IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-13, NO. 6 , JUNE 1977 413

High Power Optically Pumped Far infrared Laser Systems

Z. DROZDOWICZ, PAUL WOSKOBOINIKOW, K. ISOBE, DANIEL R. COHN, R. J. TEMKIN, KENNETH J. BUTTON, SENIOR MEMBER, IEEE, AND J . WALDMAN

Abstract-Single mode, 60-80 ns pulse width, 50-70 kW peak power laser oscillators operating on the 384.6 pm line of DzO have been developed. The characteristic linewidths of these oscillators are less than 25 MHz full width at half maximum which favorably compares with the intrinsic width of 6-8 MHz associated with the pulse length of about 60 ns. A 12.7 mJ, 195 kW, 384.6 pm D2O laser oscillator- amplifier combination has been constructed and tested. Although single longitudinal mode operation is attained from this oscillator- amplifier system, amplified spontaneous emission (superradiance) from the amplifier adds low power level wide-bandwidth background radi- ation. Studies of far infrared lasing action in CH3F and CH31 are also described.

T HE potential application of high power narrow linewidth far infrared radiation (FIR) for determination of ion

temperature in tokamak plasmas by Thomson scattering was proposed [ l ] , [2] after the first demonstration of optically pumped laser action in CH3F [3] and the subsequent pro- duction of higher power outputs from mirrorless lasers [4], [5]. At present it appears that power levels on the order of 1 MW, pulse energies on the order of 200 mJ, and full linewidth of 20-40 MHz between 10 dB points are required. Also full widths of less than 100 MHz at the 30 dB and 200 MHz at the 50 dB points are required for Thomson scattering measure- ments of tokamak plasmas and other hot plasmas with elec- tron densities of about 1014 ~ m - ~ . In this paper we discuss various means of achieving high power, narrow linewidth output from a FIR laser system.

Attempts have been made to generate high power narrow linewidth radiation in CH3F by pumping it with the 9.55 pm P(20) line of high power pulsed C02 lasers. Reasonably good power conversion efficiencies were obtained in amplified spon- taneous emission (ASE) type lasers [6] -[ 101 . A variety of linewidths were reported for these lasers, all of them in the

Manuscript received November 8 , 1976; revised January 13, 1977. This work was supported in part by the U.S. Energy Research and Development Administration and the National Science Foundation. Z. Drozdowicz is with the Department of Physics and the Francis

Bitter National Magnet Laboratory, Massachusetts Institute of Tech- nology, Cambridge, MA 02139.

P. Woskoboinikow, D. R. Cohn, R. J. Temkin, and K. J. Button are with the Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139.

K. Isobe was on leave at the Francis Bitter National Magnet Labora- tory, Massachusetts Institute of Technology, Cambridge, MA 02139. He is with the Nippon Electric Company, Kawasaki, Japan.

J . Waldman is with the Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, and the University of Lowell, Lowell, MA.

range from 300 MHz to 700 MHz FWHM. Such large line- width was attributed to the possibility of simultaneous pumping, due to the off resonant pumping effect [ 111, of a number of rotational K-sublevels of the J = 12 rotational level of CH3F. These levels can then lase simultaneously, giving a frequency spread of (K t - K f ) X 13 MHz. To overcome the linewidth problems various oscillators were constructed [ 121 - [14]. All of them provided narrow linewidth outputs on a number of longitudinal or transverse modes. To increase the power, oscillator-amplifier assemblies were constructed [ 151 - [18] , [ lo] . All of the published scanning Fabry-Perot inter- ferograms of the outputs of these systems exhibit similar shape: a relatively narrow central peak resting on a broad base of ASE arising from the amplifier. Our highest power CH3F oscillator-amplifier system, sketched in Fig. 1, clearly exhibited this type of behavior, as shown in Fig. 2. This system consisted of a 1.25 m long oscillator and a 2.8 m long amplifier pumped by 20 and 80 percent of a 200 MW COZ laser output, respectively. The maximum output on the 496 pm line was 130 kW peak power in a 60 ns FWHM pulse and was achieved at a CH3F pressure of 3 torr in both the oscil- lator and the amplifier. Our FIR energy measurements were performed using a Laser Precision RkP-335, 1 cm2 area pyro- electric detector with an extended spectral response coating. The time evolution of the pulses was observed with a Schottky diode detector.

The linewidth quality can be significantly improved by pur- suing two new directions: l ) employing a lasing medium with only one level excited by the pump radiation and 2) by developing a single mode cavity with a very high power out- put, thus placing far less reliance upon a very high gain amplifier section. The results of these attempts are described below.

A preliminary search indicated promising results for the 447 pm line of CH31. The 10.57 pm P(18) line of C02 resonantly pumps the RR5 (44) transition of the vg bending mode and the 447 pm lasing transition is QP6(45) [19] -[22]. Only one CH31 level is pumped, the other allowed pump transitions being separated by large frequency differences. The spectral width of the output of a 3 m long ASE type laser operating with CH31 was measured to be 100 MHz FWHM [23] which is quite narrow when compared with the CH3F [6] -[lo] and Dz 0 [24] results. The energy output from the CH3 I gas in all our laser systems was always at least a factor of 10 below the output from CH3 F or Dz 0 in the same systems. We explain this low energy output by the very low population level at

414 IEEE JOURNAL OF QUANTUM ELECTRONICS, JUNE 1977

2 0 G M W CC2 PUMP ODTICA- DELAY n r I \ \

BEAU SPLITTER

I h . > / I i

I 3 C K W SMM BEAM

20M R A D I U S F I R B i A M ‘ W A R T Z C R Y S T A L 9 - C O A T E 2 FOR C O z

I 2 5 M O S C I L L A T O R 2 8 M A M P L I F I E R

Fig. 1. Schematic of the 130 kW CH3F oscillator-amplifier system. NaCl windows for C02, teflon windows for FIR.

Fig. 2. Scanning Fabry-Perot interferogram of the output of the 130 kW CH3F laser.

room temperature of the (v6 = 0 , J = 44, K = 5) level of CH31. Only about 0.07 percent of all of the CH3 I molecules lie in this level as compared to about 1.8 percent for the 533 level of D 2 0 and about 4 percent for the K = 1 to K = 6 sublevels of theJ= 121evelofCH3F [25].

A narrow linewidth output is not the only laser requirement for plasma diagnostics. High power is also necessary and there- fore we have concentrated our efforts on CH3F and DzO. D 2 0 has proven to provide up to three times more output than CH3F in similar systems. This can be attributed to the fact that, disregarding cascade and refilling lines, Dz 0 has only one lasing transition, while CH3F, because of its closely spaced K sublevels, has 5-7 transitions, only one of which can be in resonance with a single mode cavity. The other CH3F transi- tions lase less efficiently because they are very far off reso- nance [26]. Furthermore, for ion Thomson scattering in a tokamak, the 384.6 pm line of Dz 0 may be better suited than the 496 pm line of CH3F because it is further away from the radiation of the low-order harmonics of the cyclotron fre- quency for the high magnetic field tokamaks [27].

The advantages of DzO caused us to concentrate our effort on the development of a suitable D2 0 laser system. Following the description of the D 2 0 levels participating in the laser action we will describe the four distinct laser systems we have built and tested. These were an oscillator-amplifier system, a mode injection system, a high power short oscillator, and a

high power long oscillator with an interferometric mode selector.

Fig. 3 shows the level diagram of the DzO laser. The 9.26 pm R(22) line of the COz laser pumps the (vz = 0, 533) to (v2 = 1, 422) transition in DzO, the center of the C02 line being offset from the center of the Dz 0 transition by -3 18 MHz [28]. The lasing occurs on the 422 to 413 transition at 384.6 pm * 0.5 pm [24], [28] - [30] and on a cascade 413 to 404 transition at 359.3 pm * 0.5 pm [24], [29] - [30]. Our highest power system [24] consisted of a. short 0.36 m oscil- lator pumped by 20 percent of the COz beam and an 8 m long amplifier pumped by the remaining 80 percent of the COz beam. A quartz crystal at 45” angle acted as a transmitter for the FIR beam and a reflector for COz [31] in the amplifier. This system produced 195 kW pulses, 70 MHz FWHM, at 384.6 pm at the DzO pressure of 5.5 torr in the oscillator and 4.0 torr in the amplifier. The spectral output also showed the presence of the 359.3 pm line and a broad background of ASE from the amplifier. The breadth of the ASE output, 450 MHz FWHM [24], was much larger than could be expected from the homogeneous pressure broadening of the FIR transition. This broadening of 26 MHz FWHM torr-’ [28] should have produced only 100-1 30 MHz linewidths at the operating pres- sures of 4-5 torr. We attribute this linewidth to the fact that at these pressures the 384.6 pm line is a result of a Raman type coherent scattering resonantly enhanced by the proximity of the 422 level [23], [32] -[33], Fig. 3 . This type of process is broadened by pressure broadening, the AC Stark effect and the large linewidth of the selfmodelocked TEA COz laser. The AC Stark effect broadening occurs because the pump field varies in time and space, while the COz linewidth broadening occurs because of a spread in the energy of the virtual level in the Raman process. The time resolved picture of the COz laser pulse taken with a germanium photon drag detector and dis- played on a Tektronix 7904 oscilloscope is shown in Fig. 4(a).

To cut down on the ASE background while retaining a long gain path an injection method, based on similar C 0 2 laser systems [34], was tested. The system is shown in Fig. 5. 20 percent of the 200 MW COz pump beam was directed to the 0.36 m single mode cavity and 80 percent to the 1.55 m cavity which usually oscillated on 3-5 modes. By tuning the length of the two cavities one of the modes of the 1.55 m cavity was made to coincide in frequency with the optimized mode of the 0.36 m cavity. When the output of the single mode cavity was then injected, through a 45” mesh beam splitter, into the 1.55 m cavity the latter was made to oscillate predominantly on the matching mode. Both cavities were oscillating on both 384.6 and 359.3 pm lines. The “before and after” injection situation is depicted on Fig. 6. The maximum output from this system was achieved with pres- sures of 6 Torr of D2 0 in both cavities and amounted to about 100 kW peak power on all lines and modes. The injected single mode signal was effective in mode selection even at intensities of a few watts/cm2.

The injection method was only partially successful in pro- ducing a single mode radiation. A more successful method was the use of a short cavity pumped with all of the available C 0 2 power. Only about 30 percent of the C02 pump power was

DROZDOWICZ e t al.: FAR INFRARED LASER SYSTEMS 41 5

318 MHz

359.3prn

404

COz PUMP

Fig. 3. Pumping and lasing transitions of DzO.

Fig. 4. (a) Typical time resolved COz pump pulse. (b) Typical time resolved FIR pulse from the single mode DzO laser cavity (67 kW).

INJECTED OSCILLATOR C02PUMP SINGLE MODE OSCILLATOR I I & nMESHES

Fig. 5. Schematic of the mode injection system. NaCl windows for COz, teflon windows for FIR.

transmitted through the two meshes of the 0.36 m long cavity, the same as in Fig. 5.

Fig. 7 shows a scanning Fabry-Perot interferogram of the output of the 0.36 m single mode cavity. Fig. 4(b) shows the laser output versus time from the same cavity using a Schottky diode detector and a Tektronix 7904 oscilloscope. A compari- son of this pulse with the COz pump pulse, Fig. 4(a), shows that the structure of the pump pulse is not reproduced in the single mode FIR beam. The single mode operation was achieved up to the average pump intensities of 1.7 MW/cm2 for a 40 percent reflective output mesh mirror and 1.2 MW/cm2 for a 50 percent reflective mesh. Above these pump intensities, the output became multimode at all cavity length settings within the free spectral range. Fig. 8 shows the pres- sure dependence of the energy of the output of the 0.36 m cavity for various COz average pump intensities and the two different output mesh mirrors. For 1.7 MW/cmZ average input pump intensity, which gave the highest power while still retaining a single mode output, we obtained 4.2 mJ FIR

I 55 m C A V I T Y INJECTED, I 5 5 m CaVI 'Y

ID

Fig. 6. Effects of the injection of the single mode radiation on the operation of the multimode cavity. Roman numerals mark the modes of the 384.6 pm DzO line, capital letters mark the modes of the 359.3 pm D20 line.

3 2 0 M H z 4 ' 385 prr

Fig. 7. Spectral output of the 0.36 m cavity at 67 kW output power level on the 384.6 pm and 359.3 pm lines of DzO.

energy at the optimum pressure of 10 torr. This energy cor- responds to approximately 67 kW peak power on both lines and to over 50 kW peak power on the 384.6 pm line. The energy conversion efficiency, FIR energy out/COz energy in, was about 0.03 percent in this case, or about 0.1 percent if COz beam insertion losses are taken into account. There is an absolute quantum limit on the conversion efficiency, 2.4 percent, corresponding to one FIR photon being emitted for every C 0 2 photon absorbed. This limit, theoretically attain- able in Raman processes, is further cut down by the off resonant character of the absorption process and gain shape considerations [32]. Maximum efficiency attained in any of the DzO lasers in this laboratory was about 0.4 percent in an ASE type of laser [35] .

4 1 6

4

4 5 6 7 8 9 I O I I I 2 13 14 15 Torr D 2 0 p r e s s u r e

J 0% 5 0 %

j Fig. 8. DzO pressure and COz power input dependence of the FIR

energy output from the 0.36 m cavity. The cavity operated on a single mode over the region spanned by the lower six curves and in a multimode fashion over the two highest curves.

COz PUMP RADIATION

MESH MIRROR A Y E S H MIRROR

‘SUBMILLIMETER R A D I A T I O N

Fig. 9. Schematic of the high power 1.7 m D2O cavity with a Fox- Smith mode selector.

Another promising technique of obtaining high power single mode FIR radiation from a rather long oscillator is to use a Fox-Smith [36] mode selector. A 1.7 m long DzO cavity, shown in Fig. 9, with this type of mode selector has been developed to determine the effectiveness of this approach. Preliminary results indicate that the Fox-Smith mode selector suppresses all but one longitudinal mode. The linewidth of this mode is less than 30 MHz FWHM. When the 45” angle quartz coupler was placed inside the cavity, thus eliminating the COz beam losses in transmission through the mesh mirror, 6 mJ, 70 kW output pulses at 384.6 pm were obtained from this system pumped by about 250 MW from our COz system operating with an improved gas mixture.

The presence of the 359.3 pm line in the output of most of the D2 0 lasers should not be treated as a negative factor in the Thomson scattering experiment. The scattered radiation will be detected by heterodyne mixing in a Schottky diode and this line is too far removed in frequency to play any role. Our measurements show that this cascade line, unlike the refilling and cascade lines in CH3F, oscillates at all DzO pressures. We attribute this to the influence of nuclear spin statistics on the degeneracy of the levels [25]. The ratio of the degeneracies of

IEEE JOURNAL OF QUANTUM ELECTRONICS, JUNE 1977

the levels involved is 2 : 1 : 2 for the 422 :413 : 4~,4 levels, respectively. This ratio works for the shorter, and against the longer wavelength.

It should be stressed that due to the very high gain of the systems we are dealing with, there is always a possibility of some low level ASE type radiation being present. As indicated previously the ASE radiation is characterized by a very large linewidth. Since for Thomson scattering the ratio of the scattered to the input power is about it is extremely desirable to have a truly ASE free system. According to the analysis of Allen and Peters [37]-[39] it is obvious that the shorter the cavity and the larger its diameter the better the ratio of the power emitted in a single mode to the ASE power in the same angle of divergence as the single mode beam. Thus, short, large diameter oscillator and oscillator-amplifier units appear highly promising for high power laser systems for Thomson scattering measurements.

To get an upper estimate on the possible ASE content in the output of our 0.36 m long single mode cavity, we removed the output mesh mirror in that cavity while externally attenuating the COz beam by the same amount as the mesh previously did. The ASE output from this system was about 0.6 mJ. This should be compared with the 4.2 mJ output when the cavity was in operation. Obviously, the competition from the very high intensity single mode radiation should attenuate the ASE radiation very strongly. From our scanning Fabry-Perot inter- ferograms of the output of the cavity we can put an upper limit of lod2 on the ratio of the ASE emission to the single mode power. The signal-to-noise ratio made an exact measure- ment impossible. More sensitive measurements of the ratio of ASE emission to single longitudinal mode power will be made by using heterodyne detection techniques to measure intensity of the output in the wings of the frequency spectrum.

In conclusion, it appears that high power far infrared laser systems can be constructed with the spectral quality necessary for Thomson scattering determination of ion temperature in tokamak plasmas. Great care, however, has to be exercised to prevent ASE contributions to the laser output. The use of very high power oscillators and decreased reliance upon long, high gain amplifier sections seems to be required. Fox-Smith mode selection techniques may provide a means of obtaining single longitudinal mode operation in a relatively long laser oscillator.

ACKNOWLEDGMENT The authors would like to express their gratitude to Prof. €3.

Lax for his constant support and valuable discussions, to Dr. H. Praddaude for the discussion of the laser requirements for a Thomson scattering experiment, to Dr. H. R. Fetterman of the M.I.T. Lincoln Laboratory for the use of the Schottky diode, and to Dr. D. P. Hutchinson for useful discussions con- cerning CH31. The excellent technical assistance of F. Tam- bini and W. Mulligan is also gratefully acknowledged.

REFERENCES [ I ] D. L. Jassby, D. R. Cohn, E. Lax, and W. Halverson, “Tokamak

diagnostics with the 496 pm CH3F laser,” Nucl. Fusion, vol. 14, pp. 7’45-147, NOV. 1914.

DROZDOWICZ et al.: FAR INFRARED LASER SYSTEMS

[ 21 D. E. Evans and M. L. Yeoman, “Spatialjy resolved measurement of impurities and the effective charge Z in a tokamak plasma,” Phys. Rev. Lett., vol. 33, pp. 76-78, July 8,1974.

[3] T. Y. Chang and T. J. Bridges, “Laser action at 452,496, and 541 pm in optically pumped CH3F,” Opt. Commun., vol. 1 , pp. 423- 426, Apr. 1970.

[4] T. A. DeTemple, T. K. Plant, and P. D. Coleman, “Intense super- radiant emission at 496 pm from optically pumped methyl fluoride,” Appl. Phys. Lett., vol. 22, pp. 644-646, June 15, 1973.

[5] F. Brown, S. R. Honnan, and A. Palevsky, “Characteristics of a 30-kW-peak, 496 pm, methyl fluoride laser,” Opt. Commun., vol. 9, pp. 28-30, Sept. 1973.

[6] T. K. Plant, L. A.~Newman, E. J. Danielewicz, T. A. DeTemple, and P. D. Coleman, “High power optically pumped far infrared lasers,’’ IEEE Trans. Microwave Theory Tech., vol. MTT-22, pp. 988-990, Dec. 1974.

[7] D. E. Evans, L. E. Sharp, P. W. James, and W. A. Peebles, “Far infrared superradiant action in methyl fluoride,” Appl. Phys. Lett., vol. 26, pp. 630-632, June 1975.

[8] R. J. Temkin, D. R. Cohn, Z. Drozdowicz, and F. Brown, “Pumping and emission characteristics of a 4 kW submillimeter CH3F laser,” Opt. Commun., vol. 14, pp. 314-317, July 1975.

[9] D. E. Evans, B. W. James, W. A. Peebles, and L. E. Sharp, “Spec- tral composition of far-infrared laser radiation optically excited in methyl fluoride,” Infrared Phys., vol. 16, pp. 193-195, 1976.

[ 101 T. K. Plant and T. A. DeTemple, “Configurations for high-power vulsed CHqF 496 um lasers.” J. Auul. Phvs., vol. 47, UP. 3042- 3044, July-1976. . H. R. Fetterman, H. R. Schlossberg, and J. Waldman, “Submilli- meter lasers optically pumped off resonance,” Opt. Commun.,

F. Brown, S . Kronheim, and E. Silver, ‘Tunable far infrared methyl fluoride laser using transverse optical pumping,” Appl. Phys. Lett., vol. 25, pp. 394-396, Oct. 1 , 1974. L. E. Sharp, W. A. Peebles, B. W. James, and D. E. Evans, “10 kW cavity operation of a submillimetre CH3F laser,” Opt. Commun.. vol. 14. vu. 215-218. June 1975.

_ . ~. - - _

V O ~ . 6, pp. 156-159, Oct. 1972.

[14] D. R. Cohn, T. Fuse, K. J. Button, B. Lax, and Z. Drozdowicz, “Development of an efficient 9-kW, 496-pm CH3F laser oscil- lator,” Appl. Phys. Lett., vol. 27, pp: 280-282, Sept. 1, 1975.

[15] 2. Drozdowicz, R. J. Temkin, K. J . Button, and D. R. Cohn, “Efficient high-power CH3F amplifier for a 496-pm cavity laser,”Appl. Phys. Lett., vol. 28, pp. 328-330, Mar. 15, 1975.

[ 161 F. Brown, P. D. Hislop, and S. R. Kronheim, “Characteristics of a linearly pumped laser oscillator-amplifier at 496 pm,” Appl. Phys. Lett., vol. 28, pp. 654-656, June 1 , 1976.

[17] A. Semet and N. C. Luhmann, “High-power narrow-line pulsed 496 pm laser,” Appl . Phys. Lett., vol. 28, pp. 659-661, June 1, 1976.

[ 181 D. E. Evans, L. E. Sharp, W. A. Peebles, and G. Taylor, “A high diagnostics,” IEEE J. Quantum Electron., vol. QE-13, pp. 54-58, Feb. 1977.

[19] S. F. Dyubko, V. A. Svich, and L. D. Fesenko, “Submillimeter laser emission of CH31 molecules excited by COz laser radi- ation,”Opt. Spectrosc. (USSR), vol. 3, p. 118,1974.

[20] G. Graner, “Assignment of submillimeter laser lines in CH3I,” Opt. Commun., vol. 14, pp. 67-69, May 1975.

I.-

417

[21] T. Y. Chang and J. D. McGee, “Millimeter and submillimeter- wave action in symmetric top molecules optically pumped via perpendicular absorption bands,” IEEE J. Quantum Electron., vol. QE-12, pp. 62-65, Jan. 1976.

[22] G. Kramer and C. 0. Weiss, “Frequencies of some optically pumped submillimeter laser lines,”Appl. Phys., vol. 10, pp. 187- 188,1976.

[ 231 J. Wiggins, Z. Drozdowicz, and R. J. Temkin, unpublished results. [24] P. Woskoboinikow, Z. Drozdowicz, K. Isobe, D. R. Cohn, and R.

J. Temkin, “High power narrow linewidth DzO laser a t 384.6 pm,” Physics Lett., vol. 59A, pp. 264-266, Dec. 13, 1976.

[25] C. H. Townes and A. L. Schawlow, Microwave Spectroscopy. New York: Dover, 1975.

[26] R. J. Temkin and D. R. Cohn, “Rate equations for an optically- pumped, far infrared laser,” Opt. Commun., vol. 16, pp. 213- 217, Feb. 1976.

[27] D. R. Cohn, R. R. Parker, and D. L. Jassby, “Characteristics of high-density tokamak ignition reactors,” Nucl. Fusion, vol. 16, pp. 31-35, Feb. 1976.

[28] F. Keilmann, R. L. Sheffield, J. R. R. Leite, M. S. Feld, and A. Javan, “Optical pumping and tunable laser spectroscopy of the v2 band of DzO,” Appl. Phys. Lett., vol. 26, pp. 19-22, Jan. 1, 1976.

[29] D. E. Evans, L. E. Sharp, W. A. Peebles, and G. Taylor, “Far- infrared super-radiant laser action in heavy water,” Opt. Com- mun.,vol. 18,pp.479-484, Sept. 1976.

[30] The spectroscopic data used for the assignment of DzO tran- sitions came from the unpublished Ph.D dissertation of J. G. Williamson, “YZ bands of HA80, Hq60, and DA60,” The Ohio State University, Columbus, 1969.

] W. G. Spitzer and D. A. Kleinman, “Infrared lattice bands of quartz,”Phys. Rev., vol. 121, pp. 1324-1335, Mar. 1 , 1961.

] R. L. Panock and R. J. Temkin, “Interaction of two laser fields with a three level molecular system,” this issue, pp. 425-434. (The authors show that at high FIR and COz pump power levels the gain at the Raman frequency is larger than at the transition’s center frequency; also, the Raman frequency tends to be pushed further away by the high power pump beam and is pushed toward the natural transition frequency by the high power FIR beam.)

[33] R. J. Temkin, “Theory of optically pumped submillimeter lasers,” this issue, pp. 450-454.

[34] P.-A. BBlanger and J. Boivin, “Gigawatt peak-power pulse gener- ation by injection of a single short pulse in a regenerative ampli- fier above threshold (RAAT),” Can. J. Phys., vol. 54, pp. 720- 727,1976.

[ 351 2. Drozdowicz and K. Isobe, unpublished results. [36] A. G. Fox, “Optical maser mode selector,” U.S. Patent 3 504

299. P. W. Smith, “Stabilized, single frequency output from a long laser cavity,” IEEE J. Quantum Electron., vol. QE-1, pp.

[37] L. Allen and G. I. Peters, “Amplified spontaneous emission and external signal amplification in an inverted medium,”Phys. Rev.,

[38] G. I. Peters and L. Allen, “Amplified spontaneous emission I.

[39] -, “Amplified spontaneous emission IV: Beam divergence and

343-348, NOV. 1965.

V O ~ . A8, pp. 2031-2047, Oct. 1973.

The threshold condition,” J. Phys., vol. A4, pp. 238-243,1971.

spatial coherence,” J. Phys., vol. A5, pp. 546-554, Apr. 1972.