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:
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.
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. Download #22, "Photometry and Radiometry: A Tour Guide for Computer Graphics Enthusiasts". This is a .zip file containing both an MSWORD and PostScript version of the paper. Also available from Ledalite Library: Photometry and Radiometry.
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: 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).
(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 Photodiodes and UDT Sensors Photodiode Characteristics Page.
Some specific technical information for silicon includes:
A resistance heater is usually 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.
Except for minor details, the description below is similar to the sensors 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: 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.
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. :)
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 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).
Wavelength PD1 Si Resp
----------------------------------
808 nm 1.38 1.27
670 nm 1.08 1.03
633 nm 1.00 1.00
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
+------/\/\------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.
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 are somewhat flakey, most likely due to dirty "zebra stripe" connectors attaching the LCD to the mainboard. However, it would appear that to clean these requires removing 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.
I'm now in search of 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 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. :) (I've since gotten 2 more, one for only $10, as well as a mating sensor head for $10! The readouts are now showing up quite regularly on eBay.) 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. :)
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. 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!)
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.
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.
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. :)
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.
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 beam splitters (e.g., microscope slides) in series with the reflected beam from beam splitter 1 going to beam splitter 2 and sending only the reflected beam from beam splitter 2 to your laser power meter's sensor. Each beam splitter 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 beam splitter 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 beam splitter 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. If the angle of incidence is arranged to be close to 90 degrees (normal incidence) rather than 45 degrees, the error will be small. Commercial beam splitters are also available which are fairly polarization insensitive.
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!!!
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 e
