Abstract

A method for calculating arbitrary-order diffraction efficiencies of thick, lossless transmission gratings with arbitrary periodic grating shapes has been developed. This represents an extension of previous work to nonsinusoidal gratings and to higher-order Bragg angles. A Fourier-series representation of the grating is employed, along with a coupled-mode theory of diffraction. For illustration, numerical values of the diffraction efficiencies at the first three Bragg angles are calculated for sinusoidal, square-wave, triangular, and saw-tooth gratings. Numerical results for the same grating shapes with the same parameters are also calculated for comparison, by extending Burckhardt’s numerical method for analyzing thick sinusoidal gratings. The comparison shows that the coupled-mode theory provides results with relative computational ease and results that are in agreement with calculations obtained by extending the more-rigorous Burckhardt theory to nonsinusoidal grating shapes and to higher-order Bragg angles.

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  1. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  2. M. R. B. Forshaw, Opt. Laser Technol. 6, 28 (1974).
  3. B. H. Crawford, J. Sci. Instrum. 31, 333 (1954).
  4. J. N. Latta and R. C. Fairchild, J. Opt. Soc. Am. 63, 487 (1973).
  5. R. Shubert and J. H. Harris, J. Opt. Soc. Am. 61, 154 (1971).
  6. H. Kogelnik and C. V. Shank, Appl. Phys. Lett. 18, 152 (1971).
  7. I. P. Kaminow, H. P. Weber, and E. A. Chandross, Appl. Phys. Lett. 18, 497 (1971).
  8. H. Kogelnik and T. P. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).
  9. M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
  10. J. M. Hammer, Appl. Phys. Lett. 18, 147 (1971).
  11. P. J. Van Heerden, Appl. Opt. 2, 393 (1963).
  12. K. S. Pennington and L. H. Lin, Appl. Phys. Lett. 7, 56 (1965).
  13. G. W. Stroke and A. E. Labeyrie, Phys. Lett. 20, 368 (1966).
  14. C. B. Burckhardt, J. Opt. Soc. Am. 56, 1502 (1966).
  15. P. Phariseau, Proc. Indian Acad. Sci. A 44, 165 (1956).
  16. C. F. Quate, C. D. W. Wilkinson, and D. K. Winslow, Proc. IEEE 53, 1604 (1965).
  17. R. S. Chu and T. Tamir, IEEE Tran. Micro. Thry. Tech. 18, 486 (1970).
  18. H. Kogelnik, J. Opt. Soc. Am. 57, 431 (1967).
  19. F. G. Kaspar, J. Opt. Soc. Am. 63, 37 (1973).
  20. T. Tamir and H. C. Wang, Can. J. Phys. 44, 2073 (1966).
  21. T. Tamir, Can. J. Phys. 44, 2461 (1966).
  22. D. A. Watkins, Topics in Electromagnetic Theory (Wiley, New York, 1958).
  23. M. G. Cohen and E. I. Gordon, Bell Syst. Tech. J. 45, 945 (1966).
  24. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), p. 71.
  25. W. W. Rigrod, J. Opt. Soc. Am. 64, 97 (1974); 64, 895E (1974).
  26. F. S. Chen, J. T. LaMacchia, and D. B. Fraser, Appl. Phys. Lett. 13, 223 (1968).
  27. J. J. Amodei, RCA Rev. 32, 185 (1971).

Amodei, J. J.

J. J. Amodei, RCA Rev. 32, 185 (1971).

Burckhardt, C. B.

C. B. Burckhardt, J. Opt. Soc. Am. 56, 1502 (1966).

Chandross, E. A.

I. P. Kaminow, H. P. Weber, and E. A. Chandross, Appl. Phys. Lett. 18, 497 (1971).

Chen, F. S.

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

Chu, R. S.

R. S. Chu and T. Tamir, IEEE Tran. Micro. Thry. Tech. 18, 486 (1970).

Cohen, M. G.

M. G. Cohen and E. I. Gordon, Bell Syst. Tech. J. 45, 945 (1966).

Crawford, B. H.

B. H. Crawford, J. Sci. Instrum. 31, 333 (1954).

Dakss, M. L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).

Fairchild, R. C.

J. N. Latta and R. C. Fairchild, J. Opt. Soc. Am. 63, 487 (1973).

Forshaw, M. R. B.

M. R. B. Forshaw, Opt. Laser Technol. 6, 28 (1974).

Fraser, D. B.

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

Gordon, E. I.

M. G. Cohen and E. I. Gordon, Bell Syst. Tech. J. 45, 945 (1966).

Hammer, J. M.

J. M. Hammer, Appl. Phys. Lett. 18, 147 (1971).

Harris, J. H.

R. Shubert and J. H. Harris, J. Opt. Soc. Am. 61, 154 (1971).

Heidrich, P. F.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).

Kaminow, I. P.

I. P. Kaminow, H. P. Weber, and E. A. Chandross, Appl. Phys. Lett. 18, 497 (1971).

Kaspar, F. G.

F. G. Kaspar, J. Opt. Soc. Am. 63, 37 (1973).

Kogelnik, H.

H. Kogelnik and T. P. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).

H. Kogelnik and C. V. Shank, Appl. Phys. Lett. 18, 152 (1971).

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

H. Kogelnik, J. Opt. Soc. Am. 57, 431 (1967).

Kuhn, L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).

Labeyrie, A. E.

G. W. Stroke and A. E. Labeyrie, Phys. Lett. 20, 368 (1966).

LaMacchia, J. T.

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

Latta, J. N.

J. N. Latta and R. C. Fairchild, J. Opt. Soc. Am. 63, 487 (1973).

Lin, L. H.

K. S. Pennington and L. H. Lin, Appl. Phys. Lett. 7, 56 (1965).

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), p. 71.

Pennington, K. S.

K. S. Pennington and L. H. Lin, Appl. Phys. Lett. 7, 56 (1965).

Phariseau, P.

P. Phariseau, Proc. Indian Acad. Sci. A 44, 165 (1956).

Quate, C. F.

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

Rigrod, W. W.

W. W. Rigrod, J. Opt. Soc. Am. 64, 97 (1974); 64, 895E (1974).

Scott, B. A.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).

Shank, C. V.

H. Kogelnik and C. V. Shank, Appl. Phys. Lett. 18, 152 (1971).

Shubert, R.

R. Shubert and J. H. Harris, J. Opt. Soc. Am. 61, 154 (1971).

Sosnowski, T. P.

H. Kogelnik and T. P. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).

Stroke, G. W.

G. W. Stroke and A. E. Labeyrie, Phys. Lett. 20, 368 (1966).

Tamir, T.

R. S. Chu and T. Tamir, IEEE Tran. Micro. Thry. Tech. 18, 486 (1970).

T. Tamir and H. C. Wang, Can. J. Phys. 44, 2073 (1966).

T. Tamir, Can. J. Phys. 44, 2461 (1966).

Van Heerden, P. J.

P. J. Van Heerden, Appl. Opt. 2, 393 (1963).

Wang, H. C.

T. Tamir and H. C. Wang, Can. J. Phys. 44, 2073 (1966).

Watkins, D. A.

D. A. Watkins, Topics in Electromagnetic Theory (Wiley, New York, 1958).

Weber, H. P.

I. P. Kaminow, H. P. Weber, and E. A. Chandross, Appl. Phys. Lett. 18, 497 (1971).

Wilkinson, C. D. W.

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

Winslow, D. K.

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

Other (27)

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

M. R. B. Forshaw, Opt. Laser Technol. 6, 28 (1974).

B. H. Crawford, J. Sci. Instrum. 31, 333 (1954).

J. N. Latta and R. C. Fairchild, J. Opt. Soc. Am. 63, 487 (1973).

R. Shubert and J. H. Harris, J. Opt. Soc. Am. 61, 154 (1971).

H. Kogelnik and C. V. Shank, Appl. Phys. Lett. 18, 152 (1971).

I. P. Kaminow, H. P. Weber, and E. A. Chandross, Appl. Phys. Lett. 18, 497 (1971).

H. Kogelnik and T. P. Sosnowski, Bell Syst. Tech. J. 49, 1602 (1970).

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).

J. M. Hammer, Appl. Phys. Lett. 18, 147 (1971).

P. J. Van Heerden, Appl. Opt. 2, 393 (1963).

K. S. Pennington and L. H. Lin, Appl. Phys. Lett. 7, 56 (1965).

G. W. Stroke and A. E. Labeyrie, Phys. Lett. 20, 368 (1966).

C. B. Burckhardt, J. Opt. Soc. Am. 56, 1502 (1966).

P. Phariseau, Proc. Indian Acad. Sci. A 44, 165 (1956).

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

R. S. Chu and T. Tamir, IEEE Tran. Micro. Thry. Tech. 18, 486 (1970).

H. Kogelnik, J. Opt. Soc. Am. 57, 431 (1967).

F. G. Kaspar, J. Opt. Soc. Am. 63, 37 (1973).

T. Tamir and H. C. Wang, Can. J. Phys. 44, 2073 (1966).

T. Tamir, Can. J. Phys. 44, 2461 (1966).

D. A. Watkins, Topics in Electromagnetic Theory (Wiley, New York, 1958).

M. G. Cohen and E. I. Gordon, Bell Syst. Tech. J. 45, 945 (1966).

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972), p. 71.

W. W. Rigrod, J. Opt. Soc. Am. 64, 97 (1974); 64, 895E (1974).

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

J. J. Amodei, RCA Rev. 32, 185 (1971).

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