Abstract

A simple procedure is described to obtain the modes of propagation in square-law lens-like media. This procedure consists of evaluating the geometrical-optics field created by a point source at the input plane of an optical system (called mode-generating system) with nonuniform losses. An expansion of the field in power series of the coordinates of the point source gives the modes of propagation. In the case of optical resonators, the mode-generating system is described by the modal matrix of the resonator round-trip ray matrix. This representation of modes by point sources allows the coupling factor between two modes with different parameters (beam radii, wave-front curvatures, and axes) to be evaluated without integration. Only matrix algebra is used. In the general three-dimensional case, the coupling factor is expressed as a product of Gauss functions and Hermite polynomials in four complex variables. The quantities introduced are generalized ray invariants.

PDF Article

References

  • View by:
  • |
  • |

  1. H. Kogelnik, in Quasi-Optics, edited by J. Fox (Polytechnic Press, Brooklyn, 1964).
  2. J. A. Arnaud, Bell System Tech. J. 49, 2311 (1970). Note that a factor j is missing in Eqs. (15a), (20), (43) and that the minus sign in front of h in Eqs. (47) and (50) should be deleted.
  3. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964).
  4. J. H. Van Vleck, Proc. Natl. Acad. Sci. (U.S.) 14, 178 (1928).
  5. G. S. S. Avila and J. B. Keller, Commun. Pure Appl. Math. 16, 363 (1963).
  6. J. S. Dowker, J. Phys. A.: Gen. Phys. 3, 451 (1970).
  7. P. Appel and J. Kampé de Fériet, Fonctions Hypergéomètriques et Hypersphérique/Polynomes d'Hermite (Gauthier-Villars, Paris, 1926).
  8. J. A. Arnaud, Appl. Opt. 8, 1909 (1969).
  9. H. Grad, Commun. Pure Appl. Math. 2, 325 (1949)

Appel, P.

P. Appel and J. Kampé de Fériet, Fonctions Hypergéomètriques et Hypersphérique/Polynomes d'Hermite (Gauthier-Villars, Paris, 1926).

Arnaud, J. A.

J. A. Arnaud, Bell System Tech. J. 49, 2311 (1970). Note that a factor j is missing in Eqs. (15a), (20), (43) and that the minus sign in front of h in Eqs. (47) and (50) should be deleted.

J. A. Arnaud, Appl. Opt. 8, 1909 (1969).

Avila, G. S. S.

G. S. S. Avila and J. B. Keller, Commun. Pure Appl. Math. 16, 363 (1963).

de Fériet, J. Kampé

P. Appel and J. Kampé de Fériet, Fonctions Hypergéomètriques et Hypersphérique/Polynomes d'Hermite (Gauthier-Villars, Paris, 1926).

Dowker, J. S.

J. S. Dowker, J. Phys. A.: Gen. Phys. 3, 451 (1970).

Grad, H.

H. Grad, Commun. Pure Appl. Math. 2, 325 (1949)

Keller, J. B.

G. S. S. Avila and J. B. Keller, Commun. Pure Appl. Math. 16, 363 (1963).

Kogelnik, H.

H. Kogelnik, in Quasi-Optics, edited by J. Fox (Polytechnic Press, Brooklyn, 1964).

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964).

Van Vleck, J. H.

J. H. Van Vleck, Proc. Natl. Acad. Sci. (U.S.) 14, 178 (1928).

Other (9)

H. Kogelnik, in Quasi-Optics, edited by J. Fox (Polytechnic Press, Brooklyn, 1964).

J. A. Arnaud, Bell System Tech. J. 49, 2311 (1970). Note that a factor j is missing in Eqs. (15a), (20), (43) and that the minus sign in front of h in Eqs. (47) and (50) should be deleted.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964).

J. H. Van Vleck, Proc. Natl. Acad. Sci. (U.S.) 14, 178 (1928).

G. S. S. Avila and J. B. Keller, Commun. Pure Appl. Math. 16, 363 (1963).

J. S. Dowker, J. Phys. A.: Gen. Phys. 3, 451 (1970).

P. Appel and J. Kampé de Fériet, Fonctions Hypergéomètriques et Hypersphérique/Polynomes d'Hermite (Gauthier-Villars, Paris, 1926).

J. A. Arnaud, Appl. Opt. 8, 1909 (1969).

H. Grad, Commun. Pure Appl. Math. 2, 325 (1949)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.