Abstract

A thick hologram grating with modulation that decreases along the direction perpendicular to the grating vector has been analyzed using coupled-wave theory developed by Kogelnik. General solutions of two predominant waves, undiffracted and first-order diffracted waves, are given for transmission and reflection types of hologram gratings. Calculated efficiency of diffraction for some special cases is compared with that for the uniform grating. The influence of the attenuation of grating modulation upon the validity of the theory when applied to the Bragg reflection is also discussed.

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  1. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, Appl. Opt. 5, 1303 (1966).
  2. C. B. Burckhardt, J. Opt. Soc. Am. 56, 1502 (1966); J. Opt. Soc. Am. 57, 601 (1967).
  3. D. Gabor and G. W. Stroke, Proc. R. Soc. (Lond.) A304, 275 (1968).
  4. H. Kogelnik, in Proceedings of the Symposium on Modern Optics, edited by J. Fox (Polytechnic Press, Brooklyn, 1967), pp. 605–617.
  5. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  6. P. Phariseau, Proc. Indian Acad. Sci. A44, 165 (1956).
  7. F. S. Chen, J. T. LaMacchia, and D. B. Fraser, Appl. Phys. Lett. 13, 223 (1968).
  8. G. E. Peterson, A. M. Glass, and T. J. Negran, Appl. Phys. Lett. 19, 130 (1971).
  9. J. J. Amodei, W. Phillips, and D. L. Staebler, Appl. Opt. 11, 390 (1972).
  10. See, for instance, E. Kamke, Differentialgleichungen, Lösungsmethoden und Lösungen (Chelsea, New York, 1959), pp. 437–440.
  11. N. Uchida, Japan. J. Appl. Phys. 8, 935 (1969).
  12. C. F. Quate, C. D. W. Wilkinson, and D. K. Winslow, Proc. Inst. Electr. Eng. 53, 1604 (1965).
  13. G. W. Willard, J. Acoust. Soc. Am. 21, 101 (1949).
  14. W. R. Klein and B. D. Cook, IEEE Trans. Sonics Ultrason. 14, 123 (1967).

Amodei, J. J.

J. J. Amodei, W. Phillips, and D. L. Staebler, Appl. Opt. 11, 390 (1972).

Burckhardt, C. B.

C. B. Burckhardt, J. Opt. Soc. Am. 56, 1502 (1966); J. Opt. Soc. Am. 57, 601 (1967).

Chen, F. S.

F. S. Chen, J. T. LaMacchia, and D. B. Fraser, Appl. Phys. Lett. 13, 223 (1968).

Cook, B. D.

W. R. Klein and B. D. Cook, IEEE Trans. Sonics Ultrason. 14, 123 (1967).

Fraser, D. B.

F. S. Chen, J. T. LaMacchia, and D. B. Fraser, Appl. Phys. Lett. 13, 223 (1968).

Gabor, D.

D. Gabor and G. W. Stroke, Proc. R. Soc. (Lond.) A304, 275 (1968).

Glass, A. M.

G. E. Peterson, A. M. Glass, and T. J. Negran, Appl. Phys. Lett. 19, 130 (1971).

Kamke, E.

See, for instance, E. Kamke, Differentialgleichungen, Lösungsmethoden und Lösungen (Chelsea, New York, 1959), pp. 437–440.

Klein, W. R.

W. R. Klein and B. D. Cook, IEEE Trans. Sonics Ultrason. 14, 123 (1967).

Kogelnik, H.

H. Kogelnik, in Proceedings of the Symposium on Modern Optics, edited by J. Fox (Polytechnic Press, Brooklyn, 1967), pp. 605–617.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Kozma, A.

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

LaMacchia, J. T.

F. S. Chen, J. T. LaMacchia, and D. B. Fraser, Appl. Phys. Lett. 13, 223 (1968).

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).

Negran, T. J.

G. E. Peterson, A. M. Glass, and T. J. Negran, Appl. Phys. Lett. 19, 130 (1971).

Peterson, G. E.

G. E. Peterson, A. M. Glass, and T. J. Negran, Appl. Phys. Lett. 19, 130 (1971).

Phariseau, P.

P. Phariseau, Proc. Indian Acad. Sci. A44, 165 (1956).

Phillips, W.

J. J. Amodei, W. Phillips, and D. L. Staebler, Appl. Opt. 11, 390 (1972).

Quate, C. F.

C. F. Quate, C. D. W. Wilkinson, and D. K. Winslow, Proc. Inst. Electr. Eng. 53, 1604 (1965).

Staebler, D. L.

J. J. Amodei, W. Phillips, and D. L. Staebler, Appl. Opt. 11, 390 (1972).

Stroke, G. W.

D. Gabor and G. W. Stroke, Proc. R. Soc. (Lond.) A304, 275 (1968).

Uchida, N.

N. Uchida, Japan. J. Appl. Phys. 8, 935 (1969).

Upatnieks, J.

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

Wilkinson, C. D. W.

C. F. Quate, C. D. W. Wilkinson, and D. K. Winslow, Proc. Inst. Electr. Eng. 53, 1604 (1965).

Willard, G. W.

G. W. Willard, J. Acoust. Soc. Am. 21, 101 (1949).

Winslow, D. K.

C. F. Quate, C. D. W. Wilkinson, and D. K. Winslow, Proc. Inst. Electr. Eng. 53, 1604 (1965).

Other (14)

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

C. B. Burckhardt, J. Opt. Soc. Am. 56, 1502 (1966); J. Opt. Soc. Am. 57, 601 (1967).

D. Gabor and G. W. Stroke, Proc. R. Soc. (Lond.) A304, 275 (1968).

H. Kogelnik, in Proceedings of the Symposium on Modern Optics, edited by J. Fox (Polytechnic Press, Brooklyn, 1967), pp. 605–617.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

P. Phariseau, Proc. Indian Acad. Sci. A44, 165 (1956).

F. S. Chen, J. T. LaMacchia, and D. B. Fraser, Appl. Phys. Lett. 13, 223 (1968).

G. E. Peterson, A. M. Glass, and T. J. Negran, Appl. Phys. Lett. 19, 130 (1971).

J. J. Amodei, W. Phillips, and D. L. Staebler, Appl. Opt. 11, 390 (1972).

See, for instance, E. Kamke, Differentialgleichungen, Lösungsmethoden und Lösungen (Chelsea, New York, 1959), pp. 437–440.

N. Uchida, Japan. J. Appl. Phys. 8, 935 (1969).

C. F. Quate, C. D. W. Wilkinson, and D. K. Winslow, Proc. Inst. Electr. Eng. 53, 1604 (1965).

G. W. Willard, J. Acoust. Soc. Am. 21, 101 (1949).

W. R. Klein and B. D. Cook, IEEE Trans. Sonics Ultrason. 14, 123 (1967).

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