Abstract

General sets of higher-order beam modes are derived for light propagation in media having spatial variations of the gain or loss. The resulting expressions are also valid for propagation through conventional optical elements and graded transmission filters. The four basic mode sets obtained include off-axis Hermite-Gaussian and Laguerre-Gaussian modes of both real and complex argument. A procedure is developed for finding the resonant modes of laser oscillators containing arbitrary complex lens elements, and the mode stability properties of lasers can be interpreted physically by means of these formulas.

© 1976 Optical Society of America

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  1. G. Goubau and F. Schwering, IRE Trans. Antennas Propag. AP-9, 248 (1961).
  2. G. D. Boyd and J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).
  3. H. Kogelnik, Appl. Opt. 4, 1562 (1965),
  4. L. W. Casperson, Appl. Opt. 12, 2434 (1973), and references therein.
  5. Y. Suematsu, T. Shimizu, and T. Kitano, Electron. Commune. Jpn. 53-B, 77 (1970).
  6. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), p. 275.
  7. J. A. Arnaud, J. Opt. Soc. Am. 61, 751 (1971).
  8. J. A. Arnaud, Progress in Optics (North-Holland, Amsterdam, 1973), Vol. 11, p. 247.
  9. L. W. Casperson and S. J. Sheldrake, Opt. Commun. 12, 349 (1974).
  10. L. W. Casperson and S. D. Lunnam, Appl. Opt. 14, 1193 (1975).
  11. Handbook of Mathematical Functions, Natl. Bur. Stand. Appl. Math. Ser. 55 (U. S. Government Printing Office, Washington, D. C., 1964), Chap. 22.
  12. H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
  13. L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974).
  14. N. G. Vakimov, Radio Eng. Electron. Phys. 10, 1439 (1965).
  15. J. A. Arnaud, Proc. IEEE 62, 1561 (1974).
  16. U. Ganiel and Y. Silberberg, Appl. Opt. 14, 306 (1975).
  17. U. Ganiel, A. Hardy, and Y. Silberberg, Opt. Commun. 14, 290 (1975).

1975

L. W. Casperson and S. D. Lunnam, Appl. Opt. 14, 1193 (1975).

U. Ganiel and Y. Silberberg, Appl. Opt. 14, 306 (1975).

U. Ganiel, A. Hardy, and Y. Silberberg, Opt. Commun. 14, 290 (1975).

1974

J. A. Arnaud, Proc. IEEE 62, 1561 (1974).

L. W. Casperson and S. J. Sheldrake, Opt. Commun. 12, 349 (1974).

L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974).

1973

L. W. Casperson, Appl. Opt. 12, 2434 (1973), and references therein.

1971

J. A. Arnaud, J. Opt. Soc. Am. 61, 751 (1971).

1970

Y. Suematsu, T. Shimizu, and T. Kitano, Electron. Commune. Jpn. 53-B, 77 (1970).

1966

H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).

1965

N. G. Vakimov, Radio Eng. Electron. Phys. 10, 1439 (1965).

H. Kogelnik, Appl. Opt. 4, 1562 (1965),

1964

Handbook of Mathematical Functions, Natl. Bur. Stand. Appl. Math. Ser. 55 (U. S. Government Printing Office, Washington, D. C., 1964), Chap. 22.

1961

G. Goubau and F. Schwering, IRE Trans. Antennas Propag. AP-9, 248 (1961).

G. D. Boyd and J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).

Arnaud, J. A.

J. A. Arnaud, Proc. IEEE 62, 1561 (1974).

J. A. Arnaud, J. Opt. Soc. Am. 61, 751 (1971).

J. A. Arnaud, Progress in Optics (North-Holland, Amsterdam, 1973), Vol. 11, p. 247.

Boyd, G. D.

G. D. Boyd and J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).

Casperson, L. W.

L. W. Casperson and S. D. Lunnam, Appl. Opt. 14, 1193 (1975).

L. W. Casperson and S. J. Sheldrake, Opt. Commun. 12, 349 (1974).

L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974).

L. W. Casperson, Appl. Opt. 12, 2434 (1973), and references therein.

Ganiel, U.

U. Ganiel and Y. Silberberg, Appl. Opt. 14, 306 (1975).

U. Ganiel, A. Hardy, and Y. Silberberg, Opt. Commun. 14, 290 (1975).

Gordon, J. P.

G. D. Boyd and J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).

Goubau, G.

G. Goubau and F. Schwering, IRE Trans. Antennas Propag. AP-9, 248 (1961).

Hardy, A.

U. Ganiel, A. Hardy, and Y. Silberberg, Opt. Commun. 14, 290 (1975).

Kitano, T.

Y. Suematsu, T. Shimizu, and T. Kitano, Electron. Commune. Jpn. 53-B, 77 (1970).

Kogelnik, H.

H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).

H. Kogelnik, Appl. Opt. 4, 1562 (1965),

Li, T.

H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).

Lunnam, S. D.

L. W. Casperson and S. D. Lunnam, Appl. Opt. 14, 1193 (1975).

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), p. 275.

Schwering, F.

G. Goubau and F. Schwering, IRE Trans. Antennas Propag. AP-9, 248 (1961).

Sheldrake, S. J.

L. W. Casperson and S. J. Sheldrake, Opt. Commun. 12, 349 (1974).

Shimizu, T.

Y. Suematsu, T. Shimizu, and T. Kitano, Electron. Commune. Jpn. 53-B, 77 (1970).

Silberberg, Y.

U. Ganiel and Y. Silberberg, Appl. Opt. 14, 306 (1975).

U. Ganiel, A. Hardy, and Y. Silberberg, Opt. Commun. 14, 290 (1975).

Suematsu, Y.

Y. Suematsu, T. Shimizu, and T. Kitano, Electron. Commune. Jpn. 53-B, 77 (1970).

Vakimov, N. G.

N. G. Vakimov, Radio Eng. Electron. Phys. 10, 1439 (1965).

Other

G. Goubau and F. Schwering, IRE Trans. Antennas Propag. AP-9, 248 (1961).

G. D. Boyd and J. P. Gordon, Bell Syst. Tech. J. 40, 489 (1961).

H. Kogelnik, Appl. Opt. 4, 1562 (1965),

L. W. Casperson, Appl. Opt. 12, 2434 (1973), and references therein.

Y. Suematsu, T. Shimizu, and T. Kitano, Electron. Commune. Jpn. 53-B, 77 (1970).

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), p. 275.

J. A. Arnaud, J. Opt. Soc. Am. 61, 751 (1971).

J. A. Arnaud, Progress in Optics (North-Holland, Amsterdam, 1973), Vol. 11, p. 247.

L. W. Casperson and S. J. Sheldrake, Opt. Commun. 12, 349 (1974).

L. W. Casperson and S. D. Lunnam, Appl. Opt. 14, 1193 (1975).

Handbook of Mathematical Functions, Natl. Bur. Stand. Appl. Math. Ser. 55 (U. S. Government Printing Office, Washington, D. C., 1964), Chap. 22.

H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).

L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974).

N. G. Vakimov, Radio Eng. Electron. Phys. 10, 1439 (1965).

J. A. Arnaud, Proc. IEEE 62, 1561 (1974).

U. Ganiel and Y. Silberberg, Appl. Opt. 14, 306 (1975).

U. Ganiel, A. Hardy, and Y. Silberberg, Opt. Commun. 14, 290 (1975).

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