Understanding Co2 Lasers

8/8/2019 Understanding Co2 Lasers

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UNDERSTANDING CO2 LASERS

A detailed treatment of a laser system that holds greatpromise for high-power applications includes design

procedures and parameter tradeoff considerations

David R. WhitehouseManager, Laser Advanced Development Center

Raytheon Co., Waltham, Mass.

The great interest in carbon dioxide lasers stems from their continuous power

capability, high efficiency and ease of construction. Table 1 graphically illustratestheir advantages over other gas lasers.

The CO2 laser system is shown in Fig. 1. Three gases (CO2, N2 and He) are mixed

and fed into one end of a discharge tube at a pressure of a few torr. The gas flowsdown the end of the tube in about one second and is pumped out the far end with a

mechanical forepump. An electrical discharge is maintained between the metallicend flanges of the tube. The ballast resistance is required because of the negative

dynamic resistance of the discharge. With a fully reflecting mirror on the left and a

partially transmitting mirror on the right, the device becomes a laser which radiatesin the far infrared at 10.6 microns.

The CO2 laser is comparable in simplicity, if not in size, to the microwave klystron.Both have a high-Q electromagnetic cavity, a highly efficient power-output coupling

technique, and an active medium fed from a simple dc power supply. Also, withslight modifications either can be used as an oscillator or an amplifier.

The possibility of using molecular vibrations for laser action was clearly pointed outby Polanyi in 1961. More recently, Patel has described in some detail the laser

action on the vibrational-rotational (V-R) transitions of CO2 in an electrical

discharge. Shortly afterwards, progress towards high power and efficiency wasachieved by Patel with the addition of N2 and by Moeller and Rigden with the

addition of He. Other molecular systems have been made to lase, but so far CO 2 isthe most important power producer.

Many parameters affect the design and operation of the CO2 laser. The gas

discharge can be powered with dc, ac, RF, repetitive pulses, or any combination

thereof. The mirrors can be fixed, rotated for Q-switching, or vibrated for reactiveQ-switching. The discussion here will be limited to dc excitation with fixed mirrors.

Most of the technical data were obtained from Horrigan and Whitehouse; moredetail can be obtained by referring to their reports.

OPTIMIZING THE CO2 LASER

Performance of CO2 lasers may be optimized in several ways: Maximize multimode



power; maximize single-mode power; maximize efficiency; and/or minimize size

and complexity. The parameters that affect such optimization for flowing gassystems are:

y Tube length, diameter and wall temperature y G

as mixture, pressure, and flow speed

y Optical mode control, wavelength control, and output coupling y Electrical discharge control and current density In addition, for sealed-off CO2 lasers, it appears that the gas purity and tubematerials are also important. Optimization is by no means simple, because the

various parameters are strongly interrelated. All results, therefore, should beviewed only as indicative of performance trends. The engineer should be preparedto perform experimental exploration of his own system .

LASER OPTICSThe most common electromagnetic laser cavity consists of two mirrors with circularapertures, as shown in Fig. 2. The reflecting surfaces are segments of spheres with

radii R1 and R2 and separated by a distance, L. The best alignment occurs when

the line joining the centers of curvature is coincident with the geometrical axisthrough the mirror centers and the laser medium. For gas lasers, these mirrors may

be directly mounted on the discharge tube, or one or both o f them may beexternally mounted. If externally mounted, the vacuum exists between optically

polished flat transmitting windows mounted at the Brewster angle given byEquation A where n is the refractive index of the window material. The advantagesof a Brewster-window system are that the laser radiation is polarized and that

mirror tuning is independent of the tube. Its disadvantage is that the windows mustwithstand the high-power laser radiation field inside the optical cavity.

If system aperture is sufficiently large, the radiation pattern inside the laser cavity

can be approximated by a summation of normal modes--each with a different

frequency and spatial distribution determined by the mirror curvatures and spacing.The longitudinal modes have a radial gaussian power distribution approximated by

Equation B where the gaussian width , w , or spot size varies as a function of axial

position. One such mode is sketched in Fig. 2. For convenience the confocalgeometry is shown with R1 = R2 = L, where the spot size at the beam waist is

given by Equation C and at the mirrors by Equation D.

The spot size generally increases as a function of distance from the beam waist; therelation is described by Equation E. This leads to the normal full -angle beamdivergence in the far field given by Equation F.

At 10.6 microns, and with a cavity length of 1 meter, the waist diameter is 2w 0 = 2.6 mm . If large-diameter tubes and mirrors are used, the radial or off-axis modes

may be generated, thus contributing to the total output power. However, for single -

frequency operation the size of the longitudinal mode must be increased byincreasing the curvature of the mirrors. It is usually desirable to make the

transmitting mirror optically flat. Thus, with R2 = infinity , the spot sizes at the two



mirrors are given by Equations G and H.

If R1 is now increased to 50 meters, the spot diameter increases to about 10 mm

and a single mode begins to fill a reasonable volume. Ideally, the curvature could

be further increased, depending on available optical components.

Output from the cavity can be obtained in various ways. The best of these is to use

an output transmitting mirror with a uniform transmission coefficient over thewhole aperture. Other techniques include hole coupling, spot coupling and iris

coupling; but these tend to generate irregular modes in the cavity and should beavoided. When coupling through a transmitting mirror, it is possible to see the

Fresnel reflection (whose magnitude is given by Equation J) from the bare mirrormaterial as the feedback for the oscillator. Otherwise, the mirror may have amultilayer dielectric coating on one face to achieve any desired reflectivity while the

other face has an antireflection coating. Coatings for high-power CO2 lasers

operating at 10.6 microns are not very reliable, so bare surface reflectors should beused if possible for such applications. Another technique is to use a plane parallel

mirror which then acts as a Fabry-Perot etalon and has any degree of reflectivity

from 0 to a value given by Equation K, depending on wavelength. The reflectivitiesand physical properties of presently available materials for use at 10.6 microns are

given in Table 2.



OUTPUT SPECTRUM

The output spectrum of the CO2 laser is determined by the exact mirror separation

and its relationship to the CO2 amplifying medium. When the discharge is on and

the tube is not lasing, the medium exhibits a single-pass gain given by Equation L,

where alpha is a function of frequency (see Fig. 3, and refer to "CO2 LaserTheory"). This gain curve is a series of bumps or lines about 50 MHz wide whereeach line corresponds to one of the J rotational levels of the 001 vibrational state

with an excess density over the J + 1 level in the 100 state. The wavelengths of

these lines are determined by the CO2 molecule and are separated on the averageby about 55 GHz.

The widths of the lines are determined mainly by the thermal spread and, to alesser extent, by the collision broadening. The total area under all the P transition

gain curves is proportional to the difference in density between the 001 and the

100 vibrational levels. The distribution among the P branch lines is determined bythe effective rotational temperature of the molecules. At room temperature the

peak gain or area occurs when P = 20. The longitudinal cavity modes occur atregular frequency intervals equal to c / 2L, where c is the speed of light in the

medium. For a 1 meter cavity, these modes are separated by 150 MHz, which is

larger than the 50 MHz Doppler width of the various P transitions. If it is assumedthat the radial modes have been suppressed by appropriate choice of mirror

curvature and the tube diameter, the longitudinal mode that experiences the

highest gain under any of the P transitions will be the first mode to grow in time.For example, if one mode happens to be at the center of P 20 , it will dominate the

oscillation. The other modes that happen to be within P 18 or P22 may not

oscillate, since the collisional relaxation between the rotational levels, and hence P transitions, is very fast. In Illustration C, this time is 100 nanoseconds - sufficiently

small, when the power density in the cavity becomes high and burns out the

inversion on P 20 for the other rotational levels to feed into this one and all of thegain profiles to decrease together. The P branch transitions are thus

homogeneously broadened; only one mode tends to oscillate, and this one suppliesmost of the available power from the vibrational level. As the length of the cavity

slowly changes, the mode at the center of P 20 will shift off center with a resultant

decrease in the output power. If another mode peaks up at the center of P 18 orP 22, it will take over and supply the available power. It is also possible for several

P branches to oscillate at once if all the modes are off in the wings of the profile.The other extreme occurs for a long cavity, such as a 10 meter cavity where themode separation is 15 MHz. Here, the P branch with the maximum gain always

oscillates, because one mode is always within the peak of the Doppler gain profile .

DISCHARGE PROPERTIES

Although the CO2, N2, and He discharge can be operated either with dc, ac, RF, or

pulses, it appears that the maximum average output power can be achieved eitherwith dc or low-frequency ac applied directly to the electrodes. The power is less

with RF, probably because it is hard to keep a long length of the dischargeuniformly excited. Where the discharge must be pulsed, the average power may be

only 1/10 to 1/8 of the dc value; also the optimum pressure and output coupling



conditions change.

Electrical characteristics of the CO2 laser are high voltage and low current with a

negative dynamic resistance. Except for the large negative resistance, the

discharges are similar to cold-cathode, glow discharges. In flowing gas systemssuch as these, almost any material may be used for the electrodes. For glass tubes

which are bolted together with O rings, metal flanges between the sections are

most convenient. For glass-to-metal seal systems, the Kovar seals themselves canbe used for the electrodes.

The volt-ampere curves for typical tubes and gas mixtures are given in Fig. 4. Toobtain these curves, the voltage was converted to field strength by dividing the

tube voltage by the electrode separation. Therefore, except for the small error

introduced by the cathode drop, these data can be scaled to any length tube. Thenegative resistance represented by these curves varies from about 50 kW/m at low

currents to 10 kW/m at high currents, and the circuit requires a ballast resistancefor current stabilization.

CO2 LASER CHARACTERISTICS

Important CO2 laser characteristics are high unsaturated gain, high-power outputand good efficiency. It has been experimentally determined that gain is a strong

function of tube diameter and that output power is essentially independent of

diameter. The measured gain for three tube diameters is plotted in Fig. 5 as afunction of the tube current at optimum gas pressures for maximum output power.

The gain curves for larger diameter tubes can be substantially changed simply by

adding some turbulence to the gas flow. The gain reaches its maximum at lowcurrents, falling off as current increases. This fall-off is apparently caused in part by

the heating of the gas on the tube axis. Note that the current for maximum gain issmaller than that for maximum output power.

These tubes can be used as amplifiers as well as oscillators by simply directing a

laser beam down the length of the tube. Once the power density in the beamexceeds 25 to 50 W per square cm, the gain becomes saturated and decreases to

a low value. Thus, for power densities much less than this figure, power

amplification is achieved by using small bore tubes at low currents. For power

densities much larger than 25 to 50 W per square cm, the power amplification if almost independent of the tube bore; thus, the tube should be operated at currents

which produce maximum power.

When used as an oscillator, the laser output and efficiency will vary with the

discharge current, as shown in Fig. 6. For this laser, a peak output power of 230 W

at 17 per cent efficiency was achieved with 120 mA discharge current. The peakefficiency of 21.5 per cent occurred at 60 mA. Optics used produced a multimode

pattern. If only longitudinal modes were desired, the maximum power would

decrease about 20 per cent. Because of high-efficiency power conversion, the laseraction has a strong effect on the volt-ampere characteristics. Under lasing

conditions, the whole potential -discharge current (No. 1 in Fig. 4) is raised about200 V/m or a total of about 600 V.

Research data lead to the conclusion that the available power from different-sizedtubes is independent of diameter and linearly proportional to length. If optimally

designed, a CO2 laser should thus produce from 60 to 80 W per meter-length of

discharge in the optical cavity. This has proven true in tube lengths from 1 to 20 m.



So far, the optimum transmission coefficient of the output mirror has been

determined by trial and error. Ideally, to achieve the maximum power, thetransmission coefficient for a tube with a given diameter and length should be

known. Fortunately, the power curve is quite broad with variation in transmission

coefficient, so exact values are not needed. Based on tube diameter and dischargelength, a rough estimate of the required transmission coefficients can be obtained

from Fig. 7.

The discharge tubes should normally have water jackets for cooling, but in theflowing gas system the effect of cooling is only marginal. For example, the output

power from the 50 mm bore tube may decrease by only 10 per cent as the walltemperature increases 30° to 40° C. Sealed-off lasers, however, do not dissipate

their power by dumping the stored energy into the flowing gas, but must dissipate

their heat to the walls. Thus, water jackets are a must in order to cool the centralgas and thereby avoid loss in output power.

Two other important parameters are the partial pressures and the flow speed of the

gas. The picture is complex, however, because all the variables are interrelated. For

example, if the nitrogen pressure is changed, the output power may decrease; butit could conceivably be recovered by a change in the transmission coupling or

discharge current. Nevertheless, when all the parameters are optimized and onlyone of the partial pressures is changed incrementally around its optimum value, theoutput power will change in accordance with Equation M where P = output power

and p = partial pressure. For nitrogen and helium, alpha is about 0.5; for CO2,

about 2.0

Power increases with pumping speed at about 0.2 W/m/cubic ft/min to at least 100cubic ft/min. Below about 10 cubic ft/min, the power decreases rapidly, and this

region of operation is to be avoided for high-performance operation.

DESIGN PROCEDURES

Problem: What are the parameters for a CO2 laser with a certain power level, P 0,

and a minimum physical length?

Assuming an effective pumping speed of at least 15 cubic ft/min and that the

partial pressures and discharge current can be adjusted during operation, thefollowing procedure can be followed: 1. For a multimode output power of P 0 watts, the active length of the dischargemedium is the first parameter to be specified. Length = P 0/60 meters With careful optical design, this length could also produce P 0 watts with onlylongitudinal modes; however, a 20 to 30 per cent increase in length will safely

handle this additional requirement.

2. Next, choose the optical material for the output mirror and determine the tube

diameter. If uncoated optics are desired, consult the list of usable material to

determine what reflectivities are available. With the reflectivity and tube length



specified, determine the tube diameter from Fig. 7. If the tube diameter is specified

from other considerations (e.g., available power supply voltage), then Fig. 7. isused to determine the required reflectivity. If necessary, this reflectivity can be

obtained with dielectric coatings on an appropriate substrate. Beyond this

consideration is a power limitation caused by heating of the optics. The powerlimitations of materials which have been used are given in Table 3.

3. Design the optics, using the mode-size calculations to fill the volume of the tube.The full mirror is usually a gold-coated substrate of glass or metal. Gold onlyabsorbs about 1.5 per cent of the incident energy and is chemically inert. The

choice of an internal-mirror tube or a Brewster window tube with external mirrors isusually determined by the application. With high-power lasers, the Brewster

windows must transmit a high-intensity beam, they should therefore be avoided, if

possible.

4. Design the power supply with tube length and diameter in mind, using Fig. 4 Theapplicable curve in Fig. 4 is determined by tube diameter, and the over-all tube

voltage is determined from the ordinate multiplied by the tube length. The power

supply voltage is then determined by adding sufficient voltage for the requiredballast resistor and the increase in tube voltage caused by lasing. The optimum

current level is somewhat dependent on diameter, and several values are indicatedin Fig. 5. For long tubes, the required voltage becomes excessively high and thetotal discharge path must be divided into parallel sections. For dc excitation, this

requires careful balancing of the electrical circuit and the gas-flow conditions.

5. Consider physical length of the laser. If it must be held to a minimum, it is

possible to fold the laser one or more times. Mirror alignment is a problem,however, and a slight reduction in output power must be accepted because of the

additional losses in the turn-around mirrors.

6. If the system is high-power (above 1 kW), plan to employ an oscillator of 500 to

1000 W followed by amplifiers of the same general construction. The same principal

can also be used at lower power levels; however, keep in mind that the amplifierswill be unsaturated until the power density gets well above 25 W per square cm .

APPLICATIONS

Many applications have been suggested for CO2 lasers, but only a few of thesehave been given serious consideration and analysis. This is partly because little

engineering has been done at 10 microns. Photon energy of about 0.1 eV is onlyabout five times room temperature. Therefore it is impossible to use photoelectric

emission to detect this radiation, and cryogenically cooled photoconductors are

necessary to achieve fast, low-level detection. Furthermore, although modulation of this radiation can be achieved with electro-optic materials, there is so much

residual absorption in these materials that high-power modulation is a difficultthermal problem. However, the potential importance of being able to beamkilowatts of power with a divergence of 100 microradians with a 1-meter antenna

(mirror) has stirred efforts to solve these problems. It is impossible to say yet what

form these lasers will take in such applications as long-range radar orcommunications systems. Many of the engineering decisions will be based on such

system problems as atmospheric attenuation and distortion, and beam-pointingaccuracy. The government is presently supporting work on CO2 laser radarproblems and also on CO2 Doppler systems for navigational aids. An immediate use

of a Doppler system would be the measurement of vehicle speeds. With short-term



frequency stabilities of 1 kHz, the resolution in speed measurement is 1 cm/s. With

its small beam divergence, the CO2 Doppler system would have far superior spatialresolution than a comparable microwave system.

All applications mentioned require a stable, single-frequency source of radiation.Other applications could exploit the multimode, multiline output of the CO2 laser.

These include all processes that can use a concentrated source of power for thermal

processing. A kilowatt of radiation at 10 microns, focused down to its diffractionlimit, is a power density of 1 gigawatt per square cm. However, it is more practicalto think of focusing the power down to 100 times the diffraction lim it which is 0.040

in. Because most materials absorb at 10 microns, considerable interest has beenshown in CO2 lasers for cutting applications. This means cutting such things as

paper, cardboard, plastics, glass, quartz, wood (tree surgery), meat, flesh

(bloodless surgery), metal, and rock. Except for the last two items, the cuttingprocess is just what one might imagine if a small intense flame were to burn

through the material. In a sense, the process is very similar to electron-beamcutting and welding, but it is much simpler to use. For metal, the initial absorption

depends on the surface condition, and the cutting depends strongly on the size and

thermal conductivity of the material. Thin-sheet stock can be cut, but molten metaltends to freeze out on the edges giving a rough cut. Thick metal, however, tends to

form a molten pool which must be removed by some means if further penetration isto occur. It was discovered that irradiation of hard rocks with power densities of theorder of 200 W per square cm caused the surface to become white hot. The

resulting mechanical stress would cause a general weakening of the rock; in some

cases, it caused the rock to crumble. At higher power densities, the rock wouldmelt, relieving the stress locally. Further research into the comminution of hard

materials is under way. Most materials are opaque at 10 microns, and any problemwhich requires controlled surface heating or burning might find a potential solution

with the CO2 laser. Call 650 575-4919 or e-mail us for more information.

Understanding Co2 Lasers

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