Contains reports on two research projects.Joint Services Electronics Programs (U. S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 28-043-AMC-02536(E)U. S. Air Force (ESD) Contract F19628-70-C-006

George, E. Victor

Granek, H.

Haus, Hermann A.

Lyon, D. L.

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VII. ELECTRODYNAMICS OF MEDIAAcademic and Research StaffProf. L. J. Chu Prof. P. W. Hoff Dr. L. FrenkelProf. H. A. Haus Prof. J. A. Kong T. E. SullivanProf. P. Penfield, Jr.Graduate StudentsH. Granek D. L. Lyon E. E. Stark, Jr.E. R. Kellet, Jr. L-h. WangA. AN EXPERIMENTAL DETERMINATION OF CROSSRELAXATION IN CO 2The purpose of the experiments reported here is to study the relative strength ofthe various relaxation processes in a CO 2 laser at 10.6 [pm; the relaxation of the popu-lation in velocity groups within a single line, and the relaxation of the population in dif-ferent rotational levels. The experiments represent a refinement of experimentsreported previously. Sufficient data have been obtained to determine the relaxationrates of interest.A saturating CO 2 laser tuned to the P(20) transition at 10. 6 pim is chopped at 260 Hzand modulates the population in a CO 2 cell (Fig. VII-1). A low-intensity beam, colinearwith the saturating beam and with its polarization at right angles to that of the saturatingbeam and isolated through a polarizer is used to probe the effect of the modulation onthe gain or absorption in the cell. The probe beam is piezoelectrically tunableacross the linewidth of six R transitions. The sweep of the piezoelectric oscillatorcan be calibrated in frequency by beating this laser against the fixed laser on thesame line. The probe beam is separated beyond the amplifier by a grating andafter detection is synchronously amplified at the chopper frequency. The saturatingoscillator also contains a piezoelectric tuner and its frequency can be adjustedwithin the P(20) transition.A theory of cross relaxation describing the phenomena in the CO 2 laser hasbeen presented previously. The theory included three rate parameters: the rateof relaxation within the velocity profile of a single energy level, 1/T, the rate ofcross relaxation among rotational levels, 2 A, and the rate of relaxation out of thevibrational energy states, y. In the previous analysis, it was assumed that negli-gible velocity changes occur as the particles change rotational levels. The con-sequence of this assumption is that a saturating laser would produce a populationThis work was supported by the Joint Services Electronics Programs (U. S. Army,U.S. Navy, and U.S. Air Force) under ContractDA28-043-AMC-02536(E), and in partby U. S. Air Force (ESD) Contract F19628-70-C-0064.QPR No. 99(VII. ELECTRODYNAMICS OF MEDIA)PIEZOELECTRICSSATURATINGOSCILLATORGERMANIUMBREW STER WINDOWPOLARIZERFig. VII-1. Experimental arrangement.decrease in all upper rotational levels over the homogeneous linewidth, in addition toan over-all pull-down of each of the levels. A corresponding fine structure wouldappear in all lower levels. The experiments are matched better by a theory thatassumes that the particles may change velocity appreciably when they change rotationallevel. The rate equation describing this process is given below for the upperrotational levels.-v) =n ) '(v (, v) n .(v) dv' + (v, v') n (v')dv' - S T(v', ) n (v) dv'kupperS)jk v vI nk (v) dv' - W (v) n (v) - n (, 6 + R (v).k glowerHere the notation coincides with that reported previously. Only in the induced transitionrate is the lower level explicitly indicated. The subscript t applies to the lasing level.The assumption of complete randomization after one collision is made. That is,e en. (v) ne(v ')F(v',v) n.(v) = F(v, v') ne (v )  --JJ - f n.(v) dvQPR No. 99(VII. ELECTRODYNAMICS OF MEDIA)n ee e n(v) nK vrKJ(', v) n (v) V, v') nK(v ) = AI NemmA corresponding rate equation can be set up for the lower level. In general, differentrelaxation rates would have to be assumed for the lower level. It is to be expected,however, that the rotational cross-relaxation rates should depend only weakly on thevibrational state of the system. Hence, one might expect the A's for the upper andlower levels to be the same. The same can be expected about the velocity cross-relaxation rate, 1/7. Clearly, the vibrational cross-relaxation rate y cannot beassumed, in general, to be independent of the vibrational state. In our experiment wehave found, however, that the rate at which particles leave the interaction with thesaturating beam or probe beam is not determined by the internal vibrational relaxationrate, but rather is dominated by spatial diffusion in view of the low pressure (1 Torror less) employed in the experiment. This fact has two consequences. First, it meansthat the vibrational relaxation rate cannot be determined from our experiment.Second, however, it implies a great simplification because in this way all of the relaxa-tion rates of the upper level become equal to the corresponding relaxation rates of thelower level. Solving the rate equations for the upper level and the corresponding rateequations for the lower level, we find the following expressions for the signal detectedin the experiment:NeAa(v) = -bpNe9f(v) W(sd + 3 sd + W(v) (3)R(18) N37 e2 0 1 +----Aa(v) = -pf(v) W sd + 1 N + 43 e d + 43 N W(v) (4)R(20) K +-(ZO)  A/zsd + 1 NAa(v) -pf(v) W e + Ne 2J + 3 19 J 18, 0 (5)y() J+1 2J + 1 I eR(J) N1 + --whereNe N39 200= 1 N , p19 8 -rt +- + A 1-QPR No. 99(VII. ELECTRODYNAMICS OF MEDIA)(y +A/z) A(1 - i/z)sE , d -+y(y+A) T 1 +A/zE Nemmz -Nfand X and t are, respectively, the wavelength and spontaneous lifetime. Equation 3spholds for the case when the probing signal shares a common upper level with thesaturating signal; Eq. 4 when the probing signal shares a common lower level; and Eq. 5when the probe and the saturating oscillator have no common levels. From the obser-vation of the signal vs frequency of the probe laser, one may determine the relaxationrates y, 1/T, and A. One further note of caution is in order. The theory containsonly three relaxation rates, whereas the actual situation calls for several more: therate of relaxation among the different vibrational excitations in the same vibrationalmode; the rate of relaxation between CO Z and N2 levels when N2 is added. The actualexperiment only measures three parameters. A more detailed theory, with more thanthree relaxation rates arrives at final equations for the three parameters measuredwhich contain combinations of all relaxation rates. Because of the relative magni-1tudes of -, A and y, and of the other relaxation rates not included in the simple the-ory, one finds that the parameters s, p, and d of the simple theory are not greatlymodified by the inclusion of the other relaxation rates. It was decided, therefore,to interpret the experiment in terms of the simple theory taking into account onlythree relaxation rates. Figure VII-2 shows the experimental result obtained whenthe saturating oscillator was operating at P(20) and a probe oscillator was operatingat R(18). The pressures are as indicated. Note the very clear appearance of a "pip"which is due to the change of population induced by the saturating laser over thehomogeneous linewidth of the material. Clear signals were obtained for the CO2-N 2cell unexcited, as well as excited by a discharge. Also indicated in Fig. VII-2 isthe signal obtained when only CO 2 was introduced into the cell. If all relaxationrates were dominated by collisional changes of energy and velocity, then one wouldexpect that the addition of nitrogen to the CO 2 would decrease the signal level becausethe relaxation rates are increased. We found the opposite to be true. We explainthis phenomenon by the fact that the relaxation rate y was diffusion-dominated,3 andin fact decreased when the nitrogen was added to the cell. Computations of themagnitude of the diffusion effect confirmed this explanation. Figure VII-3 showsa curve obtained when the probe oscillator did not share a common level with thesaturating oscillator.QPR No. 99CHANGE IN ABSORPTIONSaturating P(20)Probing R(18)0 1 Torr CO2,NoiseS- FREQUENCY1MHz(a)J=19001P(20)/ R(18)J 18 J=20 100(c)IMHz(b)CHANGE INAMPLIFICATION0 1 Torr CO2O Torr N232 mAFig. VII-2.Signal as a function of frequency: sat-urating laser P(20); probe laser R(18).(a) Unexcited, pure CO 2 .(b) Unexcited, CO Z -N mixture.(c) Discharge-excited, CO 2 - N 2 mixture.CHANGE IN ABSORPTIONSaturating P(20)Probing R (22)0 2 Torr CO20 2 Torr N2J=19 J-21 J=23P(20) / R(22)J=20 J=22FREQUENCY1MHzFig. VII-3. Signal as a function of frequency; saturating laserP(20); probe laser R(16).QPR No. 990 1 Torr COO 1 Torr N2(VII. ELECTRODYNAMICS OF MEDIA)Table VII-1. Summary of relaxation rates.Cold Cold DischargedCO2 CO2 -N2 CO2 - N2y Torr/sec] 3.7 102  5.5 102  8.5 102\ sec Torr! - 1  5 106  9.9 106  11 1061/r [sec Torr] - 1 12 106 13 x 106 12 x 106The relaxation rates were determined from a total of 50 such experimental curvesand are summarized in Table VII-1 in terms of relaxation rate as a function of pressure.A resonant absorption effect predicted by Hansch and Toschek 4 for co-traveling andcountertraveling waves is not believed to be observable, because of the high M-degeneracy and orthogonal polarization. An analysis is in progress.H. Granek, H. A. HausReferences1. H. Granek, "An Experimental Determination of Cross Relaxation in CO2," Quar-terly Progress Report No. 96, Research Laboratory of Electronics, M. I. T., Jan-uary 15, 1970, pp. 69-73.2. P. K. Cheo and R. L. Abrams, " Rotational Relaxation Rate of CO Laser Levels,"Appl. Phys. Letters 14, 47 (1969).3. C. P. Christensen, Jr., H. A. Haus, and C. Freed, "Effect of Diffusion on GainSaturation in CO2 Lasers," Technical Report 464, Lincoln Laboratory, M. I. T.,Lexington, Massachusetts, February 7, 1969.4. T. H. Hansch and P. Toschek, "Perturbation Spectroscopy of Allowed and ForbiddenLines in a 3-Level Gas Laser," presented at The Sixth International Quantum Elec-tronics Conference, Kyoto, Japan, September 7-10, 1970.B. INVESTIGATION OF NONLINEAR EFFECTS INHIGH-PRESSURE CO 2 LASERSWe have been building and investigating high-pressure CO2 laser systems,1 withspecial emphasis on nonlinear interactions, mode locking, saturation broadening, andso forth. We have constructed two discharge tubes with the following characteristics2:Tube 1: 2" OD X 3/16" wall X 4' Plexiglas.Anode: 36" brass rod; 3/8" diameter.Cathode: 191 - 1 KQ (1/2 W) resistors, spaced 3/16" apart for a dis-tance of approximately 35".NaCl Brewster angle windows mounted at either end.QPR No. 99(VII. ELECTRODYNAMICS OF MEDIA)Tube 2: 2" OD X 3/16" wall X 14" Plexiglas.Anode: 12" brass rod; 3/8" diameter.Cathode: 55 - 1 K (1/2 W) resistors spaced 3/16" apart for a dis-tance of approximately 11".NaCl Brewster angle windows.During normal operation a mixture of CO Z , N Z , and He gases in ratios of 1. 5: 1:11are flowed through these tubes at rates of the order of 1/2 liter/min. Total pressurein the tubes is usually kept in the 250-350 Torr range. Voltages applied to the anodeare in the 15-20 kV range. The lasers are pulsed by using a capacitor bank-sparkgap circuit similar to the one described previously.2 Capacitance for the long tube is0. 025 iF, and for the short one 0. 01 iF. The discharge current pulses have a half-intensity width of -1 ps and peak amplitudes of 400 A and 250 A for the long andshort tubes, respectively. Pulsing rates are in the 5-10 pps range.Three experiments have been performed.1. Observation of self-mode locking. Using the long tube in a 2. 2 m optical cavityformed by a 4 m radius of curvature (50% transmissivity) Ge mirror and PTR gratingthe following observations were made with a Ge: Cu(Sb) liquid He-cooled detector. Thelaser output pulse lagged the discharge current pulse by -2-3 ps. The laser pulseenvelope was filled with a very fast modulation (Fig. VII-4). The modulation had a depthof 100% and was nearly sinusoidal, with a frequency equal to the, c/2L intermode fre-quency spacing of the cavity (Fig. VII-5). The cavity length was shortened to 1.5 m andsimilar modulation behavior was observed.The short tube was then used in a cavity, 0. 5 m long, formed by an 80% reflec-tivity flat IRTRAN mirror and a high-reflectivity (R= 1. 25 m) aluminized mirror.The fast modulation was again observed, this time with frequency equal to 300 MHz(=c/ZL), but the depth of modulation was not 100%. This could very likely be due tofrequency response limitations in the Ge: Cu(Sb) detector 3 or to the monitoring Tek-tronix 7704 oscilloscope.From the shape of the modulation, we surmise that two modes, with possibly anadmixture of one or two additional modes, are running stably in the laser. The detectoris roughly an & 2 sensitive device and from the figures we see that it was producing asteady-beat signal as an output. This steady beat may be viewed as a type of self-locking of the oscillating modes of the laser. It should be noted that the presence ofself-locking was critically dependent on adjustment of the internal cavity aperture tothe smallest settings allowable. Presumably this forces the laser to emit in theTEM00 transverse mode.The PTR grating was adjusted in the 2. 2 m cavity so that the laser could be run inany one of 11 different P transitions at 10. 6 p (centered about P(20)). Self-mode lockingQPR No. 99P IiiIFig. VII-4.Giant laser pulse filled with self-lockedmodulation. Long tube: L = 2. 2 m; 500ns/div.Fig. VII-5.Same laser configuration as Fig. VII-4:self-locked pulses; 10 ns/div.Fig. VII-6.Giant laser pulse after 0. 5 Torr SF 6 wasadded to intracavity cell. L = 2. 2 m;500 ns/div.QPR No. 99Fig. VII-7.Giant laser pulse. 0. 5 Torr SF 6 . PTRgrating has been tuned to achieve locking.Same conditions as in Fig. VII-6. 500ns /d iv.AiAI 'A k IALiVI1'777 7C /'I IA IA I A IA II f--f(VII. ELECTRODYNAMICS OF MEDIA)was observed on all transitions. The self-locking was also observed at the 9. 4 [ trans-ition of CO 2 '2. Absorption by SF 6 . A cell with optical length of -1 " was placed in both the longand short tube laser cavities near the flat mirror. The cell was. positioned so that theoptical beam was incident upon its NaC1 end windows at the Brewster angle. With thelaser running self-mode locked, the introduction of -0. 5 Torr of SF 6 generally killedthe pulsing and left only a clean giant pulse envelope (Fig. VII-6). Presumably, the verystrong frequency dependence of the SF 6 absorption 4 has discriminated against one ofthe two oscillating modes and left us with only one mode above threshold. Slight tuningof the grating or the cavity length will bring back the mode-locked behavior(Fig. VII-7).When He is added as a buffer gas to the 1" cell, the frequency dependence of theabsorption is broadened. The characteristic relaxation time of the absorbing mediumis thus shortened, and it seems possible that the SF 6-He combination may act as a satu-rable absorber, producing even more strongly mode-locked pulses with a duty rateequal to c/2L, and pulse widths greatly narrowed. There has been some fastoscillation at approximately a 15 MHz rate in a 2. 2 m cavity that has been inducedby the cell. We believe this to be an optical ringing of the SF 6 -He gases at a frequencyclosely related to their T 1 relaxation times. Further study is being made of this sys-tem.3. Amplification. The short tube was placed in a 1 m cavity formed by a flat 80%reflectivity mirror and an R = 1. 25 m high reflectivity mirror.' The long tube wasplaced coaxially with the 1 m laser cavity so that the output would travel the entirelength and thus be amplified by the inverted medium. Apertures were placed internalto the laser cavity and between the laser and the long amplifier tube. Preliminaryobservations showed that the power gain for the long tube is -4-5 dB. Varying the delaytime between the discharge pulses in the two tubes had no startling effects. As longas the amplifier was fired within a time less than 1. 5-2.0 O sec after the laser firingtime, the amplification was roughly uniform for the entire giant pulse. For delaysgreater than ~2 jisec between laser and amplifier firing times (in that order) onlythe latter portions of the giant pulse were amplified. It should be noted that no indepen-dent test was made to determine whether the amplifier was saturated at any time duringthe passage of the laser pulse.Further amplification work is planned using high-pressure CO lasers in conjunc-tion with low-pressure cw CO2 amplifiers. Also, the discharge tube design will bevaried in order to study and maximize the gain of the medium and the output powerof high-pressure lasers. One of our aims is to achieve saturation broadening of ourmode-locked pulses through fast saturation of the amplifier medium. 5D. L. Lyon, E. V. George, H. A. HausQPR No. 99(VII. ELECTRODYNAMICS OF MEDIA)References1. A. J. Beaulieu, Appl. Letters 16, 504 (1970).2. E. V. George and L. D. Pleasance, Quarterly Progress Report No. 98, ResearchLaboratory of Electronics, M. I. T., July 15, 1970, p. 47.3. T. J. Bridges, H. A. Haus, and P. W. Hoff, IEEE J. Quantum Electronics,Vol. QE-4, p. 777, 1968.4. E. D. Hinkley, Appl. Phys. Letters 16, 351 (1970).5. P. W. Hoff, H. A. Haus, and T. J. Bridges, Phys. Rev. Letters 25, 82 (1970).QPR No. 99

Electrodynamics of Media

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Electrodynamics of Media

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