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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 5, Iss. 6 — Jun. 1, 1966
  • pp: 1023–1029

Rays and Ray Envelopes within Stable Optical Resonators Containing Focusing Media

Noritaka Kurauchi and Walter K. Kahn  »View Author Affiliations


Applied Optics, Vol. 5, Issue 6, pp. 1023-1029 (1966)
http://dx.doi.org/10.1364/AO.5.001023


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Abstract

In stable resonators any given initially paraxial rays remain close to the axis of the structure and are, in fact, confined within well-defined contours—the envelope of the ray system. Previously, envelopes of rays in empty resonators had been found and their form identified with the variation of the spot size. This geometric optical approach is extended to general resonators, comprising arbitrary arrangements of lenses and convergent or divergent inhomogeneous focusing media. An invariant quadratic form involving parameters descriptive of any of the ray segments that result from a given initial ray segment leads to a differential equation satisfied by the ray segments and their envelope in portions of the resonator. A maximum–minimum problem for the envelope is formulated and solved. In convergent media the envelope function is found to be periodically modulated. The period of the modulation depends only on the properties of the convergent medium; the location of relative maxima and minima, as well as their ratio, depends on both the medium and associated optics. In special cases, results are compared with available solutions of the corresponding electromagnetic problem. A particularly simple resonator is analyzed, and envelope characteristics correlated with the stability limits.

© 1966 Optical Society of America

History
Original Manuscript: January 3, 1966
Published: June 1, 1966

Citation
Noritaka Kurauchi and Walter K. Kahn, "Rays and Ray Envelopes within Stable Optical Resonators Containing Focusing Media," Appl. Opt. 5, 1023-1029 (1966)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-5-6-1023


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References

  1. J. R. Pierce, Theory and Design of Electron Beams (D. Van Nostrand Co., Inc., Princeton, N.J., 1954), 2nd ed., Chap. 11, pp. 194–213.
  2. G. D. Boyd, H. Kogelnik, Bell System Tech. J. 41, 1347 (1962).
  3. W. K. Kahn, “Ray Theory of Optical Resonators Containing an Inhomogeneous Medium”, 1964 U.R.S.I. Spring Meeting, Abstract 6–1–6, 84 (April1964).
  4. M. Bertolotti, Nuovo Cimento 32, 1242 (1964). [CrossRef]
  5. B. Macke, J. Phys. Appl. 26, 104A (1965).
  6. G. A. Deschamps, P. E. Mast, in Proceedings of the Symposium on Quasi-Optics (Polytechnic Press, Brooklyn, N.Y., 1964), pp. 379–395.
  7. A. E. Siegman, Proc. IEEE 53, 277 (1965). [CrossRef]
  8. W. K. Kahn, Appl. Opt. 5, 407 (1966). [CrossRef] [PubMed]
  9. V. P. Bykov, L. A. Vainstein, Soviet Phys.-JETP 20, 338 (1965).
  10. W. K. Kahn, in Ref. 6, pp. 399–402.
  11. W. K. Kahn, Appl. Opt. 4, 758 (1965). [CrossRef]
  12. W. K. Kahn, “A Ray Theory of Optical Resonators and Beam Waveguides,” P.I.B.-MRI-1285–65, Polytechnic Institute of Brooklyn (July1964). A summary of this report was presented at the 1965 G-MTT Symposium in Clearwater, Florida, 5–7 May 1965. Symp. Dig. Ref. 1–5, pp. 21–24.
  13. M. Born, E. Wolf, Principles of Optics (Pergamon Press, Ltd., London, 1959), Chap. 4.
  14. W. Brouwer, Matrix Methods in Optical Instrument Design (W. A. Benjamin, New York, 1964).
  15. E. L. O’Neill, Introduction to Statistical Optics (Addison–Wesley Publishing Co. Inc., Reading, Mass., 1963).
  16. L. B. Felsen, W. K. Kahn, in Proceedings of the Symposium on Millimeter Waves (Polytechnic Press, Brooklyn, 1959) pp. 477–512.
  17. D. R. Herriott, H. Kogelnik, R. Kompfner, Appl. Opt. 3, 523 (1964). [CrossRef]
  18. G. Goubau, F. Schwering, Trans. Inst. Radio Engrs. AP-9, 248 (1961).
  19. J. Hirano, Y. Fukatsu, Proc. IEEE 52, 1284 (1964). [CrossRef]
  20. S. A. Collins, Appl. Opt. 3, 1263 (1964). [CrossRef]
  21. H. Kogelnik, Bell System Tech. J. 44, 455 (1965).
  22. P. K. Tien, J. P. Gordon, J. R. Whinnery, Proc. IEEE, 53, 129 (1965). [CrossRef]
  23. H. G. Unger, Arch. Elek. Übertrag. 19, 189 (1965).
  24. E. A. Marcatili, Bell System Tech. J. 43, 2887 (1964).
  25. S. E. Miller, Bell System Tech. J. 44, 2017 (1965).
  26. D. Marcuse, Bell System Tech. J. 44, 2065 (1965).
  27. D. Marcuse, Bell System Tech. J. 44, 2083 (1965).
  28. D. W. Berreman, Bell System Tech. J. 44, 2117 (1965).
  29. H. Kogelnik, Appl. Opt. 4, 1562 (1965). [CrossRef]
  30. J. R. Pierce, Proc. Natl. Acad. Sci. U.S. 47, 1808 (1961). [CrossRef]
  31. E. L. Ince, Ordinary Differential Equations (Dover Publications, Inc., New York, 1956); first American ed.; Chap. 3.
  32. Reference 13, p. 121.
  33. S. Barone, W. K. Kahn, B. Lippmann, N. Marcuvitz, S. Schneider, Res. Rept. R–628–57, PIB 556 Polytechnic Institute of Brooklyn (October1957).

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