing has stopped. You could draw a picture. How does the laser (or the frequency spectrum ) take away more energy. How does it speed up the process?
(From: Stephen (stephmon@aol.com).)
Stimulated emission occurs when a photon strikes an 'excited' atom and causes it to drop back to its ground state. This happens at all of the wavelengths, but at the 'greener' wavelengths, the 'give' (excitation) outweighs the 'take' (emission).
I've done some animated GIFs about stimulated emission (as they relate to lasers) at Stephen's Web Site under How'zit Work?: Laser Light.
(From: William Buchman (billyfish@aol.com).)
Stimulated emission occurs when a photon strikes an 'excited' atom and causes it to drop back to its ground state. This happens at all of the wavelengths, but at the 'greener' wavelengths, the 'give' (excitation) outweighs the 'take' (emission).
The key to answering this question is what is known as a metastable state. These are states above the ground state that energetically would decay but the time to do so is long. The incident radiation, red light in this case, excite a higher energy level from which decay is faster. The limitation is from a selection rule on angular momentum.
Think of a metasable state as being a local depression in a hill where something can get stuck. If it could just get nudged over the lip, it could roll a long way down. The light nudges.
(From: Stephen (stephmon@aol.com).)
I like this analogy, with one caveat. Rolling down a hill is a very un-quantum-like activity for an electron to engage in. But, such are the pitfalls of trying to draw metaphors for particle physics, from a Newtonian world.
A pulsed laser is generally used since it can be quite small (a fraction of a joule) and doesn't need to be held steady while the beam melts the balloon. Depending on pulse energy, focusing may be required and then the balloons will have to be within some range of distances from the laser. There will also be a range of pulse energies over which the 'trick' will be successful since all materials will absorb some light! Too much energy and both balloons will burst. Too little and neither will be affected.
Here are some options:
The extension to more than two balloons should be obvious. :)
Note that the effect exists equally strongly whether you are focused on the surface or not. Where the laser spot is large compared to the speckle pattern, the direction and speed of movement of the pattern will be affected by whether you are focused in front (opposite direction, nearsighted) or behind (same direction, farsighted). However, if you are far enough away to not resolve structure inside the spot, you get one big speckle which will get brighter or darker without appearing to move.
Sources with high spatial and temporal coherence properties like gas lasers should produce the most spectacular speckle effects. However, since speckle is a result of small path-length differences, it is really the short term coherence that matters which is the reason there will still be very visible speckle effects from even common diode laser based laser pointers though how dramatic these are may vary from one model to another. Even their coherence length - which for some types may be a fraction of a millimeter - is large compared to surface roughness. (However, some types of laser diodes actually have coherence lengths better than typical gas lasers.) The existence of a noticeable speckle effect is one indication that the source is a true laser and not just a light bulb or LED. :) Also see the section: Laser Speckle from Laser Pointer and Candle?.
For those applications where the laser's bright light and its ability to be sharply focused or easily collimated are important but coherence is irrelevant, speckle is an undesirable side effect to be avoided. See the section: Controlling Laser Speckle.
(From: Mike Poulton (tjpoulton@aol.com).)
Laser speckle, usually called the interference pattern, has nothing to do with your eyes and has no bearing on how well you can see as it is a real phenomenon. Laser light is completely monochromatic and is also in phase. When this light is scattered, it gets out of phase and the waves collide. When a wave at a low point and a wave at a high point collide, they cancel each other out (just like those noise-reduction machines that send out ambient sound 180 degrees out of phase, except this is with light). Where the light cancels itself out, there is a dark space, where it does not, there is a light space. This creates a three-dimensional lattice-work of light and dark spaces.
As you move around it, you see different parts of the lattice and your view appears to move. The more "saturated" the area is with light, the more impressive this effect is. I have a 15 mW Helium-Neon laser, and its effect is incredible. To say that this is in your head is like saying that it is an optical illusion when you look at different sides of a house. One cool thing to try is shining the laser into flood light (while it is turned off). The reflective coating on the inside of the bulb makes this effect very intense.
(From: Zane (zanekurz@ix.netcom.com).)
There's really nothing mysterious about speckle. Each "pixel" of your camera (or receptor of your retina) images a reflecting area with dimension larger than the wavelength. If the surface roughness (in the range dimension) is larger than a wavelength, the optical phase of each reflecting area (pixel) is the phase of the sum of a large number of point sources (within the pixel) at random distances from the sensor. This produces a random phase at the detector. Since the phase is in the argument of a sine function, the resulting measured power is random with a Rayleigh distribution. So each pixel has a random power and appears as speckle.
If the illumination stays the same and each pixel images the same rough area, the speckle pattern will not change. BTW, radar "fading" is an exact analog of this. The well-known "Swerling 2" radar statistics is just speckle at longer wavelengths, with only one spatial sample at a time. It results from illuminating an object where the reflecting points are distributed in range randomly with a depth larger than the wavelength (e.g. tail surfaces of a airplane summed with body and wing surfaces).
"I noticed an interesting animation effect when a laser pointer was pressed against the bottom of a red candle. While viewing through good reading glasses, the side surface of the candle was literally swimming with sharp grainy dots like a bad motion picture show. I've since observed these micro animations when illuminating other translucent objects, i.e., a white candle and white glass."This is most likely a form of laser speckle due to interference from the coherent light source. In the case of a translucent object like a candle, the wax as well as unavoidable motion of the pointer, candle, glasses, and observer, results in varying path lengths and refractive effects which produce constructive and destructive interference at the retina of the eye - thus the constantly changing pattern of bright and dark spots. A camera would also record the effect though the specific pattern and size of the dots would not be the same due to the different optics involved.
(From: J. B. Mitchell (ugez574@alpha.qmw.ac.uk).)
Speckle noise arises because of the highly coherent nature of the laser light and can thus be reduced or eliminated by reducing the coherence of the source. One easy way of achieving this is by introducing a rotating ground-glass screen into the beam. Placing the ground glass at the focus of the beam reduces the temporal coherence by introducing random phase variations while maintaining the spatial coherence (ability for the beam to be focused to a point). Putting the ground glass in an unfocussed beam reduces both the temporal and spatial coherence.
Alternatively, if you need to maintain the coherence for your application (interferometry, for example) the you can reduce the size of the speckles by increasing the aperture of the imaging system.
(From: Steve McGrew (stevem@comtch.iea.com).)
I know of three ways:
(From: Guy Mark Tibbert (gmt@weirdness.com).)
You can always use a pair of lenses, one to focus the beam down, then pass it through a pinhole and then another lens to bring it back to a co-linear beam. The pinhole method is crude but DOES reduce speckle quite well enough for most applications. You will need to experiment with the pinhole diameter for the best results. Obviously the material you make the pinhole from will need to depend on the power of the laser and the durability of the finished article.
(From: William Buchman (billyfish@aol.com).)
The easiest way, for me, to explain speckle is in terms of microwave antenna analogy:
As you view a wall or similar object illuminated by a laser, limited resolution of the eye prevents you from seeing detail in the illuminated area. Suppose the spot is small. Then that spot is not resolvable. Nevertheless, it may be many wavelengths across. Thus, if the surface is rough, the complex amplitude across the spot is random in phase. This is the equivalent of an antenna with random phase. The pattern it produces has sharp sidelobes but they point in various directions, just like a randomly illuminated aperture.
If your eye is at peak of a sidelobe, the spot will look bright. If it falls in a null, you do not see the spot at all. And you have all the intermediated conditions.
A big spot on the wall consists of many resolvable areas, each the equivalent of a randomly illuminated aperture. Your eye is in the peak for some and the null of others. Therefore: Speckle!
(From: Richard Migliaccio (rmigliaccio@home.com).)
I can't cover all aspects of the subject but have some points of view I'd like to share.
The speckle is in this case is due to the reflections of the laser off of rough surfaces in the area. The reflections that arrive at the camera sensor create an interference pattern in the image plane, hence the speckle. The amplitude and size of the speckles are mainly dependent on the speed and resolution of the camera system.
Speckle can be reduced in this case by:
Another, more basic approach is to re-address the requirement for a laser. Could the application use LED's or filtered broadband light?
A more complete solution which may allow the use of a laser is to first image the scene on a rotating disk with a "rough" surface, and re-imaging that on the camera sensor. The rotating disk would ideally rotate fast enough to blur the pattern out in a 30 millisecond frame rate, but can also be beneficial rotating at slower speeds, the speckle would appear as frame to frame white noise. Unfortunately, if the apparatus is being used to purposely monitor an interference pattern, i.e., an interferometer, this method would likely destroy that interference pattern too.
In general, speckle is a function of the:
Spatial coherence deals with how phase relationships of the waves that make up a laser (or LED, for that matter) beam change as a function of position and time and are determined by the physical length of the laser resonator, its longitudinal mode structure, and the laser's output bandwidth (these are all interrelated). The coherence length in wavelengths will be on the order of the center wavelength of the source divided by the width of its spectral output. Or equivalently, the frequency divided by the bandwidth.
Some examples:
(From: Daniel Marks (dmarks@uiuc.edu).)
There are really two coherences associated with any source; spatial and temporal coherence.
The temporal coherence is related to the bandwidth of the source. The more narrow the bandwidth of the source, the longer the coherence length. HeNe lasers have a very narrow bandwidth, as a result they have a coherence length on the order of 10-30 cm. LED's are incoherent sources, they only have a coherence length of 10-40 microns, and a large bandwidth of several kT (25.9 meV at 298K) or I'm guessing 10 nm of bandwidth (around about 650 nm). HeNe lasers are also much more spatially coherent than LEDs. The spatial coherence length is determined by the cavity and cavity reflectivity in a laser. LEDs also have a very short spatial coherence length, or only a couple of wavelengths.
The coherence length is the maximum distance at which two points in the field can be interfered with contrast. The temporal coherence length determines the maximum depth of the object in a reflection hologram, and the spatial coherence length determines the lateral size. Using techniques of "white light" interferometry, incoherence sources can be used, but they are tricky and have many restrictions on the kinds of holograms one can create.
(From: Don Stauffer (stauffer@htc.honeywell.com).)
First of all, I believe coherence is frequently thought of as a binary function - that is, a source is either coherent or it is NOT. Coherence can be quantified. Various lasers have varying coherence.
Spatial coherence refers to how spherical the wavefront is. Does EVERY portion of the wavefront appear to have EXACTLY the same center of curvature?
Temporal coherence involves how long a period in time does the source maintain a sinusoidal field with no phase modulation. A good example of the need for high temporal coherence is in coherent, or heterodyne, detection. In these systems, energy reflected off the target is mixed with energy from the original laser to create a fringe pattern. If the photons have not maintained a single frequency for the time needed to hit the target and return, the fringe pattern will not have sufficient quality, and the advantages of heterodyne detection go away.
Frequently such systems are used for Doppler velocity measurements of the target. The frequency shift from the target-reflected energy is a function of the target velocity. However, if the frequency of the laser is shifting its frequency during the time of flight, this creates a broadening or an error in the frequency of the returned beam that limits how accurately you can measure the Doppler velocity.
(From: Nelson Wallace (nelson.wallace@trw.com).)
In basic terms, coherence is a measure of the ability of a light source to produce high contrast interference fringes when the light is interfered with itself in an interferometer. High coherence means high fringe visibility, (i.e., good black and white fringes, or black and whatever color the light is), low coherence means washed-out fringes, zero coherence means no fringes.
In order to give the strongest interference, the two interfering beams must have the same polarization, have the same color, and be very well collimated so the two interfering wavefronts must lie on top of each other exactly.
If the colors don't match exactly, then the "temporal coherence" is less than ideal. The more "monochromatic" a light source is, the better its temporal coherence. Gas lasers have very narrow color bands, and thus very good temporal coherence; some laser diodes have wider spectral emission bands, and thus worse temporal coherence.
If an extented source (larger than a point source) is used to form the collimated beam, the beam spread will degrade the interference and the "spatial coherence" is less than ideal. Another way to look at spatial coherence degradation is to imagine several interference patterns, one from each point on an extended source; the maximum of one pattern falls on or near the minimum of another pattern, washing out the combined interference pattern.
There is, of course, a lot more to it. There's a number called the complex degree of coherence that quantifies the effect. If you really want to get into the serious details, I'd suggest you read Chapter 10, "Partially Coherent Light" in Born & Wolf's book "Principles of Optics", or, W. H. Steel's book, "Interferometry".
I hope this explanation has been coherent!
(From: Steve McGrew (stevem@iea.com).)
It's more complicated than that. Lasers don't really have a "coherence length". They emit a superposition of different discrete wavelengths, and there are temporal "beats" resulting from interference between them. As a result, if you set up a Michelson-Morley interferometer and slowly change the length of one arm, you get a gradually changing fringe contrast, with multiple highs and lows. The second high is when the length difference corresponds to the length of the laser cavity. In fact, you can keep increasing the arm length difference by multiples of the cavity length many times and still get decent fringe contrast. When you read that a HeNe laser has a coherence length of 30 cm, it means that the first minimum in fringe contrast occurs at a path length difference of 30 cm. The actual coherence function depends on:
A very good exposition can be found in "Optical Holography" by Collier, Burkhardt & Lin.
Or, for a non-frequency stabilized (non-single frequency) Fabry-Perot laser cavity, assume it is on the order of the distance between the mirrors. This works fairly well for a typical cheap HeNe laser tube. :)
A variety of techniques can be used to determine if a laser is operating single longitudinal mode and single spatial mode. Not surprisingly, many of the approaches are similar to those for determining coherence length, above.
For example, the Ando AQ6317B OSA claims a resolution of 0.01 nm. At 1,064 nm, this is equivalent to a mode spacing of 3 GHz, equivalent to a 2 inch (50 mm) long laser cavity. Thus, a laser shorter or equal to this should result in resolvable longitudinal modes on this OSA.
I've tested this approach with a short HeNe laser which probably has no more than 2 longitudinal modes (a Melles Griot 05-LHR-911). Where the path length difference was close to a multiple of the cavity length (L), the fringes had high contrast and didn't change their appearance significantly over time. When the path length difference was (n*L)+L/2, the fringe contrast and position changed as the tube heated up and expanded, and the modes shifted in location and intensity.
Caution: Operating a perfectly aligned Michelson interferometer - where there is a single dark blob on the screen - will result in light being sent directly back into the laser. (See the section: Where Does All the Energy Go?/) Many lasers will become unstable under these conditions which for some, may even result in damage (e.g., where a light feedback loop attempts to maintain constant output power and increases current to an excessive value). The chance of this happening will be reduced or eliminated by always aligning for multiple fringes or using a Mach-Zehnder instead of a Michelson interferometer. The Mach-Zehnder is slightly more complex but all light exits in a forward direction.
The last method is perhaps the best for the hobbyist to set up as it require no expensive test equipment. A very stable platform will be required but if the ultimate goal is holography, then it's a good excuse to start construction of one if a commercial optical table and mounts aren't available. But if you're already equipped for holography and just trying out a new laser, then the hologram test would most likely be easiest.
For the Michelson interferometer, the only optics needed will be a beam expander and collimator (e.g., a low power microscope objective or one from a CD or DVD optical pickup, followed by a 1 or 2 inch positive lens), a beamsplitter, a pair of decent quality first surface or dielectric mirrors, and a white card to act as a screen to view the fringes. The function of the rail can be improvised by moving the mirror mount along the edge of a metal plate or something similar. Slight variation of the location and alignment of the mirror in the movable arm of the interferometer will result in the fringes changing dramatically in their number and position but the clarity (contrast and crispness) should remain the same over a distance of multiple cavity lengths. If the contrast comes and goes with a period of the cavity length then the laser is operating in multiple longitudinal modes.
The coherence length of a typical single frequency laser is measured in multiple meters or even hundreds of meters so actually determining it is probably not possible in this manner. But if the fringes remain clear and crisp over a distance of the limits of your rail, the coherence length is probably long enough for most purposes.
(From: Phil Gurney (p.gurney@vp.com.au).)
Yes, it can be true, but it depends on the level of feedback, the distance between the laser and the reflector, the coherence length of the laser etc.
There is an excellent book on the subject by Klaus Petermann, called "Laser Diode Modulation and Noise". (Kluwer Academic Publishers).
(From: Herman Offerhaus (h.l.offerhaus@tn.utwente.nl).)
Generally the round trip outside the cavity will not be an integer number times wavelength and will not be mode-matched. Therefore the returning radiation is not in phase with the intracavity one and will interfere. This does not necessarily lead to instabilities but it is likely.
Reflections back into the cavity can also cause damage with certain types of lasers, so you might want to be very careful there.
(From: gklent (gklent@outix.netcom.com)
Any feedback into a laser cavity can be shown mathematically to affect the output with no thermal effects involved (as some might think). This is a common problem with low power HeNe lasers (effects are more pronounced with low gain, narrow linewidth lasers). I have observed power coupled from such lasers to drop to near zero and recover *immediately* when the offending reflection is removed.
(From: Len Moskowitz).
If it's controllable, this sounds like a nice way to modulate power.
(From: Bob Mueller (r.mueller@kfa-juelich.de).)
Not sure about power modulation, but it is one way by which one can control the output wavelength. Secondary (external?) cavity lasers can use this scheme for linewidth narrowing and frequency stabilization.
For grins, take a frequency stabilized HeNe laser and use it as a source for a Michelson interferometer using plane mirrors for the reflectors. If you align the system such that the reflected beams pass right back into the laser, the laser will lose its frequency lock. This happened many many times to me back in grad school before I realized where the problem was.
"Honest, Professor, whenever I got the interferometer lined up well, the laser would lose its lock..." (The professor just grinned).
For some interesting effects, do the same thing with a laser diode as the source. Watch the output fringes from the interferometer dance due to different frequency modes fighting for dominance :).
A polarized beam will result only if there is some preference for one polarization orientation inside the laser cavity. This could be due to the lasing crystal characteristics, an optical element like a Brewster plate or window, or an external influence like a magnetic field.
For many laser applications, a polarized beam is a requirement. For others, it really doesn't matter. I don't know of any cases where a polarized beam would be undesirable except in terms of the additional cost when it isn't produced automatically (e.g., requiring the addition of a Brewster plate inside the HeNe laser cavity).
(Portions from: Brian W. Rich (science@west.net).)
Light propagates as a transverse wave. That is, the vibration is sideways to the direction of travel. If the light is polarized, it means that all the waves are vibrating in the same plane. There can be a mixture of waves with different vibration orientations:
As its name implies, a quarter-wave plate retards the X polarization (say) component by 1/4 wavelength compared to that of Y. Both single line and broadband types are available.
Note that some lasers that are described as having random polarization actually have what might be described more accurately as 'slowly varying polarization'. For these (Inexpensive HeNe lasers are very commonly of this type), the polarization at any given instant may be anywhere from random to highly linear but the amount of each and the orientation of the linear component or components varies with time as the tube heats up and changes dimensions.
There are discussions of the theory of polarization and retarder plates in Melles Griot's Polarization Components Page (also in their optics catalog). Another introduction can be found on the Meadowlark Optics Principles of Retarders.
Most books on lasers and optics will cover these topics in detail. Perhaps the most comprehensive treatment is: "Polarized light - Fundamentals and Applications" by Edward Collett, Marcel Dekker, ISBN: 0-8247-8729-3. You probably should try to find this at a University library - it costs about $225 - and this is a discounted price! Comments on Polarization and Related Topics
(From: Steve McGrew (stevem@iea.com).)
Think of a photon as a packet of waves moving in some direction Z and jiggling in the perpendicular direction X. Now add a little bit of complexity: take two such waves moving together, but have the second one jiggling at right angles to the first, in the Y direction.
Quarter-Wave Plate: A quarter-wave plate is made of a birefringent material - light moving through it has different speeds depending on the orientation of the material and the direction of the jiggle in the light waves. Think of the plate as oriented so the minimum-speed wave is one that jiggles in the X direction and the maximum-speed wave is one that jiggles in the Y direction. For light of a given wavelength, there will be a certain thickness of the plate that results in an "X-wave" being delayed one-quarter step relative to the "Y-wave". In that case, if linearly polarized light goes in, jiggling at 45 degrees to X and Y, then it comes out circularly polarized because the X-wave was delayed relative to the Y-wave.
If you want to get a good intuitive understanding of polarized light, get a polarizing filter sheet from Edmund Scientific and some hunks of window glass and some clear Scotch tape. Scotch tape is birefringent. Stick the tape onto the glass, sandwich the glass and tape between two polarizing filters, and have a lot of fun. Try crossing the filters so they block all light, then putting a third filter between them, tilted in various directions. Then, using the explanation above, try to figure out where all the beautiful colors and surprising effects come from.
(From: Andy Resnick (andy.resnick@grc.nasa.gov).)
Both linearly polarized and circularly polarized light form basis states to the vector wave equation for electromagnetic radiation. Any polarization state can be described in terms of linear combinations of either horizontal and vertical polarization or left- and right-handed circular polarization. When solving the equation, textbooks usually present the linear polarization states because they are easy to write down: the electric field oscillates in the 'x' or 'y' axis, the magnetic field is perpendicular to that, and away you go. Then, they show that a second set of solutions exist - the circular polarization states, where left or right-handed circular polarization states are created by having the two linear polarization states be out of phase by 90 degrees. In this case, the electric field vector moved in a circle in the X-Y plane, either clockwise or counter-clockwise. (I forget which is left or right-handed) In any case, it turns out that circular polarization is actually more fundamental than linear polarization, as individual photons are circularly polarized: they carry angular momentum.
(From: William Buchman (billyfish@aol.com).)
On what basis can you say that circularly polarized are more fundamental than linear ones? Following the usual procedures (is this like the usual suspects in Casablanca) you can convert circularly polarized photons into linearly polarized photons. Then send them through a linearly polarized analyzer at such a low rate that only one photon goes through in a time. In Zeeman effects individual photons can be emitted either circularly or linearly polarized. Also see the section: Polarizing Materials and Optics.
"I have 2 HeNe lasers. The HeNe lasers have 0.1 to 0.2 GHz intensity noise. What kind of noise is this? Can it be eliminated?"
Assuming a stable plasma tube current, mode beating is likely to dominate in a HeNe laser. The various longitudinal modes which are active simultaneously are beating with each other in your photodetector. A typical HeNe laser will be operating with perhaps 2 to 10 lasing lines competing for attention at any given time depending on the distance between mirrors. Any change in mirror distance and alignment - even a fraction of a um or uR - may shift the mode distribution noticeably. Thus, tube heating and even the position of the laser may affect it! A frequency spread 0.1 to 0.2 GHz would correspond to a tube length of between approximately 1.6 and 0.8 m. What are your tube lengths?
There are frequency stabilized HeNe lasers which operate in a single longitudinal mode using a combination of an etalon inside the cavity and active feedback to maintain the lasing line on a particular portion of the gain curve. These should be virtually free of this type of noise. See the section: Frequency Stabilized Single Mode HeNe Lasers.
Also see the section: Operating Regions of a HeNe Laser Tube.
This phenomenon is even mentioned in a Spectra-Physics laser instruction manual from 1969!
Note that much slower variations in brightness can be easily seen or at least detected with any sort of laser power meter. While also due to the longitudinal mode structure, this behavior is not directly related to the beat frequencies - it is simply the result of the average intensity of all the modes that are active.
Further note that both of these phenomena occur no matter how stable the power supply for the laser (but can be affected to some extent by it as the gain curve shifts or changes amplitude as a function of electrical drive current).
Also see the sections starting with: Longitudinal Modes of Operation.
(James A. Carter III (jacarter3@earthlink.net).)
How long are your HeNe tubes? I'll bet that the high frequency noise your are seeing stems from multiple longitudinal modes in the laser. These modes are separated in frequency by about f=c/2*d where: c is the speed of light and d is the cavity length.
The HeNe will support several independent modes that all have a fairly random phase but are separated by a fixed frequency. These interfere with each other in the detection process and give signal variations if the detector is fast enough to respond.
There really is no practical means to eliminate this noise. On alternative is to use a semiconductor laser. You can buy these from commercial laser and optics vendors with very good beam quality for reasonable costs (depending how good the laser that you select). The semiconductor laser has such a short cavity that the mode spacing in frequency is sufficiently large that it is beyond your detection bandwidth or even large enough that only one mode can occupy the frequency region that is amplified in the laser stripe.
Note that care must also be used with the semiconductor laser (diode) to temperature stabilize its structure. Otherwise, the gain and the cavity mode may shift from one mode to another. This effect is called mode-hopping and can also be the significant source of intensity noise. For this reason, many of the more expensive research grade laser diodes have built in temperature control. However, this always costs more.
For a coherent monochromatic light source like a laser, divergence is affected mostly by the beam (exit or waist) diameter (wider is better) and wavelength (shorter is better). (A shorter laser generally produces a more divergent beam but this is mostly a result of the typically smaller beam diameter of such lasers, not their size.) This behavior is due to the diffraction limited behavior of wave propagation and cannot be overcome with optics. A very narrow low divergence beam is just not possible. Refer to the diagram: Divergence, Beam Waist, Rayleigh Length but keep in mind that the divergence in the diagram is greatly exaggerated and that the beam waist for most common lasers is actually located inside the resonator or at one of the mirrors. The equation for a plane wave source is:
4 * wavelength
Full-Angle Divergence (in radians) = theta = --------------------
pi * beam diameter
Divide by 2 for the half-angle divergence (which may be listed in some laser
spec sheets). This equation (and the normal inverse square law for light
intensity) really only applies at distances from the laser which are beyond
the Rayleigh Length (well beyond the beam waist). These are under optiimal
conditions - it isn't possible have a smaller divergence in the far field with
a given beam (waist) diameter without recollimating the beam.
Note that the location of the effective point source does not generally coincide with the laser's output aperture. Likewise, the beam diameter may not actually refer to the spot size as the beam exits the resonator but rather the beam waist (inside or outside the resonator) and optics which are part of the resonator (mirror curvature and OC outside curvature) will affect this. Also see the section: Rayleigh Length.
A related consideration is how well the beam can be focused. The basic equation for diffraction limited spot size of an ideal Gaussian beam is:
4 * wavelength * (lens focal length)
Spot Diameter = --------------------------------------
pi * (beam diameter)
Since (lens focal length)/(beam diameter) is basically how quickly the beam converges and is the "f number" of the optical system, this is equivalent to:
4 * wavelength * (f number)
Spot Diameter = -----------------------------
pi
Or, if you want to know the requiree focal length to produce a given size spot:
(spot Diameter) * pi * (beam diameter)
focal length = ----------------------------------------
4 * wavelength
(Where M-squared is not equal to 1 (not a pure circular TEM00 Gaussian mode), the size of the resulting spot will be increased. For a beam whose diameter is hard-limited by an aperture, change 4/pi to 2.44 which will result in the diameter of the first minima.)
So, for an ideal HeNe laser (common inexpensive HeNe lasers come pretty close) with a 0.5 mm bore at 632.8 nm, the divergence angle will be about 1.6 mR. Using a lens with a focal length of 25 mm, the smallest spot would be roughly 40.28 um. If the beam were first expanded to 10 mm and collimated, using the same lens, it could be focused to just over a 4 um spot.
And, as an aside: The same equations apply to microwaves or any other coherent wave source. It's amusing to see plans for a long range EMP cannon using the guts of a microwave oven attached to a 5 inch diameter metal cylinder. Guess what the divergence will be. Hint: The wavelength of a microwave oven magnetron is about 5 inches.
You might also come across a laser specification in mm-mRad:
(From: A. E. Siegman (siegman@stanford.edu).)
This is the product of beam size at the input plane, near field plane, or waist location (where the beam has its minimum size) in mm, times the far field angular divergence in milliradians.
But don't ask any embarrassing questions about whether these quantities are measured as full width, half width, full width at half maximum, 1/e width, 1/e2 width, width to first nulls, standard deviation, width containing 86% of the energy, or whatever. You pick whichever one of those will make your device look the best. :)
Unlike common light sources most people are familiar with, the beam from a laser does not immediately begin to diverge at its origin. In fact, there is a location where the beam from a laser (even without focusing optics) is a minimum called the 'beam waist' (for obvious reasons). (For most commonly used resonator configurations, the beam waist is inside the resonator or at one of the mirrors so you probably won't notice it.) Therefore, the divergence equations given above are actually approximations assuming that the measurement is made some distance beyond this point. Close to the laser, the well known inverse square law for the decrease in light intensity with distance doesn't apply either.
Another way to think of the shape of a laser beam is that it is the same as that of a light beam exiting from a hole (at the waist location). For the laser, it just happens that there is no physical hole and the waist is generally not even at the laser! Once you get far enough from the 'hole', it is effectively a point source and the inverse square law takes over.
(Portions provided by Steve Roberts: (osteven@akrobiz.com).)
If there is one optics book you must own, it is:
The following discussion on beam diameter is derived from the material on pages 232-233 in "Characteristics of Gaussian Beams":
The actual beam diameter is given by:
Z * Theta
D = Do * Sqrt(1 + (---------------)2)
Do
Where:
Io * Do2
I = --------------------
Do2 + (Z * Theta)2
Where:
So this results in:
Do
Z_Rayleigh = -------
Theta
Plugging in the equation for divergence (from the section:
How the Beam Diameter Varies with Distance,
we get:
pi * Do2
Z_Rayleigh = ----------------
8 * Wavelength
(Note: The factor of 8 originates from the basic divergence equation and the
fact that it deals with the half-angle and this equation is for the full
beam width.)
For example, assuming a large HeNe laser (632.8 nm) with a waist diameter of 2 mm Z_Rayleigh is about 2.5 meters. In practice, you might not get that far but 1 meter may be feasible. (Reality enters due to the fact, that the equation assumes that the axial intensity distribution is perfectly gaussian.) For a small 632.8 nm HeNe laser with a beam diameter of 1 mm (e.g., from a barcode scanner), the theoretical Z_Rayleigh would only be about .62 meter! And, a wide bore 10.6 um CO2 laser with a waist diameter of 10 mm would result in a theoretical Z_Rayleigh of 3.6 meters. Thus, while these are quite well collimated at least compared to a flashlight or laser diode, their beams are definitely not as parallel as is popularly believed. However, this can be dealt if you are willing to accept a larger diameter beam.
(From: Mike McCarty (jmccarty@sun1307.spd.dsccc.com).)
The inverse square law applies to all unconstrained EM radiation whatever its source. It's just a matter of being out of the near field. The radiation from a laser has an envelope (as does all radiation passing through a "hole") which is a hyperboloid of one sheet. In the far field this approximates a cone (very closely), and the inverse square law applies.
In a constrained transmission medium like an optical fiber (or lamp cord) indeed the inverse square law does not apply. But then we're no longer talking about unconstrained radiation.
For more than you could ever possibly want to know, see:
Lasers
Anthony E. Siegman
University Science Books, May 1986
ISBN: 0-935-70211-3
and some additional information from Professor Siegman:
(From: Do-Kyeong Ko (dkko@nanum.kaeri.re.kr).)
M-square is derived from the uncertainty principle and is the product of a beam's minimum diameter and divergence angle. it is a measure of how well photons in the beam are localized in the transverse plane as they propagate.
As the waist size of a beam is squeezed down, the uncertainty in the locations of the beam photons in the transverse dimension is reduced, and the uncertainty in the transverse momentum of the photons mist proportionally increase. According to the uncertainty principle, there is a minimum possible product of waist diameter times divergence, corresponding to a diffraction-limited beam.
Beams with larger constants are described as being "several times the diffraction-limit," a constant equivalent to M-square. This constant is a measurable quantity describing beam propagation as well as beam quality.
M-square is expressed as follows:
pi * Theta * Wo
M2 = -----------------
2 * Lambda
Where:
This is just a brief explanation for M-square. You can find more detailed information from following references:
Note that M-square has no direct relation to the Q factor or finesse of a laser resonator. A laser with a mediocre Q can be perfect in the M-square department and vice-versa. See the section: Q Factor and Finesse of a Laser Resonator.
(From: Bob.)
M-square is a somewhat new term. It used to be referred to as the 'B integral' back in the old days (M-square and B integral were not exactly the same things actually, but they both pertained to the 'quality' of the beam itself, and thus its focusability) basically the properties of a resonator (its optics, gain medium, thermal loads, etc.) play a role in what the laser beam coming out looks like, and affects a laser's probably most important quality, its focusability. The M-square value of a beam in a number that describes among other things, this very important beam quality.
(From: Someone who wishes to remain anonymous.)
Think of it as "times diffraction limit", i.e., the focus spot will be M-squared times larger (surface-wise) than an ideal Gaussian beam. I believe in Europe they use mostly K-number (1/M-squared). M-squared is always larger than 1 (and K-number smaller than 1, duh!)
Another way to think of it is that the Rayleigh range is M-squared times shorter than that of an ideal Gaussian beam.
Of course lens aberrations limit the performance, so weak lenses (longer focal lengths) or aspheric lenses might be desirable. Spherical aberration will be reduced by turning the curved sides of the lenses face to face.
For a typical HeNe laser barcode scanner tube with higher than diffraction limited divergence (typically 2.5 to 8 mR), this approach should work well. You can even correct it with the lens from a pair of reading (eye) glasses. If the eyeglass prescription is X diopters [diopters = 1/(focal length in meters)], then the lens will need to be about 1/X meters from the end of the laser tube. This assumes a +diopter correction (for reading or far-sightedness) and no astigmatism correction or other funny optical prescription!
See the book "Lasers" by A. E. Siegmann for the details of the propagation of laser light. (page 664 ff.)
For example, with HeNe lasers, if the tube is short and produces a wide beam at its output aperture compared to the typical tubes listed in the section: Typical HeNe tube specifications, it is quite likely to be multimode as these types produce more power for a given physical size. For those applications where light intensity but not quality is important, multimode lasers are adequate. Assuming it is supposed to be TEM00, dust on or damage to the optics inside the resonator (possible even if it is an internal mirror tube) or debris in the bore or a warped bore could result in a higher order beam.
Also note that not all lasers are designed for optimal collimation without additional optics. The combination of the curvature of the HR and OC mirrors and the curvature of the exterior surface of the OC glass combine to produce a given divergence characteristic. For example, if the OC mirror is curved (the inside surface) but the outside of the OC is planar, the beam will diverge more than would be expected from the diffraction limit based on bore diameter. However, a simple converging lens can be used to restore a parallel high quality beam.
(From: Lynn Strickland (stricks760@earthlink.net).)
A beam can be pretty far from TEM00 before you can visually detect off-axis modes - especially at power levels of a few mW. You could measure the mode purity with a beam profiler or an optical spectrum analyzer - but you probably don't have this equipment laying around. A lot of the higher power HeNe's that hit the surplus market are because of mode problems - and many of the models are multi (transverse) mode to begin with. If you have a manufacturer's model number that can be a start to see what its specifications should be.
If the problem is simply divergence, re-collimate it with an external lens. It's probably a mode problem though. Whether it has decreased the value depends completely on the application. If it is TEM00, you should be able to produce interference fringes with a path length difference approximately equal to the length of the laser (as a rule of thumb).
(From: Mark Folsom (folsomman@redshift.com).)
Three things can make your spot too big: Poor focusing, long focal length and aberration. If you know the divergence of your laser, then you can calculate the minimum spot size you should get at a given focal length. A shorter focal length will give you smaller spots, except when it is short enough to cause excessive spherical aberration. One simple trick that can reduce spherical aberration at a given focal length is to use a lens with a higher refractive index i.e., if you're using a silica lens, you could try sapphire instead. You could also try an aspheric lens or use a series of lenses to get a short equivalent focal length with reduced aberration (like a plano-convex singlet and a meniscus lens). It helps to have ray-tracing software so that you can model different setups before buying and assembling the hardware.
Because it is coherent, the beam from a laser originate from a virtual point source. For most common lasers, its actual location is somewhere inside the laser resonator - between the mirrors. However, for some configurations, it could be outside.
For the purposes of collimation, the diffraction limit is what determines how parallel the beam can be made. This is largely based on the the exit or beam waist diameter and wavelength of the laser. However, you aren't focusing an image of the bore of the gas laser or exit face of the diode.
For an incoherent light source like an LED, with a single lens, you approach pinhole geometry where the source aperture as a ratio of the source-to-lens distance (approximately the focal length) equals the image size as a ratio of the image-to-lens distance (and approximately equals the tangent of the divergence angle).
However, for a laser, this doesn't really apply and would result in a much larger divergence than is possible based on the diffraction limit. For example: The bore size of a typical 1 mW HeNe laser is .5 mm. Using geometric optics alone, a 100 mm focal length, 10 mm diameter lens would imply a full angle divergence of 5 mR, similar to what is possible with a bare LED chip. However, with the HeNe laser, such a lens results in a divergence of about .1 mR - 50 times lower.
A very useful rule of thumb that I learned at the University of Rochester's Institute of Optics from either Dr. Robert Hopkins or Dr. Philip Baumeister is for estimating the diffraction limited size of a projected spot:
For visible light the size of the spot, measured in microns, is equal to the f/number of the cone of light making the spot. (Here, the f/number is defined as the projection distance divided by the lens diameter.)
Thus we see that a camera with the lens set at f/22, if it was a perfect lens (designed and built by God), could make an image spot no smaller than 22 microns (.022 mm), regardless of the focal length. This has nothing to do with the resolution of the film or other detection method.
In another example, suppose we want to have a spot 5 microns in diameter, forming it through a 1 inch tube 10 inches long. No way! The best you can do is f/10 and a 10 micron spot.
Now let's try it on a laser: Suppose we want to shine a laser a mile and we want the beam to be an inch in diameter at that distance. An inch is 25,400 microns so our projecting lens must be f/25,400. Since the projection distance is 5,280 feet the lens diameter must be at least 5,280/25,400 or .208 feet. That's 2.5 inches, and the entire lens must be illuminated for the numbers to hold.
This idea can be easily converted into object space as well. In the above case, simply reverse the light direction and we can conclude that a 2.5 inch telescope objective is required to resolve one inch at a mile. Once at a zoo show-and-tell, the demonstrator said that if we had an eagle's visual acuity we could read a newspaper at a mile and a quarter. Well, lets see about that: The spot size would have to be one millimeter or better - that's f/1000 - the eye pupil would have to be at least 6.6 feet in diameter!
(From: Sam.)
Note that this does not include wavelength - which ultimately be a further limiting factor. However, comparing results with the equations given in the section: How the Beam Diameter Varies with Distance, the rules-of-thumb for spot size would appear to be conservative.
For example, using a red HeNe laser (632.8 nm) with a 1 mm beam diameter and 25 mm lens would yield a spot size of about 10 um using the equation but 25 um using the rule. Even if the rule assumes a wavelength range including the border of visible light (700 to 750 nm), it's still conservative by more than a factor of 2. Perhaps there is a factor of 2 missing somewhere in which case it would be much closer. More likely, different assumptions apply to the equation and the rule.
(From: George.)
The conservatism of this rule can be justified by the fact that optical systems are made by mere mortals and you should expect less than perfection. Another factor may be that the more exact formula was for the intensity of the electric vector and you need to square it to get power. It might even be that the formula was for radius instead of diameter. It could be that the cut-off point was defined in a different manner. (There's the 1/e level, or 50%, or 10%, or first minimum, etc.)
Anyway, if you're working on the back of an envelope you don't want to bother with pi and other factors and as a colleague used to say (he's dead now), "It's better than a poke in the eye with a sharp stick!" :)
The above rule tells us what is the best we can expect. The next rule helps us know how bad things are. It's a rule I invented or discovered myself. I've never seen it elsewhere although I wouldn't be surprised if it had been proposed in Newton's time.
We all have learned at an early age how curved surfaces make a lens and how image distance, object distance and focal length all relate to one another. Then we are cautioned that these rules governing light rays are for paraxial rays, rays close to the axis. An explanation of spherical aberration then follows. But what is lacking is a statement of the extent of the aberration. Werner's Rule of Thumb fills that void.
Werner's Rule of Thumb: For collimated on-axis illumination of a plano convex lens the distance by which a marginal ray falls short of the paraxial focus as it crosses the axis is equal to the center thickness of the lens.
This is assuming negligible thickness at the edge, otherwise it's the center-minus-edge thickness. The rule assumes light is going through the lens properly (focus on the flat side). If you run it backward the effect is five times as much. Remember that it is an approximation; the actual difference may be off by 5% or more. It is very accurate if the refractive index is 1.6 or 2.2 but there's not much call for these lenses.
Here's an example. Suppose I want to collect collimated light with a lens 1 inch in diameter and 1 inch focal length. The catalog shows such a lens with center thickness 9.1mm, edge thickness 1.5mm. We can conclude that such a lens will have a 7.6mm shortfall of the marginal ray, and whether or not that is acceptable depends on what the lens is used for.
In the next case we want to use a lens of 10 inch focal length, 2 inch diameter. For this the thicknesses are 4.3 mm and 1.5 mm and the shortfall of 2.8 mm is probably acceptable.
We can also use it to evaluate such things as a double convex lens with 1X magnification. To do this we divide the lens in two and figure each half as a point-to-collimation case, but in each case the light is going the wrong way so we multiply the shortfall by five. Then figure a corrected focal length for the marginal rays and make a new marginal ray pattern from the original starting point. If it's a fat lens it will show us why in these cases it's better to use two plano convex lenses with the curved sides inward.
For a TEM00 beam (e.g., from a HeNe laser), efficient coupling is relatively easy to do for both single mode and multimode fibers. A short focal length normal or GRIN lens must be mounted precisely 1 focal length from the fiber core (assuming a parallel input beam). Preassembled fiber-couplers will have this lens permanently prealigned. Then, it takes precise alignment of the coupler with respect to the laser with control of 4 degrees of freedom - X, Y, pan, tilt. Where the beam isn't parallel, the distance between the fiber tip and lens (Z) also needs to be adjustable.
With single mode fiber (a core diameter of about 4 um for a 632.8 nm HeNe laser), the output will be of similar quality to the input but will diverge and require a lens for collimation. But the collimation will be diffraction limited and thus very good, again similar to the original laser.
To maximize coupling efficiency, the mode shape of the beam going into the fiber must match the mode shape of the fiber. To put it simply, any given fiber has a Numerical Aperture (NA) spec. The beam going into it should match that for optimal coupling. A narrow beam will not couple as well as a wide one that fills the cone defined by the NA of the fiber. Thus, the lens of the fiber-couple also needs to be matched to the diameter of the input beam.
Alignment with a single mode fiber can be a challenge because there are often ghost or phantom reflections inside the coupler that may result in some coupled power. If one of these is detected, adjusting for a local maximum will result in much lower power - by orders of magnitude - than is possible for the main beam.
The easiest way to do initial alignment minimizing the chance of getting a reflection, is to send a HeNe beam through the coupler in reverse. (There are standard fiber-coupling assemblies that will attach to inexpensive HeNe laser heads which are suitable for this purpose.) The result will be a collimated beam out of the lens. When this precisely lines up with the beam from the laser being coupled into the fiber (at both the fiber-coupler and the laser), the alignment will be close enough that the alignment HeNe laser can be removed and replaced with a laser power meter or optical spectrum analyzer. Then, alignment can be optimized by monitoring optical output power from the fiber.
With multimode fiber, the output beam will be multimode with an NA similar to that of the fiber. The core diameter will limit the ability to collimate based on the focal length of the collimating lens. Flexing or twisting the fiber will dramatically affect the mode pattern of the output beam.
For other types of lasers, the original beam characteristics will determine how feasible either of these is.
Much more on this topic can be found in the technical libraries and application notes of optics and fiber-optics manufacturers.
Questions along the lines of: "How can I couple my light bulb into a fiber?" often come up. The simple answer is: "Except for very large diameter fibers or very concentrated light sources like lasers, you really can't, at least not with any efficiency.".
Another idea continues to pop up along the lines of "How about drawing the fiber out so that once the light is inserted at one end, it can be squeezed to a smaller diameter at the other?". Sorry, it won't work. If the maximum amount of light is coupled in, then the mode shape of the input beam matches the acceptance angle (NA) of the fiber. As the fiber diameter is reduced, the angle of internal reflection will become larger. (A simple drawing, left as an exercise for the student, will easily demonstrate this.) But, the angle of internal reflection is already at the maximum as determined by the fiber NA so what will happen is that light will leak out. If the fiber (well, not actually a normal fiber but a light pipe) had a mirrored boundary, then the light would be trapped, but with the larger angle of reflection, the beam exiting the other end would have a higher divergence and again, brightness would not increase. This principle - called a lens duct - is used for beam shaping of high power laser diodes.
Here are some comments on coupling any type of light source into a fiber or through an itty-bitty hole:
There is more info at U.S. Laser Corporation Fiber Optic Beam Delivery System Tech Note.
(From: A. E. Siegmen (siegman@stanford.edu).)
A passive spatial filter of any kind -- meaning any device in which you focus your initially incoherent light beam through a fiber, or a small hole, or any optical equivalent to that -- acts to "improve the spatial coherence of the light" simply and solely by filtering out a lot of the spatial modes (or angularly distributed plane waves, or whatever) in your light beam, allowing only a small fraction of the original light to pass through.
If you filter the light from any thermal or incandescent (or fluorescent, or whatever) light source strongly enough to make it really fully spatially coherent (as would be the case if for example you pass the light through a single-mode fiber), you will have, for practical purposes, no useful light left. The light from a source with a radiation temperature of 6,000 °K contains on the order of one photon per second per Hz of bandwidth in each separate spatial mode.
If your filter is a multimode fiber which propagates or transmits N spatial (a.k.a. transverse) propagation modes, multiply the above by N. You just can't couple any more spatial modes (equivalent to "spatial information") than that through your system.
Suppose you have a laser cavity with two circular and curved mirrors facing each other, and with each mirror having a very large diameter (what "large" means will come out in a minute).
Suppose the mirror spacing and the mirror radii of curvature (NOT the diameter) satisfy a certain set of conditions such that they form a so-called "stable cavity".
This cavity will then have a set of nearly lossless resonant modes which will have the form of very nearly perfect Hermite-gaussian or Laguerre-gaussian mathematical functions. The lowest-order mode will have an essentially ideal gaussian profile with a certain spot size which depends (only) on the spacing and radii of the mirrors and the wavelength of the light (but NOT on the mirror diameter, which is assumed to be very large or effectively infinite). This spot size, called the "gaussian spot size" and usually labelled as ws, is given by a simple formula in terms of the cavity length L, the end mirror radii r1 and r2, and the wavelength.
Suppose you now consider a *real* laser cavity with *finite* diameter mirrors, such that the mirror diameter is finite but still somewhat larger than this ideal gaussian mode spot size. (In practice, a mirror diameter that is 2 or 3 times larger than the ideal gaussian mode size is good enough.)
This real laser cavity will then have a set of *real*, slightly lossy, resonant modes, which will still be very close in shape to the ideal HG or LG modes for the infinite-diameter case. These real modes will, however, be slightly lossy, because energy leaks past the finite edges of the mirrors at each end (or at one end, at least).
The lowest-order real mode (also labelled as the "TEM00 mode") will be very close to gaussian in shape, and will have a smaller loss than any of the higher-order HG or LG modes. As a result, under good conditions, the laser will oscillate first, and continue to oscillate, only in this TEM00 mode. In a well-designed laser the higher-order TEMnm modes can be kept from oscillating.
OK, now look at the form (i.e., the transverse profile) of this real oscillating TEM00 mode. Inside the cavity, and especially on the end mirrors, it will be almost perfectly gaussian over almost all of the mode profile. Only out very close to the mirror edges (where the intensity value is way down on the tails of the gaussian profile) will the actual profile deviate from an ideal gaussian (in fact, the intensity will drop off to even smaller values outside the mirror diameter).
This is the *real* mode of the cavity. It's called a "gaussian mode"; and it is in fact almost perfectly gaussian over most of its diameter. Only way, way out in the wings does it deviate from gaussian.
Furthermore, as it propagates outward it will stay almost perfectly gaussian over nearly its full profile, at *any* distance outward. (The widht of the gaussian will get larger due to diffraction spreading, however.)
So, a real laser beam (from a good but realistic laser) is *almost* perfectly gaussian, at *every* distance, and the small deviations from gaussian occur mostly out in the *tails* of the beam profile.
(From: Andreas Voss (andreas_m_voss@hotmail.com).)
This is a simple task, at least in principle.
You have to put an aperture of the right diameter somewhere in the beam path inside the resonator. You will have to adjust the pinhole in the plane perpendicular to the beam to bring it on axis.
At least two questions remain:
You can calculate this (assuming you know all distances and radii in your resonator) using the complex ABCD formalism (see: "Lasers" by Anthony E. Siegman, University Science Books, May 1986, ISBN: 0-935-70211-3); there is a commercial software called PARAXIA, which can help you doing so. But in most cases it is easier simply to try different apertures and to find the best one iteratively.
Again, you can calculate it (this may be necessary when you have a strong thermal lens); typically the best place is a waist of the beam. If you have a flat output coupler or end mirror, you will have a waist on the flat mirror; place the pinhole near this mirror. In other cases simply try different positions (perhaps you can guess the position of a waist).
Assuming the laser beam is TEM00, there are several likely possibilities:
Fortunately, this is quite simple, at least in principle. A spatial filter is just a pair of lenses and a pinhole - a very very small pinhole. The first lens focuses the output of the laser precisely at the location of the pinhole and the second lens recollimates the beam. (Thus, beam expansion and collimation can be combined with this cleanup operation.) Since off-axis light will not be focused at exactly the same point in space as the desired beam, it will be blocked by the pinhole. Thus the name, spatial filter. :-)
The general optical setup for a spatial filter is shown below:
+-------+ |
| Laser |==========()=====-----:-----=====()==========> Clean Beam
+-------+ |
Focusing Pinhole Collimating
Lens Lens
The pinhole needs to be just larger than the size of the beam at its focal
point. For a typical HeNe laser, the optimal pinhole diameter is around 1 um
(the diffraction limited spot size). However, a slightly larger pinhole - say
order of a few um - should be nearly as good. Needless to say, even with such
a 'large' pinhole, all components must be rigidly mounted, and precisely
positioning the pinhole at the exact focus of the laser beam and centering it
in X and Y is a non-trivial task!
Very expensive commercial spatial filters are available but with a little resourcefulness, it should be possible to improvise:
However, if you want to expand the beam significantly without additional optics (beyond the collimating lens), a short focal length focusing lens (like a microscope objective, or CD player or diode laser module type singlet) will be needed to keep the length of the apparatus within reason and this will require much greater precision in pinhole adjustment. Alternatively, another short focal length lens can be added to expand the beam once it passes through the pinhole.
The pinhole can then be glued to a plate with a larger center hole. Positioning can be accomplished using the parts from a microscope mechanical X-Y stage or even a simple spring loaded X-Y mount of your own design.
Since it only needs to be set up once, convenience isn't essential as long as once it is adjusted properly, everything can be locked or glued in place.
The improvement in beam quality resulting from the addition of a spatial filter to an inexpensive laser (e.g., a 1 mW HeNe tube) can be quite dramatic. If you are serious about laser based optics experiments, this is essential.
Here are some more details on my proposed homemade spatial filter design. This should do 10 um easily without requiring fancy machine tools - or machining skills. :)
The critical dimensions are the distance from the focusing lens to the pinhole and the X-Y position of the pinhole. Assuming you have a short focal length lens already selected, start with a brass or aluminum tube (I really dislike working with steel) with a length just over the focal length of the lens and a diameter slightly larger than the lens. Ream out one end to hold the lens. Or, start with a pair of tubes with one being a press-fit inside the other (or it can be glued in place). In either case, it must be possible to mount this affair (and the needed collimating lens) on your optical bench (or whatever serves as your optical bench! Fashion some sort of cap to hold the lens in place. Of course, what you really want is a cap with fine threads to permit its longitudinal position to be precisely adjusted but since this setting the focal distance should be a one-time process, shims will also work.
At the other end of the tube, provide a recess deep enough to install a very fat washer (say 2 mm) with perhaps 1 mm on all sides to allow for X-Y movement. The face of the washer will be where the pinhole is mounted and should be at the focal point of your lens when positioned in its center of travel at the other end of the tube.
Drill and tap 4 holes around the circumference of the tube for adjustment screws. Use 2-56, 1-80, the finest thread taps you can find. You can use 4 adjustment screws or 2 screws and 2 springs or some other means of applying pressure to the pinhole washer as you move it. Put a ring of thin metal around the pinhole washer so that the adjustment screws don't bear on it directly.
To make your pinhole, use a piece of aluminum foil (Reynolds or your favorite store brand!) against a piece of plate glass, and a new straight pin. Glue the resulting pinhole to the washer. Center as best you can but this isn't that critical since you will have the X-Y adjustments. Once the glue sets, insert the mounted pinhole into the end of tube again with some sort of cap to keep it in position and to prevent movement along the axis of the tube.
The beam exiting the pinhole will be diverging. You then need a collimating lens and means of mounting it.
The rest is left as an exercise for the student. If you have some basic machining skills and a lathe, this is much easier but a serviceable spatial filter should still be doable with just a drill press, decent drill bits and taps, straight reamers, and basic hand tools.
(From: Thomas R Nelson (tnelson@uic.edu).)
If there are no rings, you aren't filtering anything. What you should see is the Airy pattern from the circular pinhole. Then place an aperture after the collimating lens which is closed down to the first minimum in the pattern. That way you only transmit the central maximum and remove the rings.
You want to make sure your pinhole is at the focus of the beam, which you can do my maximizing the transmission. As for the pinhole size, it depends on what your focal spot size is, and how bad the beam is to begin with. The smaller the pinhole compared to the beam's focal spot size, the more effective the filtering, but the less energy transmission through the filter. You might have to play around with it. Ideally, you might want a pinhole that's slightly smaller than your focal spot size, if your input beam isn't too bad to begin with. The worse your beam is to start, the less you can get through your filter, and still have a good beam at the output.
(From: William Buchman (billyfish@aol.com).)
Hard apertures produce fringes. There may be a number of ways to get a Gaussian beam starting with a good laser that produces one. Another way would be to use an apodized aperture and throw much of your light away. Use a transmission pattern that goes to zero at the edges and varies smoothly. A Gaussian and the various modes produced with Hermite and Laguerre transverse behaviors will retain their intensity profile except for scaling as they propagate. To the extent that they are truncated or deviate from a transverse Gaussian, side lobes or fringes will be introduced. It is a tradeoff.
(From: Thomas R Nelson (tnelson@uic.edu).)
These are all valid options, but there's nothing wrong with using a hard aperture. And it's usually less expensive. You just have to make sure you have enough contrast in the diffraction pattern after the pinhole so that you can effectively isolate the central max from the airy rings. A hard aperture can be closed down into the first minimum to do this, and this works fine.
(From: William Buchman (billyfish@aol.com).)
These do work well, but the original question referred to production of a Gaussian beam. That is not possible because a rigorous Gaussian requires an infinite aperture. The best that can be done is to produce an approximation to a Gaussian beam. If you want to avoid distinct sidelobes, you must avoid truncating the beam in a way that produces a discontinuous intensity profile.
(From: Thomas R Nelson (tnelson@uic.edu).)
How strict is the requirement? In my experience, the difference between a Gaussian beam and the central max of the pattern from a spatial filter is small, in practical terms. The requirements have to be pretty strict for it to really matter. And the intensity profile is not discontinuous. There's a minimum in the pattern, and at that point an aperture can be used to remove the outer rings. It's not discontinuous, and there are no hard edges to produce any type of diffraction pattern after this point.
(From: William Buchman (billyfish@aol.com).)
You need a set of specifications. How big can the sidelobes be? How much are you allowed to deviate from a Gaussian or do you need a Gaussian at all? How much power or energy are you willing to throw away? Without specifications or requirements, talk is cheap.
Antenna designers have tackled such questions for decades.
(From: Thomas R Nelson (tnelson@uic.edu).)
There's a minimum amount of energy that you have to throw away in either case, and that depends on how much of the incident beam energy is in the TEM00 mode. Strictly speaking, if you had a crappy beam such that ALL the energy was in a different mode like TEM01, then no filtering will change that into the other mode. All these methods are merely taking the inner product of the laser beam with the TEM00 mode. So as far as that goes, you have to throw away every other component.
As for the rest of it, how big can the side modes be, etc... I'm sure you'd agree that if your input beam is THAT bad that you get less than 50% transmission after aperturing the rings, then you should look at improving the beam at its source.
(From: Michael Brilla (mjbrilla at comcast.net).)
A spatial filter will eliminate the diffraction rings in an expanded laser beam caused by dust in, or on, an objective. It will also remove imperfections in the beam caused by dust on mirrors upstream of the objective. Using a spatial filter, you should be able to get a clean, smooth, uniform intensity distribution. But it's not perfect. It works really well if you have, say, up to 20 or so diffraction rings in your expanded beam, but not quite so good if the objective is dirtier than that or has scratches, etc.
The pinhole aperture needs to be positioned precisely at the microscope objective's focal point. The only light that will pass through the pinhole is light that comes to a nice, well defined focus. Light that is diffracted by dust in or on the lens won't focus at the focal point of the objective, instead it lands on the metal foil surrounding the aperture and is filtered out.
Spatial filters take a bit of practice to adjust properly, but once you get the hang of it, it's really easy. (It's best to have someone show you how to use one.)
The pinhole size must be matched to the objective size and the laser wavelength that you are using. For example, with 1mm beam from a 442 nm laser I would use a:
You could probably find used spatial filters on eBay or some other used optical equipment Web site for cheap. That's probably the easiest way. However, I have seen and used some home-built spatial filters that have worked well enough. If you have access to a machine shop, you could probably make one yourself using a couple of hunks of aluminum, some 72 thread per inch screws, some springs, and some pinhole apertures (available from Edmund Industrial Optics).
(From: John R. (scifind@indy.net).)
As another idea, obtain a commercial-grade "ruled grating" from Edmund Scientific. These are an order of magnitude better than the cheap quality plastic film gratings. They will easily separate all of the argon lines, especially the close, and weaker intermediate green and blue lines that are barely resolvable with the plastic grating.
But again, there are always pros and cons. Gratings give much higher dispersions than prisms, but also send laser energy into higher order (and weaker) beams. However, if the blaze wavelength is chosen close to laser lines, the efficiency is increased.
Prisms will produce one nice set of separate lines, but at less dispersion. Depending upon your application however, the prism may still be the cheaper (and better) method.
Where the lasers have significantly different wavelengths, there are a variety of options using dielectric (dichroic) mirrors, prisms, gratings, PCOAMs, and/or other optical elements. The result can closely approximate the output of a single multiline laser. There will be practical issues of matching the beam diameter, divergence, and profiles. Some of this can only be approximated since divergence and wavelength are not independent - the shorter the wavelength, the lower the divergence for a given beam diameter. Therefore, it is possible to make the beams equal in diameter at a given distance, but not at all distances from the laser.
However, combining more than two lasers that are the same wavelength to a single beam is at the very least difficult, if not impossible. Two polarized lasers can be combined into a single beam using a polarizing beamsplitter (as a combiner) but the polarization of the result will essentially be random based on the instantaneous phases of the two beams. In most cases, this is for all intents and purposes non-polarized - the polarization will be changing on a time scale of microseconds or less since even a small wavelength difference results in a large frequency difference. The combined beam is thus unsuitable for use with any device requiring a polarized beam (like a PCOAM). Multiple collimated beams can be directed so they are more or less parallel and side-by-side. Multiple beams can be arranged so they originate from sources that are close together. Multiple lasers can be focused into the same point in space (e.g., through a pinhole) so they they appear to originate from a point source will result in multiple collimated beams side-by-side. To produce a single beam which merges more than two polarized beams or multiple unpolarized beams of the same wavelength into a more intense beam would violate the second law of thermodynamics as applied to the brightness of a source and is thus impossible no matter what the technology.
But there is one special case where this can be done relatively easily, at least in principle. That is where the two lasers are the same wavelength and are locked together to have the same controllable phase relationship. Then, the two beams can be combined in a 50:50 beamsplitter by adjusting their relative phase so that they interfere constructively in one direction and destructively in the other. This works because the reflection from a beamsplitter will be at a 180 degrees phase difference to the transmitted beam. It's equivalent to the output section of a Mach-Zehnder interferometer or modulator using a single laser beam that has been split into two parts. But, this would be quite difficult to achieve in practice and isn't something that can be done in a basement lab. Aside from the mechanical stability required, locking two lasers is a non-trivial problem. And, in general, it's likely that buying a higher power laser will almost certainly be a more cost effective solution.
Also see the section: Inexpensive Combining of Argon Ion and HeNe Laser Beams.
(Portions from: P. G. Hannen (PGHannen@aol.com).)
The color splitter/combiner prism that some laser surplus companies sell are good only for specific wavelength ranges of red, green, and blue. These were designed for color video camera or projector applications and are called "Philips prisms", originally patented in 1956. This patent number is 3202039 which may be too early for some of the on-line patent databases but is available from the US Patent and Trademark Web site (you'll need a TIFF viewer plugin to display the scanned images). Also see patent number 2740829 for the "X-cube". Phil Baumeister has published material on this device. The goal is to keep the dielectric coating as near to normal incidence as possible. A 45 degree angle dielectric is the worst! Philips prisms get the angles down under 30 degrees, and are quite compact. This is especially important for fast F-numbers.
Philips prisms intended for video applications may be useful where the laser wavelengths are well within the passbands for the RGB coatings. So, for example, they may work for a red (632.8 nm) HeNe laser, green (532 nm) DPSS laser, and blue (488 nm) argon ion laser - though the last may be too close to green. Custom prisms could be designed but would obviously be very expensive.
(Portions from: Dean Glassburn (Dean@niteliteproducts.com).)
I am sure there are others.
(From: A. E. Siegman (siegman@stanford.edu).)
Suppose you have two beams that are "at the same wavelength" but are not totally coherent with each other (that is, are not totally phase-locked to each other more or less cycle by cycle), *and* suppose also that each of these two beams has some definite polarization (that is, each one is purely linearly polarized, or purely circularly polarized, or some definite elliptical polarization).
Then, there will be a variety of ways that you can combine these two beams into a "single beam" using some kind of polarization beam combiner. (Example: Convert each beam to linear polarization, one of them x-polarized, the other y-polarized, and use a polarization beam combining prism.)
If you do this, you will, sort of, have one beam with twice the power. However, I put the term "single beam" in quotes above, because this beam will have more or less random polarization; and one beam with two randomly related polarization components, that is, with no coherence between the two polarizations is really, in a fundamental sense, two overlapping beams.
If your two starting beams are, on the other hand, totally coherent (e.g., maybe both derived from the same laser source), then you can make a beam combiner with two ports in (for the two source beams) and two output ports for the two output beams. A simple beamsplitter or fiber 3 dB coupler would be examples of this.
As you vary the relative phase between the two input beams in this case, you will see that the output signal will switch back and forth between the two output ports. If you adjust the phase so all the power comes out either one of the output ports, that output will be a true *single-mode* beam, with twice the power, and a single definite polarization.
If the two starting beams are somewhere between these limits - a.k.a. "partially coherently related" - you can get somewhere in between these two limits.
(From: Christoph Bollig (laserpower@gmx.net).)
Here is a highly complicated method to combine a number of single-frequency beams of equal power:
Use a 50/50 beamsplitter to combine two beams and electronic feedback to make sure you get all the power in one direction by interference. You need to have very accurate phase front matching and the electronic feedback has to phase lock one laser to the other. To combine four lasers, you would then combine the two combined beams of two pairs, for eight lasers you need to combine in three steps and so on.
I don't know whether this has been done successfully, but I know that someone worked on it a couple of years ago with four lasers. I haven't followed it, but I could find out if anyone is interested.
Certainly not something for the hobby laserist.