Abstract

A procedure for calculating the mode structure in optical waveguides made up of multilayers of optically anisotropic media is derived. This procedure is applicable to a waveguide of any arbitrary number of layers, with each layer homogeneous but otherwise having arbitrary dielectric, magnetic-permeability, and optical-rotation tensors. The substrate is included as an end layer of large, but finite, thickness. When programmed for the computer, the method provides a powerful and useful tool for analyzing a waveguide consisting of any complex array of anisotropic layers, requiring simply specification of the relevant material tensors and layer thicknesses as inputs. The sequence of steps involved in the procedure is illustrated by two examples that can be carried out explicitly, viz., that of an isotropic dielectric layer and that of a uniaxial crystal layer.

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  1. P. K. Tien, Appl. Opt. 10, 2395 (1971).
  2. J. H. Harris, R. Shubert, and J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).
  3. R. Shubert and J. H. Harris, J. Opt. Soc. Am. 61, 154 (1971).
  4. S. Wang, M. L. Shah, and J. D. Crow, IEEE J. Quantum Electron. 8, 212 (1972).
  5. D. P. Gia Russo and J. H. Harris, J. Opt. Soc. Am. 63, 138 (1973).
  6. D. O. Smith, Opt. Acta 12, 13 (1965).
  7. S. Teitler and B. W. Henvis, J. Opt. Soc. Am. 60, 830 (1970).
  8. D. W. Berreman, J. Opt. Soc. Am. 62, 502 (1972).
  9. D. O. Smith, Opt. Acta 12, 195 (1960); Opt. Acta 13, 121 (1966); Opt. Acta 13, 195 (1966); Opt. Acta 14, 351 (1967).
  10. For a general exposition see, for example, P. H. Lissberger, Rep. Prog. Phys. 33, 197 (1970).
  11. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941); J. Opt. Soc. Am. 31, 500 (1941).
  12. F. Abelès, Ann. Phys. (Paris) 5, 598 (1950).
  13. Except for changes in notation designed to make the results more concise, this development is the same as in Sec. 2 of Ref. 8.
  14. See, for example, R. M. Thrall and L. Tornheim, Vector Spaces and Matrices (Wiley, New York, 1957), Ch. 10.
  15. See the discussion in Ref. 5 pertaining to Eqs. (7) of that reference.

Abelès, F.

F. Abelès, Ann. Phys. (Paris) 5, 598 (1950).

Berreman, D. W.

D. W. Berreman, J. Opt. Soc. Am. 62, 502 (1972).

Crow, J. D.

S. Wang, M. L. Shah, and J. D. Crow, IEEE J. Quantum Electron. 8, 212 (1972).

Harris, J. H.

D. P. Gia Russo and J. H. Harris, J. Opt. Soc. Am. 63, 138 (1973).

J. H. Harris, R. Shubert, and J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).

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

Henvis, B. W.

S. Teitler and B. W. Henvis, J. Opt. Soc. Am. 60, 830 (1970).

Jones, R. C.

R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941); J. Opt. Soc. Am. 31, 500 (1941).

Lissberger, P. H.

For a general exposition see, for example, P. H. Lissberger, Rep. Prog. Phys. 33, 197 (1970).

Polky, J. N.

J. H. Harris, R. Shubert, and J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).

Russo, D. P. Gia

D. P. Gia Russo and J. H. Harris, J. Opt. Soc. Am. 63, 138 (1973).

Shah, M. L.

S. Wang, M. L. Shah, and J. D. Crow, IEEE J. Quantum Electron. 8, 212 (1972).

Shubert, R.

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

J. H. Harris, R. Shubert, and J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).

Smith, D. O.

D. O. Smith, Opt. Acta 12, 13 (1965).

D. O. Smith, Opt. Acta 12, 195 (1960); Opt. Acta 13, 121 (1966); Opt. Acta 13, 195 (1966); Opt. Acta 14, 351 (1967).

Teitler, S.

S. Teitler and B. W. Henvis, J. Opt. Soc. Am. 60, 830 (1970).

Thrall, R. M.

See, for example, R. M. Thrall and L. Tornheim, Vector Spaces and Matrices (Wiley, New York, 1957), Ch. 10.

Tien, P. K.

P. K. Tien, Appl. Opt. 10, 2395 (1971).

Tornheim, L.

See, for example, R. M. Thrall and L. Tornheim, Vector Spaces and Matrices (Wiley, New York, 1957), Ch. 10.

Wang, S.

S. Wang, M. L. Shah, and J. D. Crow, IEEE J. Quantum Electron. 8, 212 (1972).

Other

P. K. Tien, Appl. Opt. 10, 2395 (1971).

J. H. Harris, R. Shubert, and J. N. Polky, J. Opt. Soc. Am. 60, 1007 (1970).

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

S. Wang, M. L. Shah, and J. D. Crow, IEEE J. Quantum Electron. 8, 212 (1972).

D. P. Gia Russo and J. H. Harris, J. Opt. Soc. Am. 63, 138 (1973).

D. O. Smith, Opt. Acta 12, 13 (1965).

S. Teitler and B. W. Henvis, J. Opt. Soc. Am. 60, 830 (1970).

D. W. Berreman, J. Opt. Soc. Am. 62, 502 (1972).

D. O. Smith, Opt. Acta 12, 195 (1960); Opt. Acta 13, 121 (1966); Opt. Acta 13, 195 (1966); Opt. Acta 14, 351 (1967).

For a general exposition see, for example, P. H. Lissberger, Rep. Prog. Phys. 33, 197 (1970).

R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941); J. Opt. Soc. Am. 31, 500 (1941).

F. Abelès, Ann. Phys. (Paris) 5, 598 (1950).

Except for changes in notation designed to make the results more concise, this development is the same as in Sec. 2 of Ref. 8.

See, for example, R. M. Thrall and L. Tornheim, Vector Spaces and Matrices (Wiley, New York, 1957), Ch. 10.

See the discussion in Ref. 5 pertaining to Eqs. (7) of that reference.

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