Abstract

A self-consistent perturbation method is developed for the determination of the normal modes and eigenvalues of optic cavities of small Fresnel numbers. The method permits direct determination of the field distribution and eigenvalue (i.e., the diffraction loss and resonant frequency) of a normal mode of any given order to within any desired accuracy without simultaneously solving for the other modes, and can be applied to cavities having end reflectors of arbitrary shape and curvature. The method is applied to solve the integral equation governing the relation between the normal modes and the geometry of the cavity for the particular case of infinite-strip parabolic cavities.

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  1. A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).
  2. G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
  3. L. Bergstein and H. Schachter, J. Opt. Soc. Am. 54, 887 (1964).
  4. H. Schachter, "Resonant Modes of Optic Cavities," Ph.D. dissertation, Polytechnic Institute of Brooklyn, June 1964.
  5. G. D. Boyd and J. P. Gordon, Bell System Tech. J. 41, 1347 (1962).
  6. S. R. Barone, J. Appl. Phys. 34, 831 (1963).
  7. A. G. Fox and T. Li, Proc. IEEE 51, 80 (1963).
  8. D. Gloge, Arch. Elect. Über. 18, 197 (1964).
  9. L. A. Vainshtein, Soviet Physics-JETP 17, 709 (1963).
  10. J . T. LaTourette, S. F. Jacobs, and P. Rabinowitz, Appl. Opt. 3, 981 (1964).
  11. We order the modes in order of increasing losses (or, equivalently, decreasing eigenvalues) and assign the index 1 to the dominant or lowest-order mode, the index 2 to the next higher-order mode, etc.
  12. We set [equation]
  13. It was pointed out by one of the reviewers that the zeroth-order eigenfunctions and eigenvalues can also be obtained from Eq. (17) by expanding exp{-iπHξ} in terms of the prolate-spheroidal wavefunctions14 {SonH,ξ).
  14. C. Flammer, Spheroidal Wave Functions (Stanford University Press, Stanford California, 1957).

Barone, S. R.

S. R. Barone, J. Appl. Phys. 34, 831 (1963).

Bergstein, L.

L. Bergstein and H. Schachter, J. Opt. Soc. Am. 54, 887 (1964).

Boyd, G. D.

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

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 41, 1347 (1962).

Flammer, C.

C. Flammer, Spheroidal Wave Functions (Stanford University Press, Stanford California, 1957).

Fox, A. G.

A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).

A. G. Fox and T. Li, Proc. IEEE 51, 80 (1963).

Gloge, D.

D. Gloge, Arch. Elect. Über. 18, 197 (1964).

Gordon, J. P.

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 41, 1347 (1962).

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

Jacobs, S. F.

J . T. LaTourette, S. F. Jacobs, and P. Rabinowitz, Appl. Opt. 3, 981 (1964).

LaTourette, J . T.

J . T. LaTourette, S. F. Jacobs, and P. Rabinowitz, Appl. Opt. 3, 981 (1964).

Li, T.

A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).

A. G. Fox and T. Li, Proc. IEEE 51, 80 (1963).

Rabinowitz, P.

J . T. LaTourette, S. F. Jacobs, and P. Rabinowitz, Appl. Opt. 3, 981 (1964).

Schachter, H.

H. Schachter, "Resonant Modes of Optic Cavities," Ph.D. dissertation, Polytechnic Institute of Brooklyn, June 1964.

L. Bergstein and H. Schachter, J. Opt. Soc. Am. 54, 887 (1964).

Vainshtein, L. A.

L. A. Vainshtein, Soviet Physics-JETP 17, 709 (1963).

Other

A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).

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

L. Bergstein and H. Schachter, J. Opt. Soc. Am. 54, 887 (1964).

H. Schachter, "Resonant Modes of Optic Cavities," Ph.D. dissertation, Polytechnic Institute of Brooklyn, June 1964.

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 41, 1347 (1962).

S. R. Barone, J. Appl. Phys. 34, 831 (1963).

A. G. Fox and T. Li, Proc. IEEE 51, 80 (1963).

D. Gloge, Arch. Elect. Über. 18, 197 (1964).

L. A. Vainshtein, Soviet Physics-JETP 17, 709 (1963).

J . T. LaTourette, S. F. Jacobs, and P. Rabinowitz, Appl. Opt. 3, 981 (1964).

We order the modes in order of increasing losses (or, equivalently, decreasing eigenvalues) and assign the index 1 to the dominant or lowest-order mode, the index 2 to the next higher-order mode, etc.

We set [equation]

It was pointed out by one of the reviewers that the zeroth-order eigenfunctions and eigenvalues can also be obtained from Eq. (17) by expanding exp{-iπHξ} in terms of the prolate-spheroidal wavefunctions14 {SonH,ξ).

C. Flammer, Spheroidal Wave Functions (Stanford University Press, Stanford California, 1957).

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