## Inhomogeneous broadening effects in multimode cw chemical lasers

Applied Optics, Vol. 20, Issue 2, pp. 362-373 (1981)

http://dx.doi.org/10.1364/AO.20.000362

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### Abstract

Analytic solutions are presented for inhomogeneous broadening effects in multimode cw chemical lasers. A Fabry-Perot (F.P.) resonator and a saturated amplifier are considered in the limits Δ*ν** _{h}* ≪ Δ

*ν*

*and Δ*

_{d}*ν*

*≪ Δ*

_{c}*ν*

*, where Δ*

_{h}*ν*

*, Δ*

_{h}*ν*

*, and Δ*

_{d}*ν*

*are homogeneous, Doppler, and longitudinal mode separation widths, respectively. The former inequality requires*

_{c}*p*(Torr) ⩽ 0(10). The results are believed valid for Δ

*ν*

*/Δ*

_{c}*ν*

*⩽ 0(1) and apply for resonator mirror separation lengths and amplifier lengths of the order of 10 m or more. The normalized frequency difference from line center is denoted*

_{h}*X*, and the value of

*X*corresponding to the largest longitudinal mode frequency is denoted

*X*

*. The quantity*

_{f}*X*

*is a measure of laser frequency bandwidth and the number of active longitudinal modes. For the case of an F.P. resonator,*

_{f}*X*

*varies with streamwise distance. The local value of*

_{f}*X*

*is independent of upstream conditions for the case of a saturated F.P. resonator. The variation of lasing intensity with*

_{f}*X*at each streamwise station is found to be a truncated Gaussian. The slope of the curve of

*η*− 1 (anomalous index of refraction) vs

*X*is positive in the lasing region |

*X*| <

*X*

*. The magnitude of*

_{f}*η*− 1 is proportional to the threshold gain. For a typical saturated cw chemical laser oscillator, the anomalous index of refraction is shown to be small, compared with the regular index, for medium pressures in the range

*p*(Torr) ⩾ 0(1). The present analytic results are in good agreement with the numerical results of Bullock and Lipkis.

© 1981 Optical Society of America

**History**

Original Manuscript: June 16, 1980

Published: January 15, 1981

**Citation**

Harold Mirels, "Inhomogeneous broadening effects in multimode cw chemical lasers," Appl. Opt. **20**, 362-373 (1981)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-20-2-362

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### References

- W. R. Bennett, Phys. Rev. 126, 580 (1961). [CrossRef]
- M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974), pp. 144–155.
- T. Kan, C. J. Wolga, IEEE J. Quantum Electron. QE-7, 141 (1971).
- A. Y. Cabezas, R. P. Treat, J. Appl. Phys. 37, 3556 (1966). [CrossRef]
- H. Mirels, AIAA J. 17, 478 (1979). [CrossRef]
- D. L. Bullock, R. S. Lipkis, “Saturation of the Gain and Resonant Dispersion in Chemical Lasers,” at Fourth Annual Tri-Service Chemical Laser Conference, Albuquerque, New Mex., 22 Aug. 1979.
- M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, AMS 55 (National Bureau of Standards, Washington, D.C., June1964), pp. 297–303.
- In the derivation of Eq. (12a) it was noted that the present solution is in error in a region of order Δνh about νjf and 2ν0 − νjf. The latter region corresponds to |X − Xf| = 0.04 in the present example.

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