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Applied Optics

Applied Optics


  • Vol. 12, Iss. 10 — Oct. 1, 1973
  • pp: 2353–2366

Three-Dimensional Diffraction Calculations of Laser Resonator Modes

Arthur N. Chester  »View Author Affiliations

Applied Optics, Vol. 12, Issue 10, pp. 2353-2366 (1973)

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The numerical technique of Fox and Li for computing laser resonator modes is applied to the case of three-dimensional laser resonators without circular or rectangular symmetries. The computation techniques are explained, and results are presented for several specific resonators, both stable and unstable. The effect of laser medium shock waves on the refractive index of the optical cavity is approximated by a thin sheet near one resonator mirror. The near-field burn pattern of the laser output beam exactly follows the phase pattern of the shock fronts, in good qualitative agreement with experimental results reported for gas dynamic lasers. The far-field output beam demonstrates pronounced astigmatism, being considerably broadened at right angles to the flow direction, and it suggests a breakup of the far-field pattern into several separate intensity spots. The optical phase of the resonator mode is quite smooth, even in the worst cases studied, suggesting the possibility of phase compensation by suitable optics.

© 1973 Optical Society of America

Original Manuscript: March 2, 1973
Published: October 1, 1973

Arthur N. Chester, "Three-Dimensional Diffraction Calculations of Laser Resonator Modes," Appl. Opt. 12, 2353-2366 (1973)

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  1. For example, see Refs. 2 through 5 and articles cited therein.
  2. H. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966). [CrossRef] [PubMed]
  3. A. E. Siegman, H. Y. Miller, Appl. Opt. 9, 2729 (1970). [CrossRef] [PubMed]
  4. P. F. Checcacci, A. Consortini, A. Scheggi, IEEE Trans. Microwave Theory Tech. MTT-16, 103 (1968). [CrossRef]
  5. L. A. Weinstein, Open Resonators and Open Waveguides (The Golem Press, Boulder, Colorado, 1969).
  6. G. D. Boyd, H. Kogelnik, Bell Syst. Tech. J. 41, 1347 (1962).
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  8. Yu. A. Kalinin, A. A. Mak, A. I. Stepanov, A. V. Folomeev, V. A. Fromzel’, Sov. Phys.-JETP 29, 624 (1969).
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  10. Yu. A. Anan’ev, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 263 (1971). [CrossRef]
  11. A. N. Chester, Appl. Opt. 11, 2584 (1972). [CrossRef] [PubMed]
  12. A. G. Fox, T. Li, Bell Syst. Tech. J. 40, 453 (1961).
  13. T. Li, Bell Syst. Tech. J. 44, 917 (1965).
  14. Walter K. Kahn, Appl. Opt. 5, 407 (1966). [CrossRef] [PubMed]
  15. S. R. Barone, Appl. Opt. 6, 861 (1967). [CrossRef] [PubMed]
  16. Anthony E. Siegman, Raymond Arrathoon, IEEE J. Quantum Electron. QE-3, 156 (1967). [CrossRef]
  17. William Streifer, IEEE J. Quantum Electron. QE-4, 229 (1968). [CrossRef]
  18. Robert L. Sanderson, William Streifer, Appl. Opt. 8, 131 (1969). [CrossRef] [PubMed]
  19. R. L. Sanderson, William Streifer, Appl. Opt. 8, 2129 (1969). [CrossRef] [PubMed]
  20. Robert L. Sanderson, William Streifer, Appl. Opt. 8, 2241 (1969). [CrossRef] [PubMed]
  21. A. N. Chester, IEEE J. Quantum Electron. QE-9, 209 (1973). [CrossRef]
  22. In particular, unstable resonators can be so sensitive to mirror misalignment or aberration that a perturbation treatment may not converge rapidly enough to model many experimentally interesting cases.21
  23. Since the mirrors are curved, they cannot exactly lie in a plane of constant z. However, as long as the phase shifts introduced into the reflected beam are correctly included, this is not a source of significant error.
  24. See, for example, Eqs. (8.2.1) and (8.3.20) in M. Born, E. Wolf, Principles of Optics (Pergamon Press, New York, 1965).
  25. D. B. Rensch, A. N. Chester, to be published.
  26. M. A. Lintner, “PROJ—Algorithm and Computer Programs for the Hidden Line Problem for Single Valued Surfaces,” Idaho Nuclear Corporation, Idaho Falls, Idaho.
  27. P. O. Clark, “Design considerations for high power laser cavities,” AIAA Paper 72-708, AIAA 5th Fluid and Plasma Dynamics Conference, Boston, Massachusetts, 26–28 June 1972.
  28. E. V. Locke, R. Hella, L. Westra, G. Zeiders, IEEE J. Quantum Electron. QE-7, 581 (1971); erratum: IEEE J. Quantum Electron. QE-8, 389 (1972). [CrossRef]
  29. E. T. Gerry, IEEE Spectrum 7, 51 (1970). [CrossRef]

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