Small signal gain and vibrational relaxation for 13C02

David F. Kroeker, MarkE. Moody

A. DeFaccio, Albert L. Pindroh, Dean R. Guyer, Charles H. Fisher, and Stephen

We have determined the small signal gain for the P(18) transition of the 3CO2 and 2CO2 isotopes for identicalpumping conditions in an x-ray preionized discharge amplifier. We have also determined vibrational-relaxation rate constants for He, N2, and 3 CO2 from the decay of the small signal gain on the P(18) transitionof 13CO2 in the same x-ray preionized discharge amplifier. The vibrational-relaxation rate constants for N2

and 13CO2 on the 3CO2 P(18) transition at 11.1 ,um are a factor of 3 faster than the corresponding rateconstants for the 2CO2 isotope.

1. Introduction

Because of the interest in CO2 isotopes for laserapplications involving atmospheric propagation, wehave determined the small signal gain for 13CO2 andcompared the results with measurements for 12CO2 foridentical pumping conditions. Previous work withlow pressure cw lasers found that the small signal gainfor 13CO2 was -60% of that for 12CO2.1 Small signalgain measurements have not been reported for highpressures, but similar energies have been obtainedfrom a TEA laser using both 13CO2 and 2CO2 gasmixes.2 Absorption measurements indicate that the00°1-(10°0 + 0200)I transition probability is higher for13CO2, which would result in higher small signal gain, ifthe inversion density is the same.3 Because of thisconflicting information, it is difficult to design an am-plifier operating with 13CO2. Therefore, we have in-vestigated the small signal gain for both 13CO2 and12CO2 isotopic gas mixtures for the same pumpingconditions.

II. Experiment

The measurements were made with an x-ray preion-ized discharge amplifier having a 4- X 4- X 60-cmactive volume. The discharge circuit used a ten-sec-tion Guillemin type-E pulse forming network, whichproduced a 10-,us rectangular pump pulse with a totalpump energy of -65 J/liter atm. The operating pres-sure was 400 Torr with a He/N 2 /CO2 = 13/2/1 gasmixture.

The authors are with Spectra Technology, Inc., 2755 NorthupWay, Bellevue, Washington 98004.

Received 8 March 1988.0003-6935/89/050897-04$02.00/0.© 1989 Optical Society of America.

To minimize the effects of gas degradation due todischarge dissociation of the C02, especially when han-dling the more expensive 13CO2 isotope, the dischargeamplifier was fitted with a gas recirculation loop thatincluded a catalyst to reform CO2 from CO and 02-The gas recirculation loop included a metal bellowspump to circulate the gas, a filter to remove particu-lates, a heated catalyst, and a heat exchanger coil torestore the gas to room temperature before returning itto the laser. The gas temperature was measured witha thermocouple just before the inlet to the amplifiertube. The Pt on alumina honeycomb catalyst washeated in an oven to -300'C.

The operation of the catalyst loop was verified forboth isotopes by making repeated shots on a single gasfill while monitoring the small signal gain. Once therecirculating system had been flushed sufficiently, thesmall signal gain was the same as without the catalystand remained constant over the duration of the mea-surements (limited to less than twenty shots per fill).

The purity of the 13CO2, used in these experiments,was 299.5 mole % CO2. The isotopic composition was99.1 at.% 13C. However, the enrichment process alsoenriches the 180, and the two samples of 13CO2 thatwere used in these experiments had 3.9 and 5.2 at.%180. This translates into -8 and 10% l8Ol3Cl6O mole-cules in the samples, respectively, leaving -90%3C1602 molecules.

The experimental arrangement for probing the dis-charge amplifier is shown in Fig. 1. A line-tunable cwCO2 laser was used to probe the gain in the x-raypreionized discharge amplifier. Operation on the twoisotopes was obtained by use of two sealed dischargetubes, one for each CO2 isotope. The probe laser beamwas expanded a factor of 2 to reduce its divergence andthen directed through the amplifier. The cw probelaser beam was chopped to allow determination of Ioand was focused on the chopper blade to decrease theturn on time. The amplifier discharge was fired after

1 March 1989 / Vol. 28, No. 5 / APPLIED OPTICS 897

15 r636 P(18)

1.0-r626 1 P(18)

0.5

0.0-

0 30 60 90 120 150

BEAM EXPANDER

Fig. 1. Schematic diagram of small signal gain experiment.

0F

-C

0

V)

0

0

J

100

80

60

40

20

0

100

80

60

40

20

00 20 40 0 80 100 120 140 160 180 200

TIME (mcrosec)

Fig. 2. Typical trace for LUCY x-ray preionized discharge CO 2amplifier showing the timing of the amplified probe signal relative to

the discharge voltage pulse.

the shutter had opened and the probe laser signal hadleveled off. The amplified probe signal was monitoredwith a HgCdTe detector, recorded on a digital oscillo-scope, and then transferred to a microcomputer forsubsequent analysis.

Figure 2 shows typical temporal traces of the ampli-fied probe signal relative to the amplifier dischargevoltage. The amplifier discharge is fired after theshutter has opened and the unamplified probe signalhas leveled off. This allows a direct determination ofboth the unamplified and amplified probe signals foreach shot. The noise that can be seen on the detectorsignal, shown in Fig. 2, marks the firing of the amplifierdischarge. The amplified probe signal then increasesduring the discharge pump pulse as the gain increasesand decays after the pump pulse has terminated.

The small signal gain was calculated as the loga-rithm of the ratio of the amplified probe signal I to theunamplified probe signal Io, i.e.,

gw = (1/6) cnei/I),where = 60 cm is the active gain length of the amplifi-

TIME (s)

Fig. 3. Measured small signal gain and computer model predictions(smooth curves) for the r626 I P(18) and r636 I P(18) lines. Thepumping conditions were EpUmp - 65 J/liter atm, He/N2/CO2 = 13/2/

1 at 400 Torr.

er. The unamplified probe signal Io is calculated asthe average of the points in the level portion of thedetector signal before the amplifier discharge is fired.

The cw probe laser power was - 1 W in a 7-mm diamspot, which corresponds to -3 W/cm2. The total am-plification in a single pass was a factor of 2-3, so thatthe flux is well below the saturation level throughoutthe amplifier.

The shot-to-shot reproducibility of the peak gainand the gain decay time constants, determined by theleast-squares fit to a simple exponential decay, was-5-10% for a single gas fill. The largest uncertaintyfrom fill to fill was the accuracy of the partial pressuresof the gas mixture constituents (±3 Torr). Thisuncertainty was satisfactory for the mixtures contain-ing 25 Torr CO2 but caused a problem with reproduc-ibility from fill to fill for the measurements utilizingCO2concentrations as low as 5-10 Torr. To reduce theuncertainty in the CO2 concentrations, the mixtures inthe 5-15-Torr CO2 range were made by dilution of 20-or 25-Torr CO2 mixtures. We used a maximum of twodilutions per fill to minimize the cumulative error.

Ill. Results

The small signal gain was measured-on several rota-tional lines for both 12CO2 and 13C02, but the P(18)transition was chosen as the comparison baseline be-cause it is near the peak of the room temperaturerotational distribution and because it suffers less fromaccidental overlaps, which increase the apparent gainfor the P(20) transition in 2CO2.4 Thus the P(18)transition gives a cleaner comparison between the in-trinsic gain for the two isotopes.

Figure 3 compares small signal gain traces for theP(18) transition for both 12CO2 and 3CO2 isotopic gasmixtures for the same discharge pumping conditions.For the same pump conditions, the 13CO2 P(18) transi-tion showed -30% higher peak gain than for 2 CO2 .However, the 13 CO2 small signal gain decayed abouttwice as fast as for 12CO2 . To eliminate the possibilityof rapid vibrational relaxation by H20 or some otherimpurity in the isotopic CO2 gas sample, the cylinderwas cooled to dry ice temperature (195 K). Thesame rapid decay was obtained indicating that the

898 APPLIED OPTICS / Vol. 28, No. 5 / 1 March 1989

. I I I . I I I I I I - � I I I I I

. . . .. . . . . . . . . . . . . .~~~~~~~~

2. _

TIt'tZU

0 30 60 90 120 150

TIME (s)

Fig.4. The l3 CO2 amplified probe signal decays for the r636 IP(18)line for two He concentrations. The CO2 pressure was 10 Torr, andthe N 2 pressure was 50 Torr for both cases. The smooth curves showthe best least-squares fit of the gain decay to a simple exponential

decay.

rapid relaxation was not due to H20 or to species with alow vapor pressure at dry ice temperature.

Since the small signal gain is proportional to thepopulation difference between the upper and lowerlevels for the transition, it is possible that the rapidgain decay is due to bottlenecking in the lower laserlevel. To test this hypothesis, we monitored the fluo-rescence from the asymmetric stretch vibrationalmode through a 3.5-4.5-,4m bandpass interference fil-ter by placing the HgCdTe detector adjacent to one ofthe amplifier windows. The fluorescence decays werevery similar to the respective small signal gain decaysfor both isotopes, indicating that the observed decay isdue to vibrational relaxation of the asymmetricstretching mode and not to bottlenecking in the sym-metric stretching or bending modes.

To determine the contributions of each of the gasmixture constituents to this decay, we determined the13CO2 small signal gain decay time constant as a func-tion of concentration for each of the gas constituents,while holding the concentrations of the other speciesconstant. The data were analyzed by least-squaresfitting the small signal gain decay to a simple exponen-tial decay function. Only the intervals with gainsbetween 10 and 90% of the peak were used in the fittingprocedure to eliminate nonexponential decay due to-the weak pumping caused by the reflected power pulsein the 10 ,s immediately following the main pumpingpulse.

Figure 4 presents the small signal gain decay for the13CO2 P(18) transition at 11.1 ,gm determined for twoHe concentrations with the N2 and 13CO2 concentra-tions held fixed. Also shown as the smooth curve arethe least-squares fits to the small signal gain decays forthese two gain measurements. In spite of the approxi-mations, the fits are quite good.

Similar experiments were conducted for the otherspecies present in the gas mixture. The results ofthese measurements are shown in Fig. 5, where thedecay rates determined from the least-squares fits areplotted as a function of the partial pressure of theconstituent being varied. The decay rates are multi-

RO80 2134+3jeco1 *H

25 1 tar1 k 20 a- m

Z40

0

0 200 400 800

PARTIAL PESSURE (TORR)

Fig. 5. Plots of the small signal gain decay rate as a function of thepartial pressure of one constituent of the gas mixture while holdingthe concentration of the other constituents fixed. For the He curve,[N2] = 50 Torr and [ 3CO2] = 10 Torr. For the N2 curve, [He] = 150Torr, [13CO2] = 10 Torr, and for the 3CO2 curve, [N2] = 50 Torr, andthe total pressure was kept fixed at 295 Torr, so that [He] varied from

220 to 245 Torr.

plied by a factor that accounts for the fraction of thetotal N2 + CO2 vibrational excitation carried by CO2.5Each of the points is the average of three to five shots.

Rate constants for the vibrational deactivation of13CO2 were determined as the weighted least-squaresfit of the data to straight lines for each species. Therate constant values reported in Fig. 5 were obtainedby weighting the small signal gain decay times with thex2 value obtained from the least-squares fits to theindividual decay curves. A small correction to theslope obtained from the 13 CO2 variation is necessarybecause the total pressure was held fixed rather thanthe He partial pressure. Thus the slope of the straightline fit in Fig. 5 is not kCo2 but rather kCO2 - kHe-These rate constants are listed in Table I along withthe statistical uncertainty from the least-squares fitsand compared with the rate constants determined byMoore and co-workers for 1

2CO2 using a laser-inducedfluorescence technique.5 The rate constants indicatethat the He vibrational-relaxation rate constants for13CO2 are about the same as for 12CO2 , while the N2 and13CO2 rate constants are a factor of -3 higher than for12CO2.

The veracity of these rate constants has been furthertested by incorporating them into a comprehensivecomputer kinetics model developed to predict the per-formance of 12CO2 lasers. The modified model wasused to predict the small signal gain for an electron-

Table I. C 2 (0001) Vibrational-Relaxation Rate Constants

Species 12CO2 13CO2

M km (10-15 cm3/s) 5 kM (10-15 cm3/s)aHe 2.6 2.8 0.6N2 3.3 11.0 0.3C0 2 11.0 44 5

a This work.

1 March 1989 / Vol. 28, No. 5 / APPLIED OPTICS 899

beam sustained discharge amplifier with a 30-,us pumppulse and a He/N2/13CO2 = 3/2/1 gas mixture at 1-atmtotal pressure. The discrepancy between the modeland measured gain using the above rate constants was<10% for these pumping conditions, which are verydifferent from those of the rate constant measure-ments.

The origin of this faster vibrational relaxation for13CO2 is not presently understood. The energy leveldifferences between the asymmetric stretch level,which is the upper laser level, and nearby levels in thebending and symmetric stretch modes, which havebeen identified as the dominant relaxation paths forthe 12CO2 isotope, are closer than for 12CO2, but not byenough to account for the much faster vibrational re-laxation. One possibility is that the faster relaxationis due to the asymmetric l6 O13C18O molecule, whichwas present at the 8-10% level in the 13CO2 samplesused for these experiments. Subsequent measure-ments with 13CO2 samples having only natural abun-dance 180 showed -10% higher peak gain due to thehigher concentration of 13CO2, but the same rapid de-cay times were observed as with the less pure samples.The results of other workers, which were publishedduring our investigation, tend to indicate that the rap-id vibrational decay observed for the 13CO2 does nothold for the other C02 isotopes. 6

The rate constants obtained in this work are not asaccurate as those obtained using laser-induced fluores-cence techniques, like that employed by Moore and co-workers.5 However, in the absence of such measure-ments, the rate constants determined in our smallsignal gain decay measurements can serve as a usefulguide for those needing estimates of the vibrationalrelaxation of 13CO2 for such purposes as designinglasers and laser amplifiers operating on the rare 13CO2isotope. For pulse durations shorter than the vibra-

tional relaxation time of the laser gas mixture, the gainand performance for the 13CO2 isotope will be compa-rable with that obtained with the normal 12002 iso-tope, but for long pulse and cw lasers the faster vibra-tional relaxation for the 3CO2 isotope will result inlower gain despite the higher transition probabilitywhen compared to the normal 12CO2 isotope. In addi-tion, our results explain the conflicting gain and laserperformance data reported by other workers for verydifferent pumping conditions.

The authors would like to acknowledge several help-ful discussions with John Reid of McMaster Universi-ty.

This work was supported by MIT/Lincoln Labora-tory through Rockwell International/Satellite andSpace Electronics Division contract P6L7XNG-484203M.References1. C. Freed, "Status of CO2 Isotope Lasers and Their Applications in

Tunable Laser Spectroscopy," IEEE J. Quantum Electron. QE-18, 1220 (1982).

2. C. Willis, P. A. Hackett, and J. M. Parsons, "Use of 13CO2 in High-Power Pulsed TEA Lasers," Rev. Sci. Instrum. 50, 1141 (1979).

3. M. S. Abubaker and J. H. Shaw, "Carbon Dioxide Band Intensi-ties and Linewidths in the 8-12-itm Region," Appl. Opt. 25, 1196(1986); L. S. Rothman and L. D. G. Young, "Infrared EnergyLevels and Intensities of Carbon Dioxide-II," J. Quant. Spec-trosc. Radiat. Transfer 25, 505 (1981).

4. R. K. Brimacombe and J. Reid, "Measurements of AnomalousGain Coefficients in Transversely Excited CO2 Lasers," IEEE J.Quantum Electron. QE-19, 1674 (1983).

5. C. B. Moore, R. E. Wood, B.-L. Hu, and J. T. Yardley, "Vibration-al Energy Transfer in CO2 Lasers," J. Chem. Phys. 46, 4222(1967).

6. V. 0. Petukhov et al., "Investigation of the Properties of theActive Medium of a CO2 Laser Containing Isotopically Substitut-ed Carbon Dioxide and Nitrogen Molecules," Sov. J. QuantumElectron. 16, 1135 (1986).

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