OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 22, Iss. 21 — Nov. 1, 1983
  • pp: 3338–3346

Closed-cavity solutions with partially coherent fields in the space-frequency domain

Anup Bhowmik  »View Author Affiliations

Applied Optics, Vol. 22, Issue 21, pp. 3338-3346 (1983)

View Full Text Article

Enhanced HTML    Acrobat PDF (1106 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Closed or stable optical cavities, used frequently to determine the efficiency of high performance chemical laser nozzles, are designed primarily for maximum multimode power extraction from the medium. The very large (>500) Fresnel numbers associated with such cavities have in the past necessitated their analytical modeling by representing them as plane-parallel Fabry-Perot or rooftop cavities. In this paper, a rigorous 2-D scalar diffraction formalism of the closed cavity is presented in which quasi-monochromatic partially coherent fields in the space-frequency domain are used to obtain quasi-steady state but stable solutions using a simplified gain model. Small power fluctuations in the numerical iterative solution history that displays no monotonic increasing or decreasing trends are interpreted as the redistribution of energy from one degenerate set of high-order transverse modes into another. The degree of coherence in the second-order spatial correlation function (or the mutual coherence function) required of the input fields which permit such solutions is presented. Further, it is shown that the upstream/downstream coupling in this closed cavity occurs as a natural consequence of the physical model itself rather than through some artificial geometrical means, such as that introduced in the rooftop model. The axial variation in the resulting mode width is in excellent agreement with the Hermite-Gaussian distribution predicted for the particular geometry of interest. The computed closed-cavity power variation with mode width using a simplified gain model shows qualitative agreement with experimentally observed trends; quantitative agreement is poor and is ascribed to the rudimentary nature of the gain model. In the limiting case of small Fresnel numbers (NF ∼ 1) this procedure yields, in the bare cavity, the well-known fundamental mode of the cavity when appropriate symmetry constraints are applied.

© 1983 Optical Society of America

Original Manuscript: March 31, 1983
Published: November 1, 1983

Anup Bhowmik, "Closed-cavity solutions with partially coherent fields in the space-frequency domain," Appl. Opt. 22, 3338-3346 (1983)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. J. Spencer, D. A. Durran, H. A. Bixler, Appl. Phys. Lett. 20, 164 (1972). [CrossRef]
  2. H. Mirels, D. J. Spencer, IEEE J. Quantum Electron. QE-7, 501 (1971). [CrossRef]
  3. D. J. Spencer, H. Mirels, T. A. Jacobs, Appl. Phys. Lett. 16, 384 (1970). [CrossRef]
  4. L. Forman, AFWL-TR-77-131, Rocketdyne Report RI/RD77-171 (Dec.1977).
  5. D. L. Hook et al., AFWL-TR-76-295, TRW Report 27351-6002-RU-00 (Apr.1977).
  6. G. W. Tregay et al., Bell Aerospace Report9276-928001 (Jan.1978).
  7. J. E. Broadwell, Appl. Opt. 13, 962 (1974). [CrossRef] [PubMed]
  8. S. W. Zelazny, R. J. Driscoll, J. W. Raymonda, J. A. Blauer, W. C. Solomon, AIAA J. 16, 297 (1978). [CrossRef]
  9. T. T. Yang, R. E. Swanson, AIAA Paper 79-1490, Williamsburg, Va. (1979).
  10. J. Theones, A. W. Ratcliff, AIAA Paper 73-644, Palm Springs, Calif. (1973).
  11. R. W. F. Gross, J. F. Bott, Eds., Handbook of Chemical Lasers (Wiley, New York, 1976), p. 110.
  12. A. W. Ratcliff, J. Theones, AIAA Paper 74-225, Washington, D.C. (1974).
  13. R. J. Hall, IEEE J. Quantum Electon. QE-12, 453 (1976). [CrossRef]
  14. W. L. Rushmore, S. W. Zelazny, AIAA Paper IV-5, Cambridge, Mass. (1978).
  15. T. T. Yang, J. Phys. C9, 51 (1980).
  16. On one occasion a negative branch unstable resonator was used. See, for example, D. O'Keefe, T. Sugimura, W. Behrens, D. Bullock, D. Dee, Opt. Eng. 18, 363 (1979). [CrossRef]
  17. R. R. Mikatarian, AIAA Paper 74-547, Palo Alto, Calif. (1974).
  18. R. Tripodi, L. J. Coulter, B. R. Bronfin, L. S. Cohen, AIAA J. 13, 776 (1975). [CrossRef]
  19. A. Bhowmik, T. T. Yang, J. J. Vieceli, W. D. Chadwick, Appl. Opt. 22, 3347 (1983), same issue. [CrossRef] [PubMed]
  20. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), p. 509.
  21. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Sees. 10.4.2 and 10.4.3.
  22. A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).
  23. Ref. 21, p. 119.
  24. E. O. Brigham, Fast Fourier Transform (Prentice-Hill, Engle-wood Cliffs, N.J., 1964).
  25. The propagation Fresnel number NF is defined as NF = G2a1a2/λz, where Ga1 and Ga2 are the radial extent of the field at the input and output stations, respectively, λ is the wavelength, and z is the spacing between the two stations.
  26. E. A. Sziklas, A. E. Siegman, Appl. Opt. 14, 1874 (1975). [CrossRef] [PubMed]
  27. The periodicity can easily be found by computing the reentrant condition for the cavity; see, for example, D. R. Herriott, H. Kogelnik, R. Kompfner, Appl. Opt. 3, 523 (1964). [CrossRef]
  28. Yu. A. Ananev, Sov. J. Quantum Electron. 5, 615 (1975). [CrossRef]
  29. Ref. 20, p. 509.
  30. Note that, when K ≠ 0, the input function ψ(x) in Eq. (8) is neither symmetric nor antisymmetric about the optic axis as a result of the random spatial distribution of the phase function R(xn).
  31. L. Mandel, E. Wolf, Opt. Commun. 36, 247 (1981). [CrossRef]
  32. J. K. Cawthra, “Chemical Laser Nozzle Technology,” Final Report, (Apr.1983),in preparation.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited