Absorption of 9.6-,um CO2 laser radiation by CO2 atelevated temperatures

A. M. Robinson

Absorption of 9 .6 -,Mm CO2 laser radiation by CO2 at temperatures between 296 and 625 K has been measuredat a pressure of 200 Torr. Experimental results for the R1O-R26 and P1O-P28 transitions have been ob-tained and compared with computed values of absorption. The relative optical broadening coefficients dueto He and N2 have been measured on the R16-R22 and P16-P22 transitions over the same temperaturerange.

Investigations of absorption of 10.4-gm laser radia-tion by CO2 gas mixtures at elevated temperatures havebeen performed and the results compared with calcu-lations using models of varying degrees of complexity.'1Such measurements and calculations are important forthe design and use of CO2 systems exhibiting absorptionor gain. Little work has been reported on similarmeasurements on the 9.6-gm CO2 laser transitions, al-though some measurements and computations havebeen made for laser action9"10 and room-temperatureabsorption.1-' 3 Because of the need of such data forthe 9.6-,m transition, a series of measurements hasbeen undertaken and the results are reported here.

We have measured absorption over several lines of the9.6-gm 00011-1000214 transition at temperatures be-tween 296 and 625 K, at a pressure of 200 Torr. Theabsorption coefficient k has been measured as a func-tion of temperature T for the R10-R26 and P10-P28lines inclusive. As well, the relative optical broadeningcoefficients due to He and N2 have been determined forthe R16-R22 and P16-P22 transitions. Calculationsof k as a function of T were also performed using themost recent spectroscopic and molecular data available.In general, agreement between calculation and mea-surement was not as good as reported for the 10.4-gmtransition.5-7

The experimental procedure for measuring k hasbeen described in detail,7 except that the radiationemitted by the CO2 laser source was set to the 9.6-,m

The author is with University of Alberta, Electrical EngineeringDepartment, Edmonton, Alberta T6G 2G7.

Received 12 October 1982.0003-6935/83/050718-03$01.00/0.© 1983 Optical Society of America.

transition. Determination of the relative opticalbroadening coefficients for He and N2 utilized themethod recently described.15

The variation of k with T was similar to that observedon the 10.4-gm transition, 5 ' 6 namely, a monotonic in-crease that could be approximated by a cubic polyno-minal in T. In general, the absorption was greater at9.6 gm than the transitions in corresponding conditionsat 10.4 gim, as expected from room-temperature re-sultS.3 Table I lists the coefficients of the least-squaresfit cubic polynomials determined to describe the ex-perimental variation of k with T for all transitionsstudied. The estimated uncertainty in k decreased withincreasing T; it was estimated to be 15% or less at 300K, reducing to 3% at 620 K.

As with our previous study,7 cubic polynomials of Tas a function of k were also fitted to the data in order todetermine T from a measured value of k; the coefficientsof these polynomials are listed in Table II.

Calculation of the absorption coefficient of all thetransitions studied was undertaken by methods similarto those described previously.6 The AFGL 1980 ta-bles14 were used extensively to determine which higherenergy transitions, if any, overlap and contribute sig-nificantly to the absorption coefficient at line center ofthe 00011-10002 transitions. The latter are referredto hereafter as the main transitions, and the former asoverlapping transitions.

Components needed to compute the absorptioncoefficient of the main transitions are the line centerwave number,'6 the pressure broadened linewidth,17 thetransition probability (or line strength), 12" 3" 8 andupper and lower energy levels.14 The transition prob-ability used was an average of three experimentallydetermined values. For a given main transition, alloverlapping transitions listed in the AFGL tables wereconsidered, using the wave number difference, line in-tensity, and energy levels listed. The linewidth was

718 APPLIED OPTICS / Vol. 22, No. 5 / 1 March 1983

Table 1. Coefficients of Cubic Polynomial of k vs T, 9.6-Mm Transition

k =aT3 + bT 2 + cT + d [h] = 10-3 cm'A aX10 7 bX10 4 cX10 d

R10 a -2.940 3.480 -0.8722 4.991R12 -3.468 4.187 -1.110 7.437R14 -3.696 4.527 -1.204 8.069R16 -3.871 4.759 -1.257 8.064R18 -4.624 5.839 -1.710 13.95R20 -5.305 6.808 -2.121 19.35R22 -5.074 6.631 -2.081 18.99R24 -6.278 8.513 -2.891 29.52R26 -5.702 7.851 -2.774 30.38

plob 3.048 -5.176 3.341 -63.34P12 -2.656 3.151 -0.7396 3.291P14 -3.457 4.227 -1.146 8.111P16 -3.778 4.699 -1.303 9.539P18 -3.783 4.776 -1.340 10.02P20 -4.422 5.695 -1.725 14.91P22 -4.969 6.854 -2.283 22.70P24 -4.152 5.488 -1.667 13.90P26 -4.924 6.685 -2.259 22.90P28 -5.027 6.911 -2.396 24.97

a 295 K ' T < 625 K for all R-branch transitions listed except R26,for which 385 < T < 620 K.

b 295 K • T < 635 K for all P-branch transitions listed except P10,for which 405 • T < 595 K.

Table II. Coefficients of Cubic Polynomial of T vs k, 9.6-Mm Transition

T =ek3 +fk 2 +gk + h [hi = 10-3 cm-A e f g h

R10a 0.1751 -3.713 43.80 216.1R12 0.1029 -2.524 36.25 222.8R14 0.0597 -1.665 29.80 228.4R16 0.0445 -1.322 26.49 234.7R18 0.0379 -1.231 25.75 236.4R20 0.0341 -1.168 25.08 239.4R22 0.0259 -0.9340 22.98 246.3R24 0.0150 -0.6581 19.70 255.8R26 0.0269 -1.073 25.72 242.4

p1 0 b -0.0633 2.722 -16.04 402.3P12 0.1517 -3.399 42.89 213.3P14 0.1066 -2.703 38.06 218.5P16 0.0640 -1.819 31.25 228.9P18 0.0480 -1.445 28.29 233.7P20 0.0409 -1.316 26.96 239.0P22 0.0163 -0.7000 21.15 252.6P24 0.0267 -0.9086 23.07 255.0P26 0.0300 -1.061 24.96 254.4P28 0.0284 -1.002 24.20 263.1

a 295 K < T < 625 K for all R-branch transitions listed except R26,for which 385 K < T < 625 K.

b 295 K < T < 635 K for all P-branch transitions listed except P10,for which 405 K ' T S 595 K.

assumed to be the same as that of the main transi-tion.

Figure 1 shows an example of comparison betweenexperimental and calculated absorption coefficients forall transitions studied at T = 620 K. The solid lines ofthe plot smoothly connect the absorption coefficientscalculated ignoring any contribution from the over-lapping transitions, and the solid circular dots are thetotal calculated absorption coefficients. At transitionswhere the line appears to pass through the solid dots,the overlapping transition contributions amounted to

30

25

.E

I0x 20

15

T=620K - Experiment

- Colculation

a

J- 26 24 22 20 18 6 14 12 10

R-BRANCH

J- I0 12 14 16 i8 20 22 24 26 28

P- BRANCH

Fig. 1. Experimental and calculated values of absorption coefficientk at T = 620 K over the R and P branches of the 9 .6-,um CO 2

transition.

<0.5%. The stars signify the experimentally measuredabsorption coefficients, determined from the cubicpolynomial fits to the data. At T = 620 K, the experi-mental points generally fall below the calculated points;the R-branch points are consistently lower, while theP-branch points drop off more at higher J value. Atlower temperatures, the relative difference betweencalculated and measured values of k becomes consid-erably larger, reaching typical values of 30% at 300 K.Both experiment and calculation indicate a strongcontribution from overlapping transitions on the R24,P10, and P22 lines. Most of the overlap is due to the01111-111102 transition. Table III lists the significanttransitions involved. The lines mentioned above havepreviously been observed to exhibit super absorptionor gain.' 0

The relative optical broadening coefficients for Heand N2 , determined as a function of temperature overthe 300-600-K range, showed the same general variationas observed for the 10.4-gum transitions. 15 Also theestimated uncertainty of the broadening coefficientsover the temperature range exceeded the variation ofthe coefficients, and so a temperature-averaged valueis presented here for each transition. Table IV lists theaverage values, which represent an average of thecoefficients determined every 100 K over the temper-ature range. Note that the variation of the coefficients

Table Ill. Percentage Contribution to Calculated Absorption Coefficient atT = 620 K

OverlappingMain Percent transition Percent

transition contribution (01111-11102)a contribution

R14 99.4 R3 0.6R24 85.3 R12 14.6P10 74.7 P19 25.2P12 99.3 P21 0.6P16 97.9 R8b 2.0P22 90.1 P30 9.8

a See Ref. 14.b The overlapping transition is (10011-20002).

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. . . . . . . .

* * *

Table IV. Temperature-Averaged Relative Optical BroadeningCoefficients, 9.6-Mim Transition

A a = YHe/YCO2 b = YN 2 /YC0 2

R16 0.60 i 0.05 0.82 ± 0.08R18 0.62 i 0.04 0.74 L 0.07R20 0.62 ± 0.06 0.75 ± 0.08R22 0.63 ± 0.04 0.76 i 0.04

P16 0.62 ± 0.04 0.75 ± 0.04P18 0.62 ± 0.04 0.75 ± 0.04P20 0.62 1 0.05 0.74 ± 0.04P22 0.66 ± 0.04 0.76 ± 0.04

with J value is small and differs little from the 10.4-gmvalues.'5 The uncertainties listed in Table IV weredetermined using the estimated uncertainties at eachtemperature and assuming the normal error law is ap-plicable.'9

The technical assistance of P. Haswell and D. Garandis greatly appreciated. The work was supported by theNatural Sciences and Engineering Research Council ofCanada.

References1. R. Ely and T. K. McCubbin, Jr., Appl. Opt. 9, 1230 (1970).2. S. A. Munjee and W. H. Christiansen, Appl. Opt. 12, 993

(1973).3. R. L. Leonard, Appl. Opt. 13, 1920 (1974).4. A. R. Strilchuk and A. A. Offenberger, Appl. Opt. 13, 2643

(1974).5. A. M. Robinson and N. Sutton, Appl. Opt. 16, 2632 (1977).6. A. M. Robinson and N. Sutton, Appl. Opt. 18, 378 (1979).7. A. M. Robinson and E. F. Girczyc, Appl. Opt. 19, 1969 (1980).8. A good review of calculations of gain and absorption in CO 2 may

be found in J. C. Goldstein, "Calculation of Small Signal GainCoefficients in C0 2," Los Alamos Scientific Laboratory reportLA-UR-79-1149 (1979).

9. A. J. Alcock, R. Fedosejevs, and A. C. Walker, IEEE J. QuantumElectron. QE-il, 767 (1975).

10. P. Lavigne, J.-L. Lachambre, and G. Otis, J. Appl. Phys. 49, 3714(1978).

11. C. Rossetti, F. Bourbonneux, R. Farrenq, and P. Barchewitz, C.R. Acad. Sci. Ser. B 262, 1684 (1966).

12. R. Farrenq, C. Rossetti, F. Bourbonneux, and P. Barchewitz, C.R. Acad. Sci. Ser. B 263, 241 (1966).

13. C. Cousin, C. Rossetti, and C. Meyer, C. R. Acad. Sci. Ser. B 268,1640 (1969).

14. All CO2 energy levels are designated using the notation of theAFGL 1980 atmospheric absorption line parameters compilation,described in L. S. Rothman, Appl. Opt. 20, 791 (1981).

15. A. M. Robinson and J. Weiss, Can. J. Phys. 60, 1656 (1982).16. C. Freed, L. C. Bradley, and R. G. O'Donnell, IEEE J. Quantum

Electron. QE-16, 1195 (1980).17. A. D. Devir and U. P. Oppenheim, Appl. Opt. 8, 2121 (1969).18. E. R. Murray, C. Kruger, and M. Mitchner, Appl. Phys. Lett. 24,

180 (1974).19. J. Topping, Errors of Observation and Their Treatment

(Chapman & Hall, London, 1972), pp. 73-74.

B. Keith Jenkins of the University of Southern California. Photo:F. S. Harris, Jr., 1982 Tucson.

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