Abstract

A simple, three-dimensional, holographic grating consists of a sinusoidally modulated dielectric slab. The assumption that the modulation index, δ, is constant is at most a first-order approximation. Usually, the light beams used in making the grating are attenuated inside the recording material, hence δ varies within the dielectric slab. From known solutions for the electromagnetic field diffracted by a uniform dielectric grating, solutions for the case when δ is not constant are found, first for a lossless and then for a lossy dielectric grating. The effective modulation index of the grating at exactly Bragg-angle incidence is given by the averaged value of δ over the slab thickness.

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), p. 593.
  2. E. I. Gordon and M. G. Cohen, IEEE JQ-1, 191 (1965).
  3. H. Kogelnik, in Proc. Symposium on Modern Optics 1967, Jerome Fox, Ed. (Polytechnic Press, Brooklyn, 1968; John Wiley & Sons, Inc., New York, distr.), p. 605.
  4. P. Phariseau, Proc. Indian Acad. Sci. 44A, 165 (1953).
  5. L. Bergstein and D. Kermisch, in Proc. on Modern Symposium Optics 1967, Jerome Fox, Ed. (Polytechnic Press, Brooklyn, 1968; John Wiley & Sons, Inc., New York, distr.), p. 655.
  6. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).
  7. We assumed, as is usually the case with practical three-dimensional gratings, that the absorption per wavelength is small, that is, α«1.
  8. D. Kermisch, Ph.D. dissertation, Polytechnic Institute of Brooklyn, June 1968.

Bergstein, L.

L. Bergstein and D. Kermisch, in Proc. on Modern Symposium Optics 1967, Jerome Fox, Ed. (Polytechnic Press, Brooklyn, 1968; John Wiley & Sons, Inc., New York, distr.), p. 655.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), p. 593.

Cohen, M. G.

E. I. Gordon and M. G. Cohen, IEEE JQ-1, 191 (1965).

Gordon, E. I.

E. I. Gordon and M. G. Cohen, IEEE JQ-1, 191 (1965).

Kermisch, D.

D. Kermisch, Ph.D. dissertation, Polytechnic Institute of Brooklyn, June 1968.

L. Bergstein and D. Kermisch, in Proc. on Modern Symposium Optics 1967, Jerome Fox, Ed. (Polytechnic Press, Brooklyn, 1968; John Wiley & Sons, Inc., New York, distr.), p. 655.

Kogelnik, H.

H. Kogelnik, in Proc. Symposium on Modern Optics 1967, Jerome Fox, Ed. (Polytechnic Press, Brooklyn, 1968; John Wiley & Sons, Inc., New York, distr.), p. 605.

Kozma, A.

E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).

Leith, E. N.

E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).

Marks, J.

E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).

Massey, N.

E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).

Phariseau, P.

P. Phariseau, Proc. Indian Acad. Sci. 44A, 165 (1953).

Upatnieks, J.

E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), p. 593.

Other (8)

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), p. 593.

E. I. Gordon and M. G. Cohen, IEEE JQ-1, 191 (1965).

H. Kogelnik, in Proc. Symposium on Modern Optics 1967, Jerome Fox, Ed. (Polytechnic Press, Brooklyn, 1968; John Wiley & Sons, Inc., New York, distr.), p. 605.

P. Phariseau, Proc. Indian Acad. Sci. 44A, 165 (1953).

L. Bergstein and D. Kermisch, in Proc. on Modern Symposium Optics 1967, Jerome Fox, Ed. (Polytechnic Press, Brooklyn, 1968; John Wiley & Sons, Inc., New York, distr.), p. 655.

E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).

We assumed, as is usually the case with practical three-dimensional gratings, that the absorption per wavelength is small, that is, α«1.

D. Kermisch, Ph.D. dissertation, Polytechnic Institute of Brooklyn, June 1968.

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