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    Introduction to Items of Interest

    This chapter represents a potpourri of general laser information. Basically, when something interesting and relevant to lasers shows up on one of the USENET newsgroups or elsewhere, it gets stuck in here. Therefore, given the great breath and depth of the laser field, the content is quite sparse - but growing. As always, I welcome contributions to help expand quantity and level of detail of laser related topics.

    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.

  • Back to Items of Interest Sub-Table of Contents.

    Laser Power Meters, Photons, How Much Light?

    What Makes a Laser Power Meter So Expensive?

    Commercial laser power meters cost $300 and up - $1,000 is a more typical price for something that works over a wide range of power levels and wavelengths. Where the precision and automatic wavelength calibration of these instruments is not needed, a basic laser power meter can be built inexpensively. See the section: Sam's Super Cheap and Dirty Laser Power Meter.

    There are several ways to design a device that will determine the power in a beam of light. Here are two:

    Here are some comments on these approachs:

    (From: Bill Sloman (sloman@sci.kun.nl)).

    The important thing to note is that a photo-diode actually detects photons, not power. Up to about 850nm, each photon actually reaching the diode junction generates one pair of charge carriers. A 425nm photon, carrying twice the energy of an 850nm 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 meands --- sam).

    Measuring Power of Short Pulses

    If your laser puts out short pulses - 15 ns at a 20 Hz rate, for example, a simple photodetector that is good for a CW beam may not provide all the information you need - and may not even be accurate if its frequency response is too limited.

    (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.

    Sam's Super Cheap and Dirty Laser Power Meter

    Hobbyists and experimenters may not need the super precision or automatic features of a commercial (and costly) laser power meter. For example, the wavelength or wavelength distribution of the laser source is almost always known. Therefore, if a correction needs to be computed using mushware (i.e., the stuff between your ears), so be it. There will be no absolute reference either but calibration using a source with known output power and wavelength like a 1 mW HeNe 632.8 nm laser will work just fine. And, if you really want a 16 digit LCD display, one can always be added. :-)

    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:

                         R1 1K           1       2
            Vcc o---------/\/\---------+----|<|----+
                                       | 4       3 |
                                       +----|<|----+ U1
                                       | 5       6 | AE1004
                                       | 8       7 |
                            M1                     |
                       +---------+                 |
                     - | 0-10 mA | +               | PD
            Gnd o------|  \      |-----------------+
                       |    o    |       <- I

    A pair of op-amps can be added to provide more flexibility. The following circuit is substituted for the meter (M1), above. Any general purpose op-amps (e.g., 741) powered from +/- 12 VDC (for 10 V full scale) can be used.

                     R2 1.11K
                +------/\/\------o X1
                |    R3 11.1K  X10    S1 Range Select
                +------/\/\----o <---o--+
                |    R4 100K            |
                +------/\/\---+--o X100 |             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. With R7 set to 1.22 K, the ranges will be .01 mW, .1 mW, and 1 mW per V of Vout at 632.8 nm. 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.

    Many variations and enhancements to this circuit are possible.

    So How Many Photons are Coming Out of My Laser?

    This is a simple calculation based on knowing the energy of each photon (based on wavelength):
                                  1,240 nm
              E = 1.602E-19 J * -------------
  • Lambda is the wavelength of your light source.
  • 1,240 nm is the photon wavelength with an energy of 1 ev.

    Then, photon flux = P/E where P is the beam power.

    For example, a 1 mW, 620 nm source will produce about:

                 1E-3 / (1.602E-19 * 2) = 3E15 photons/second.

    How Much Light Does a 5 W Laser Really Produce?

    The somewhat surprising answer is: About the same as a 100 W incandescent or 40 W xenon HID lamp. But, a 5 W mixed gas ion laser requires several KW from a 240/208 V three-phase line and is water-cooled! Of course, what you do get for all that global warming is a nice collimated beam which would be difficult or impossible from a conventional light source. And, with single line optics, the beam is also monochromatic and coherent. So, it may all be worth it!

    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 xenon 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!

    (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 1000 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. :-)

  • Back to Items of Interest Sub-Table of Contents.

    Pulsed/Average Power, Q-Switching

    Average Power from Pulsed Laser


    What is Q-Switching?

    A Q-switched laser is a type of (or modification to) a pulsed laser which shortens it output pulse width, boosts peak output power, and improves the consistency of the output from pulse to pulse.

    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.

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    Difference between Fabry-Perot and DFB lasers

    The Fabry Perot laser design is what most people think of: lasing medium with mirrors at each end.

    (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 .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 Feed Back) 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.

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    What is a Brewster Window?

    Where a (usually gas) laser does not use internal mirrors, the windows between the inside and outside of the tube are not mounted perpendicular to the axis of the resonator but are angled. This isn't just to make the apparatus look sort of cool. :-) At this 'Brewster angle', light polarized parallel to the plate or window is totally reflected and light polarized perpendicular to it is totally transmitted. 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 laser at all!

    The Brewster angle, theta(b), is computed as:

                            theta(b) = arctan(n)
    where n is the index of refraction of the window material and the index of refraction on either side of the window is assumed to be exactly 1. Theta(b) is measured with respect to a plane perpendicular to the tube axis.

    For an n of 1.5, typical of optical glass, this results in a Brewster angle of approximately 57 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.

    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 and the output beam will therefore 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!

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    Laser Wavelengths, Visibility, and Color

    Wavelengths of Some Common Lasers

    Source: Rockwell Laser International Laser Tutorials.
         Laser Type                                  Wavelength (Micrometers)
       Argon Fluoride (Excimer-UV)                            0.193
       Krypton Chloride (Excimer-UV)                          0.122
       Krypton Fluoride (Excimer-UV)                          0.248
       Xenon Chloride (Excimer-UV)                            0.308
       Xenon Fluoride (Excimer-UV)                            0.351
       Helium-Cadmium (UV)                                    0.325
       Nitrogen (UV)                                          0.337
       Helium-Cadmium (violet)                                0.442
       Krypton (blue)                                         0.476
       Argon (blue)                                           0.488
       Copper Vapor (green)                                   0.510
       Argon (green)                                          0.514
       Krypton (green)                                        0.528
       Frequency Doubled Nd:YAG (green)                       0.532
       Helium-Neon (green)                                    0.543
       Krypton (yellow)                                       0.568
       Copper Vapor (yellow)                                  0.570
       Helium-Neon (yellow)                                   0.594
       Helium-Neon (orange)                                   0.610
       Gold Vapor (red)                                       0.627
       Helium-Neon (red)                                      0.633
       Krypton (red)                                          0.647
       Rhodamine 6G Dye (tunable)                          0.570-0.650
       Ruby (Cr:AlO3) (red)                                   0.694
       Gallium Arsenide (diode-NIR)                           0.840
       Nd:YAG (NIR)  Nd:YAG (NIR)                             1.064
       Helium-Neon (NIR)                                      1.15
       Nd:YAG (NIR)                                           1.33
       Erbium (NIR)                                           1.504
       Helium-Neon (NIR)                                      3.39
       Hydrogen Fluoride (NIR)                                2.70
       Carbon Dioxide (FIR)                                   9.6
       Carbon Dioxide (FIR)                                  10.6

    Relative Visibility of Light at Various Wavelengths

    The following table lists the relative sensitivity of the Mark-I eyeball to wavelengths (including common laser sources) of light throughout the visible spectrum and somewhat beyond. Of course, not eveyone comes equally equipped. Your mileage may vary (and the number of significant figures in some of these entries should not be taken too seriously)!

    (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
        420 nm    .0175    Violet
        442 nm    .0398    Violet-blue    Violet blue line of HeCd laser
        450 nm    .0468    Blue
        457.9 nm  .0562     "             Blue line of argon ion laser
        488       .191     Green-blue     Green-blue line of argon ion laser
        500 nm    .323     Blue-green
        514 nm    .588     Green          Green line of argon ion laser
        532 nm    .885      "             Green freq.-doubled Nd (including YAG)
        543.5 nm  .974      "             Green HeNe laser
        550 nm    .995     Yellow-green
        555 nm   1.000      "             Reference (peak) wavelength
        568 nm    .964      "             Y-G line of some krypton ion lasers
        580 nm    .870     Yellow
        594.1 nm  .706     Orange-yellow  Yellow HeNe laser
        600 nm    .631     Orange
        611.9 nm  .479     Red-orange     Orange HeNe laser
        632.8 nm  .237     Orange-red     Red HeNe laser
        635 nm    .217      "             Laser diode (DVD, newer laser pointers)
        647.1 nm  .125     Red            Red line of krypton or Ar/Kr ion laser
        650 nm    .107      "             Laser diode
        660 nm    .061      "             Laser diode
        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    3.7E-6    "
        850 nm    1.1E-7    "
        900 nm    3.2E-9    "
      1,064 nm    3E-14     "             Nd lasers (including YAG)
      1,523.1 nm  0.0000    "             IR HeNe laser
     10,600 nm    0.0000   IR             CO2 laser
    This is according to the 1988 C.I.E. Photopic Luminous Efficiency Function. 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 way you will seen them is for about a microsecond before your eyeballs, your head, or you in the entirety is vaporized due to the high power required --- sam).

    I know that argon lasers have a blue line (457 nm), a green-blue one (488 nm), an emerald-green one (514), and a yellow-green one. I don't know the other wavelengths. I have seen them in the less extreme two (deep blue-green color), and the more extreme two (slightly whitish blue-green color). Every time I ever got a spectrum of these, I saw the 488/514 lines or the roughly 457 and 560 lines. Never 1 or 3 or 4 nor other combinations of 2 in my very small sample. The strongest lines for argon are at 488 and 514 nm. The one at 488 nm is found in single line argon ion lasers.

    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 indicates 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: Visibility of Near-IR (NIR) Laser Diodes and Spectra of Visible and IR Laser Diodes.

    Determining the Wavelength of a Laser

    You may be able to tell the difference between a 670 nm laser and one at 635 nm by eye. The shorter wavelength will be more towards the orange part of the spectrum. But to distinguish a difference of 10 nm, not likely - you need a spectroscope. So, what is the easiest way to do this to confirm that the bargain laser pointer you purchased really is at the advertised wavelength?

    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. See the section: Use of a CD, CDROM, CD-R, or DVD Disc as a Diffraction Grating for sources of free diffraction gratings.

    As another cure for insomnia, consider how to determine the wavelength of a laser with just a Stanley ruler (machinist's scale)!

    Wavelength versus Frequency

    (From: Hoffman (hoffman@northeast.net)).

    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: Skywise (skywise@spamless.internetmci.com)).

    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. 632.9nm 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 (terahertz = 10^12 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 (c) = 299792458 m/s exactly.)

    Comments on Various Color Lasers

    (From: Mike Poulton (tjpoulton@aol.com)).

    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!

    What About X-Ray Lasers

    Constructing a coherent source of X-rays is made difficult by a number of factors including: There have been several approaches: (From: Allen L. Johnson (alj@alumni.caltech.edu)).

    To which I add:

    If you are looking for coherent X-rays, then undulators work. If you are looking for very intense X-ray sources, pinch tungsten plasmas were looked at in the USSR.

  • Back to Items of Interest Sub-Table of Contents.

    Speckle, Coherence, Stability

    What is Laser Speckle?

    Speckle is a mottled pattern that arises when laser light falls on a non-specular reflecting surface. Lasers with high spatial and temporal coherence properties are likely to produce dramatic speckle effects. Thus, gas lasers like HeNe types are more likely to exhibit this effect than laser diodes.

    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).

    Controlling Laser Speckle

    Where a laser is used for its feature as a bright light source that can be easily manipulated, speckle and other interference phenomena resulting from its coherent nature may be undesirable:

    (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:

    1. Increase the spatial frequency of the speckle so that it is so high it ceases to be a problem.

    2. Use only specular objects and sources.

    3. Decrease the temporal and/or spatial coherence of your laser beam by running it through something like a rotating diffuser.

    (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!

    Comments on Spatial and Temporal Coherence

    Also see the section: Coherence length of HeNe lasers.

    (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!

    Laser Instability

    You may have even noticed this effect when lining up a HeNe laser where a reflection of its beam returns to the output end of the tube. Under these conditions, the output can become unstable and fluctuate widely.

    (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 :).

  • Back to Items of Interest Sub-Table of Contents.

    Beam Collimation, Divergence, Focus, Cleanup

    Collimation, Divergence, Focus

    Collimation refers to the degree to which the beam remains parallel with distance. A perfectly collimated beam would have parallel sides and would never expand at all. Its divergence angle would be exactly 0. This is impossible except in Sci-Fi movies.

    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). (Refer to the diagram: Divergence, Beam Waist, Rayleigh Length but keep in mind that the divergence in the diagram is greatly exaggerated.) The equation for a plane wave source is:

                                                         Wavelength * 4
            Divergence Angle (in radians) = Theta/2 = --------------------
                                                       pi * Beam Diameter
    where Theta is the total divergence angle. 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). And, the location of the effective point source does not generally coincide with the laser's output aperture. 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 is:

                                 2 * wavelength * (lens focal length)
                Spot Diameter = --------------------------------------
                                           pi * diam(beam)
    So, for an ideal HeNe laser (common inexpensive HeNe lasers come pretty close) with a .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 20.14 um.

    Rayleigh Length

    Another way of characterizing divergence is to calculate how far the beam can travel before it expands significantly. There is a maximum distance that a beam of light can be kept collimated. Usually it is called the 'Rayleigh length' or 'Rayleigh range' as shown in the diagram: Divergence, Beam Waist, Rayleigh Length. (Note that the divergence in the diagram is GREATLY exaggerated). The Rayleigh length depends on the wavelength and the minimum diameter 'waist' of the beam (as well as the beam cross-section but that is for the advanced course!).

    Unlike an ordinary light source, 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). Therefore, the divergence equations given above are actually approximations assuming that the measurement is made some distance beyond this point.

    (Portions provided by Steve Roberts: (osteven@akrobiz.com)).

    If there is one optics book you must own, it is:

    It contains a nice balance of practicality and real world design problems including the sensor electronics and theory. Good for high school students and Ph.D. types, as well as tinkerers. Oshea is an engineer's engineer.

    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)
    where: We define the Rayleigh range, Z_Rayleigh, as the distance from the beam waist where the beam diameter has increased to: Sqrt(2) * Do. Obviously that occurs when the second term under the radical is unity.

    So this results in:

                                Z_Rayleigh = -------
    Plugging in the equation for divergence (from the section: Collimation, Divergence, Focus, we get:
                                           pi * Do^2
                           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:

    What is M-Square?

    For more than you could ever possibly want to know, see: Professor Anthony E. Siegman's References on Laser Beam Quality

    (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
                   M^2 = -----------------
                             2 * Lambda
    Where: For the ideal gaussian beam with the fundamental mode, M-square is 1. It increases for modes of greater divergence or greater focal area. This is just a brief explanation for M-square. You can find more detailed information from following references:
    1. Laser Focus World, May 1990, pp. 173-183.

    2. Catalog of the ModeMaster, Coherent Components Group.

    3. A. E. Siegman, "New development in laser resonators," Presented at Conference on Laser Resonators SPIE/OE LASE'90, Los Angeles, CA, January 1990.

    Modifying or Improving Collimation

    The beam from a gas laser like a HeNe or Ar/Kr ion type is already very well collimated while that of a diode laser without additional optics is widely diverging (wedge-shaped). In both cases, the divergence angles are nearly optimal given the original beam diameter (cavity dimensions) but better collimation or just a different divergence may be needed depending on the application (almost always for a diode laser!). See the book "Lasers" by A. E. Siegmann for the details of the propagation of laser light. (page 664 ff.)

    Problems with Laser Beam Divergence or Focus

    So you have all your optics set up 'by the book' but that spot refuses to focus as well as theory predicts or the divergence angle resembles that from a flashlight more than a laser :-(. What else is there? Aside from obvious problems such as an error in your calculations (no way, right?!) or defective, dirty, or improperly positioned optics, consider the source itself. Is your laser really producing a high quality TEM00 beam? In addition to improperly aligned mirrors or damage, the laser may be multimode to begin with. Does it have a nice Guassiam profile at its output aperture?

    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.

    (From: Lynn Strickland (lstrickland@carlsbad.mellesgriot.com)).

    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.

    Laser Beam Cleanup - the Spatial Filter

    The raw output of a typical laser, even one that is usually considered to be of high quality like a HeNe laser, consists of the main beam (what you want) and noise (what you don't want) - extraneous light scattered from dirt or imperfections in the mirrors, the sides of the bore, not quite totally suppressed transverse modes, you name it. This will result in ghost patterns, rings, and other undesirable artifacts. For experiments with interferometry, holography, Fourier optics, and other precision optical systems, the beam really needs to be cleaned up so that this noise is removed and only the nice high quality well behaved Gaussian main beam remains.

    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:

    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.

    More on Spatial Filters

    Using just the simple pinhole isn't going to result in a nice Gaussiun beam because of diffraction from its edges. If nothing else is done, there will be a Gaussian central profile in the collimated beam and some ring artifacts surrounding it. A little more work is needed if this matters for your application.

    (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.

  • Back to Items of Interest Sub-Table of Contents.

    Diffraction gratings, Pattern Generation

    Diffraction Gratings

    A diffraction grating consists of a plate or film with a series of closely spaced lines or grooves (typically many thousands per inch/hundreds per mm). The simplest types are planar but gratings with other profiles are often used in spectroscopes and other optical instruments. Gratings may also be formed in a volume of material intentionally (see the section: Acousto-Optic Modulators and Deflectors) or as (usually undesirable) side effects of optical propagation or piezo induced stresses (in optical fibers, for example). Diffraction gratings may be of the transmission or reflection type but in both cases, their behavior is governed by the same equations. The only difference is whether the beam passes through or is reflected from the grating. The latter type will be coated with a thin film of reflective material like aluminum or gold. See Diffraction Grating Principle for an illustration of the behavior of a transmission grading with a plane wave source.

    The basic diffraction equations for a collimated beam at normal incidence are:

                             n * lambda                   s * sin(theta)
             theta = arcsin(-----------)   or   lambda = ----------------
                                 s                              n
    where: The geometrical interpretation is very simple: As a result of the fundamental behavior of waves, a new wavefront is launched whenever a light beam encounters a discontinuity. (In the case of a point discontinuity, the resulting wavefront is spherical. In the case of a line discontinuity, it is cylindrical.) When the phases of these waves are all the same, a maximum in intensity will occur. In between, the net intensity will be virtually zero. This is the same effect which make a phased array radar possible. The equations above are simply a statement of the angles for which this condition is satisfied.

    Since deflection angle is a function of wavelength, diffraction gratings are very widely used for spectroscopy. They have largely replaced prisms for this and other optical instruments.

    The 'order' of each beam is specified by the value of 'n' with the first order (n = 1) beams usually being the ones important for spectroscopy and other similar applications. By controlling the shape of the cross-section of the grooves (called blazing), the grating may be optimized for non-zero orders over a particular range of wavelengths.

    Clearly, for a given wavelength, the groove spacing (s) of the diffraction grating determines the angles and number of possible higher order beams:

    For a screen at distance, d, from the grating:
                     p = d * tan(theta)   or   theta = arctan(---)
    where: Trig conversions are left as an exercise for the student. :-)

    For example, in the case of a HeNe laser and a CD being used as a diffraction grating (lambda = 632.8 nm, s = 1.6 um), only 0th, 1st, and 2nd order beams will be produced and theta will be 0, 23.3, and 52.3 degrees respectively. After calculating these angles, I set up a very rough experiment with a 1 mW HeNe laser, gold CD-R, and tape measure. The error was less than 0.5 degrees! See the section: Use of a CD, CDROM, CD-R, or DVD Disc as a Diffraction Grating for more information about these free diffraction gratings.

    To find out more about practical uses of diffraction gratings, locate a copy of the Scientific American collection "Light and its Uses" which has a variety of articles on "Instruments of Dispersion" (in addition to those on amateur laser construction, holography, interferometers). Check out Light and its Uses - Complete Table of Contents for an idea of what is there. Finally, for more than you could possibly ever want to know about diffraction and spectroscopy - including the math - see The Optics of Spectroscopy.

    Use of a CD, CDROM, CD-R, or DVD Disc as a Diffraction Grating

    You have no doubt been impressed by the neat and nifty rainbow patterns seen in the reflection off of a compact disc. This is due to the effect of the closely spaced rows of pits acting like a diffraction grating.

    How good is it?

    I tried an informal experiment with both a normal music CD and a partly recorded CD-R (using the label side of the CD-R as the green layer on the back is a great filter for 632.8 nm HeNe laser light!).

    Both types worked quite well as reflection gratings with very sharply defined 1st and 2nd order beams from a collimated HeNe laser. There was a slight amount of spread in the direction parallel to the tracks of the CD and this was more pronounced with the music CD, presumably caused by the effectively random data pits. The plastic (readout side) or coating (label side) the beam must pass through (depending on which side you use) may also result in some degradation from surface imperfections as well as ghost images due to multiple internal reflections but I did not notice much of this.

    If you can figure out a non-destructive way of removing the label, top lacquer layer, and aluminum coating, the result should be a decent transmission type grating.

    Note that there is usually no truly blank area on a normal CD - the area beyond the music is usually recorded with 0s which with the coding used, are neither blank nor a nice repeating pattern. The CD-R starts out pregrooved so that the CD-writer servo systems can follow the tracks while recording. There is no noticeable change to the label-side as a result of recording on a CD-R.

    Track pitch on a CD is about 1.6 um or about 15,875 grooves per inch, quite comparable to some of the commercial gratings from Edmund Scientific or elsewhere. Note: I don't know how precise the value of 1.6 um is for a normal CD and some CDs may use a slightly small track pitch (violating the specs) to cram more music onto the same size disc! However, given the equations in the section: Diffraction Gratings and a laser of known wavelength, you should be able to easily determine the track pitch of any particular CD!

    For a 1 mm HeNe spot, the curvature of the tracks doesn't significantly affect the low order diffraction patterns. However, for larger area beams, this will have to be taken into account - using outer tracks will be better.

    Most other optical media can be used as diffraction gratings as well. DVDs (Digital Versatile Discs or Digital Video Discs depending on who you ask) in particular may be even better at this (greater deflection angles/higher dispersion) as their tracks are much closer together than those on CDs.

    Generating Lines or Crosses of Light

    This is easy to do with a laser - as well as with a slide projector and piece of film or aluminum foil!

    Also see the section: Diffractive Pattern Generating Optics for information on producing a variety of patterns from a single laser beam.

    Projecting a 1-D or 2-D Grid of Dots or Lines

    The natural tendency is to use a laser of some sort. However, a Kodak (or other) slide projector with a zoom lens (if needed for the distance) and appropriate grid or dot slide would be far cheaper than a sufficiently powerful laser for many applications. Splitting a laser pointer or other 5 mW diode laser n-ways may result in inadequate brightness. It will be much easier to obtain uniform brightness with the low tech approach as well!

    For the laser solution:

    The spread of the individual spots or lines is inversely related to the pitch of the diffraction grating. However, the brightness of the dots or lines may not be even close to uniform since the intensity decreases with the order of the diffracted beam. In fact, depending on the pitch of the grating and distance to the screen or illuminated object, only the 0th (undeflected), 1st, and perhaps the 2nd order spots or lines will be visible. Lower density gratings (fewer lines/mm) will result in a larger number of more uniformly spaced higher order spots or lines of more nearly equal brightness, but they will be dimmer and more closely spaced (not deflected as much).

    Also see the sections Diffraction Gratings for basic equations and Diffractive Pattern Generating Optics for information on producing a variety of patterns from a single laser beam.

    Diffractive Pattern Generating Optics

    A variety of diffractive pattern generator optics are commercially available to produce lines, crosses, arrays of spots, grids, circles, and no doubt many other (even custom) configurations (e.g., company logos) from a single collimated laser beam without the need for any other optical elements. Also see the section: Diffraction Gratings.

    These parts are fabricated using a holographic process (they are also called Holographic Optical Elements or HOEs). In ordinary light, they look just like a little slightly dirty glass plate - same as a hologram. The magic happens with a laser (though I bet you would get a nifty rainbow pattern using a high intensity white light source).

    These patterns should be quite uniform in intensity (unlike those produced using simple diffraction gratings).

    And, the answer to your next question is: No, you really can't make these in your basement - at least not unless you have a sophisticated holography setup.

    Where you have a laser pointer or other laser source, another option at least theoretically is to add an optical system at its output and project the image of a very tiny transparency in a manner similar to a slide projector but using the laser as the light source. However, while in principle this can be done with a couple of short focal length positive lenses (maybe one if your source has a focusing adjustment) and a transparency perhaps the size of the Super-8 movie frame (if you remember what they were!), your likelihood of creating a setup that is useful in practice is pretty small since everything has to mounted securely and precisely in-line but only ONCE you determine the correct position of each element and the slide. AND, as if this isn't enough, there will likely be serious interference and speckle effects from the coherent light which can totally obscure the image you are trying to project! So, add in a spatial filter which means your nice simple pointer will be turning into something more along the lines of a complex precision optical bench!

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    Modulation, Deflection

    Acousto-Optic Modulators and Deflectors

    These are devices to modulate or deflect a beam of (usually laser) light without any moving parts (at least at the macroscopic level). If a acoustic wave is induced in a cell with transparent sides containing a suitable medium, the resulting density variations will act like a diffraction grating to light passing through it. This can be used to modulate or deflect a laser beam at a very high rate.

    A piezo-electric element driven from a high frequency source (MHz or GHz) is used to generate the standing wave.

    However, these devices are complex, expensive, and not nearly as efficient as simple mechanical systems like galvos, motors, or even loudspeaker cones! Therefore, where speed isn't critical, mechanical systems are almost always a better choice. See the section: Comments on Mechanical Deflection.

    (From: Tom Yu (tlyu@mit.edu)).

    The majority of acousto-optic modulators are traveling wave designs and require an acoustic termination at the end of the crystal (or other medium) opposite the piezoelectric driver. Acousto-optic modulators can operate with either longitudinal or transverse (shear) acoustic waves. Shear wave devices seem to be used mostly in birefringent or otherwise non-isotropic materials in order to do weird tricks like polychromatic modulators (PCAOMs), which can modulate the intensities of multiple wavelengths at once while maintaining beam collinearity. These amazing devices actually seem to be relatives of the acousto-optic tuned filter (AOTF).

    Anyway, the acoustic wave creates a three dimensional (volume) phase grating in the crystal by means of the local changes in the index of refraction (the photoelastic effect). This is in contrast to most diffraction gratings that you might encounter because those are typically two dimensional. You can imagine a "normal" 2D grating as lines ruled on a thin piece of glass, and a 3D "Bragg" grating like a lot of parallel plates of metal embedded in a block of glass.

    The important difference is once the interaction length (the width of the acoustic beam that the optical beam intersects) exceeds a certain critical value, diffracted optical beam orders above the first are effectively canceled out by destructive interference. There is a parameter that relates the acoustic wavelength, the optical wavelength, and the interaction length, and can be used to determine whether the diffraction occurs in the Bragg regime, which has one principal diffracted beam or the Raman-Nath regime, which has multiple diffracted beams.

    Naturally, most AO modulators that are used for modulating laser beams want to run in the Bragg regime. Notably, in the Bragg regime, there is a certain critical angle, the Bragg angle, which the optical beam must make relative to the acoustic beam for any diffraction to occur at all. Once this happens, changing the acoustic power level will modulate the intensity of the first-order diffracted beam relative to the zero-order (undiffracted) beam. The input acoustic waveform can also be frequency modulated in order to change the deflection of the beam.

    Some references:

    (From: Michael Fletcher (oh2aue@personal.eunet.fi)).

    Acousto-Optic (AO) modulators can in many different styles, but basically the idea is to AM or PM the laser light beam passing through the modulator.

    One simple way easy to understand these is:

    Splitting the beam into two paths and mechanically modulating the other path so that when the two beams are summed again you have your modulation superimposed on the sum beam.

    Mechanical modulation can done directly via a piezo-element. More elaborate methods are also used.

    The beam can be fed through a medium like pure water (!) or Lithium Niobate.

    Now if the slab of LiNb2 is rectangular and the beam is set to a particular angle, the beam (which needs to be formed in a homogeneous fan with a set of prisms for example) may be diverged off axis by a mechanical density modulated front - like a grating. This "grating" can be also generated by acoustical pressure waves induced by a piezo-electric element. The waves emitted from the piezo need to be matched into a load for mechanical energy. The piezo can be run at RF frequencies if the medium is capable of operating in the described manner. For water you might have a few hundred MHz and for LiNb2 you might expect something in the GHz range. LiNb2 is the same stuff SAW (Surface Acoustic Filter) filters are usually made of. The RF is also launched and received by Piezo-elements.

    One of the problems with piezo-elements is of course the inherent high impedance which we would like to match to 50 ohms in a broadband fashion. Pretty tough. The power levels usually needed in several watts of RF to excite the density modulation in the medium.

    (Portions provided by Steve Roberts: (osteven@akrobiz.com)).

    An AO modulator uses ultrasonic waves to set up a virtual diffraction grating in a crystal. The special case of sinusoidal waves results in only the zeroth and first order beams emerging from the grating (assuming that the beam is aligned with the crystal). This is a consequence of the Fourier Transform of a sinusoid having only DC and a pair of fundamental frequency spikes. Turning the RF drive to the transducer that creates the standing wave on and off does the same with the first order beams; amplitude modulating the drive amplitude modulates the first order beams. Changing the frequency of the RF drive causes the unit to scan, over a very small angle, or FM modulate the beam if the AO crystal is at 0 degrees to the input beam. The AO is angle sensitive and needs a fairly high precision mount.

    Kerr Cell, Pockel's Cell, and Photo-Elastic Modulators

    These are all approaches to implementing high speed non-mechanical (at least in the macro sense) modulation by affecting the birefringence properties of an optical material and thus the polarization of the light beam passing through the device. The Kerr cell is probably the oldest of these and generally used nitrobenzene - a flammable, toxic, liquid - and required very high control voltages (e.g., thousands of V). The Pockel's cell is based on the same physical principle but uses entirely solid state materials and more modest driving voltages (e.g., a few hundred V). The opto-elastic modulator uses piezo-electrically induced stress rather than electric fields to affect the birefringence of a crystalline material. In addition to these approaches, high performance LCDs, acousto-optic, and ferro-optic modulators may be appropriate depending on the application. Also see the section: Acousto-Optic modulators and Deflectors.

    A Kerr cell consists of a rectangular clear glass or plastic container filled with nitrobenzene. A pair of electrodes on one pair of sides are connected to the source of the modulation - a high voltage driver. Polarizers in front and behind the device may be set up to normally block or pass light through the cell (90 or 0 degree orientation respectively). When a high voltage electric field is applied, the nitrobenzine acts as an intermediate polarizer. This permits (or blocks depending on how the polarizers are set up and with respect to the orientation of the electrodes) the passage of light.

    (From: Louis Boyd).

    Yes, nitrobenzene burns but it needs an oxidizer. and isn't good for you to drink for breathe fumes or pour on your skin but a few cc's in a sealed glass container isn't a tremendous hazard. Simple film polarizers on either side of the container work. If the modulation is ONLY in the KHz range a flyback transformer from a TV should make a fine modulator. 1 cm square aluminum plates 1 cm apart should do the job. The ones I have used were blown from glass but some plastics should work. Check for nitrobenzene compatibility. As for frequency response, Kerr shutters are don't cover octaves but I wouldn't call them narrow band.

    (From: Francoise Delplancke (fdelplan@ulb.ac.be)).

    Pockel's cells are based on the electro-optical effect (Kerr's effect if I remember well). What is this effect? In some special crystals (like KDP = potassium di-phosphate), one can observe that the crystal birefringence depends on the electrical field applied transversally to the crystal. This relation is linear on a certain range.

    A Pockel's cell is composed of several long aligned (KDP) crystals. An electrical field is applied perpendicularly to their longest dimension. This is a high voltage field (about 250 V, but much less than for a Kerr cell). You get so a voltage-variable wave plate. By modulating the electrical field, you modulate the birefringence of the cell. The number and geometrical arrangement of the crystals is intended to correct for parasitic birefringence (caused by double refraction...).

    The main advantages of Pockel's cells are:

    Their disadvantages are: A good paper on electro-optic modulation is: "Electro-optic modulation: systems and applications. Demands for wider-band beam modulation challenge designers" by Robert F. Enscoe and Richard J. Kocka in Lasers & Applications, June 84, pages 91-95.

    A photo-elastic modulator is, evidently, based on photo-elasticity! The birefringence of some materials (like quartz or araldite-polymer) is depending on the strain-stress state which is present in the material. Here too, the birefringence is directly proportional to the internal strain.

    The photo-elastic modulators I used were made of two identical pieces of quartz (parallelpiped prisms) glued together by one of their sides. Then one uses the piezo-electric properties of quartz to generate elastic shock waves in the quartz beam. It is : by applying a modulated electric field on the opposite sides of one of the blocks, one generates modulated deformations in this first block and the deformations are transmitted to the second block. The deformations induce stresses in the second block and so birefringence.

    The trick of this method is to arrange the block sizes, the modulation frequency and the block holders so that an elastic stationary wave is generated in the quartz beam and that an anti-node (ventral segment) corresponds to the center of the second block, where the light beam will pass through. If so, on this antinode, the birefringence will be modulated at a precise frequency with a maximum amplitude and the system will be very stable. But there is only one frequency (and its harmonics) working with one quartz beam : its resonant frequency.

    The advantages of photo-elastic modulators are :

    Their disadvantages are: I do not remember, for the moment, the titles and references of papers on photo-elastic modulators but one of the main authors was J. Badoz and it was published in known optical journals (Applied Optics, JOSA, Optics letters or Review of Scientific Instruments, I do not remember exactly). He discusses also the parasitic effects of his device.

    Comments on Mechanical Deflection

    While some supermarket UPC scanners are supposed to use holographic optics and high performance systems may use acousto-optic (Bragg) or other exotic means to deflect the beam in complex patterns, there is a lot to be said for simple mirrors, galvos, or other basic mechanical approach. However, also see the section: Acousto-Optic Modulators and Deflectors.

    (From: Gregory J. Whaley (gwhaley@tiny.net)).

    In spite of the existence of holographic bar code scanners, I have never come across one in a retail store. Of the retail store scanners I have observed, all are either polygon mirrors (cabinet built-in) or resonant scanners (hand-held). It is an impressive feat of mechanical engineering that the vast majority (>99% by number of units) of all laser and optical scanning systems use moving mass mirrors or lenses to push (massless) photons around. Here, I include laser printers using polygon mirrors, and resonant or galvo mirrors, as well as CD and other optical recording systems which literally push objective lenses back and forth at high speeds. Actuated opto-mechanics is the technology of choice even in the lowest cost, highest volume products.

    Hats off to our colleagues, the opto-mechanical engineers!

  • Back to Items of Interest Sub-Table of Contents.

    Laser Communications

    Basic Description

    The term 'laser communication' can mean many things but generally refers to the transmission of information via a laser beam in free-space or a fiber-optic cable. A laser communications system must then consist of:

    Amateur Laser Communications

    For more information and discussions on amateur laser communications, join the Laser Reflector. It is run by ham radio operators who do long distance free-space communications. One is working on laser EME (Earth-Moon-Earth), and another is into non-line-of-site weak signal operation using low baud rate long term integration and advanced DSP techniques with coherent signals!

    The Laser Reflector Web site provides archives of past discussions indexed by date (year and month) and a large set of links to other laser and laser communications sites.

    Offers of inexpensive lasers, laser components, and other related items also appear from time-to-time via this email discussion group.

    Anyone with an interest in laser communications is welcome to join. You don't need to be a ham radio operator. Just send email to majordomo@qth.net with 'subscribe laser' (without quotes) in the message body.

    See the section: Laser (Email) Listservers for more information about these private email discussion groups.

  • Back to Items of Interest Sub-Table of Contents.

    Laser Humor

    The Ultimate Laser Pen

    Unfortunately, so many supposedly educated people are unable to distinguish science from fantasy - separate out what is theoretically possible, what is practically possible, and what is simply impossible! Hey, I would like one of these super blasters as well. :-)

    (From Steve Roberts (osteven@akrobiz.com)).

    Here is what every little kid (of any age) REALLY wants:

    Hello. I need a 1 megawatt laser pointer that boils water in teacups, fits inside a pair of standard nail clippers so I can get it through security, should have a 1 mm diameter .25 mRad beam that never needs focusing, should be able to dial a color, and run off 2 lithium watch batteries CW for 1 year. In addition it should have a selectable range of 1 foot, 3 feet, 1 yard and infinity, and be able to just zap somebody in a movie theater or vaporize a body without a trace, is eye-safe and runs in bursts up to 1 gigawatt off lightning on demand. For entertainment it should generate a 3D holographic real time free space light show. The force field effect should be optional and it should have a X-Ray vision aiming mode better then the Sony HandyCam Niteshot. Oh, and the price needs to be $29.95 or less as I'm on a budget and need to illuminate the moon before Mommy sends me to bed.

    Man sounds like we really teach great science in high schools!

    BTW, I had my friend at a laser job shop aim his 3,200 W CO2 at a teacup full of H20 for laughs and giggles. This same laser can generate a CW air breakdown. He said the water just swirled a little except when the focus was just touching the water level. There it could suck some water vapor into the air breakdown and changed from a white plasma to a unstable orange one.

    How Much Optical Power to Zap a Balloon or Bug?

    The following are some findings from numerous carefully controlled and documented experiments. Translation: Fooling around when Steve had nothing better to do! Bug type and state of health (before tests) were not identified. My apologies to the SPCB (Society for the Prevention of Cruelty to Bugs). :-)

    (From Steve Roberts (osteven@akrobiz.com)).

    I own air-cooled ion lasers up to 150 mW, water-cooled argon to 1.1 watts, water cooled krypton at 620 mW, and can substantiate these figures. Bugs are hard to kill! It takes a while to burn stuff. None of these is the instant sparks kind of burn - they are all more or less slow melts.

    (From: Chuck Adams (ccadams@ionet.net)).

    I have a Q-switched ruby laser that will pop a balloon at 10 feet with no focusing. I don't know what the output power is but the input power is about 200 J. See video and still frames at: Chuck's Ruby Laser in Action.

    I have not tried a bug yet, but I suspect that it would depend greatly on the bug. This would be nowhere near enough power for a large cockroach, but a white fly would be toast. Hmmm, I wonder anyone has published a table on the "heat of vaporization" for bugs - you know - like for water: calories/gram of bug juice! Does Glendale optical make little bug-sized laser goggles? If not, will you end up with a lab full of bugs with little white canes and severe sunburn?

    Phaser Quality Control

    From a posting on alt.lasers:

    "I bought a phaser at Radio Shack but it wont burn nothing. Can I hook up a bigger battery or plug it in the wall? Did I git ripped off? Is it defective? Who made Captain Kirk's phaser?

    Don't you have the complete Starship Enterprise standard equipment specification and approved supplier manual? It comes on 75 DVDs or 1 DUD. (A DUD or Digital Ultra Disc utilizes the latest UV laser holographic data storage technology but hasn't been invented yet.) No??? You absolutely need to obtain this document to gain access to the Federation manufacturers' database. They won't sell working phasers to the general public without a properly signed and notarized phaser user's contract. However, I understand the paperwork (paper isn't used anymore but the term is more understandable on a forum such as this) is quite involved - it runs the equivalent of about 10,000 single spaced pages...

    BTW, the phaser used by Captain Kirk is no longer made. Sorry, you will either have to hunt around for a used model or get one of the SNG upgrades. I can sympathize with your unhappiness at the latter prospect. While the SNG models DO have many more bells and whistles, the original phasers had superior ergonomic design and were apparently much more effective than those used a couple of centuries later - which generate a beam that travel so slowly, getting out of its way is quite easy. And what is decidedly a step backwards, the new ones can at most only BURN things - the phasers used in Kirk's era would make large objects totally disappear requiring no messy cleanup afterwards and were thus much more environmentally friendly.

    The other problem is that you went to Radio Shack for this. :-)

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