Abstract

Monochromatic energy exchanges in thin-film dielectric waveguides can be understood in terms of a zig-zag ray picture that includes Goos-Haenchen shifts that occur at the film boundaries, as pointed out by Burke. Recently, Kogelnik and Weber have shown that, in order to predict the correct modal group velocity, the ray model should also include the time delay associated with the ray shifts at the film boundaries. In this paper, we explore in detail the ray-optical descriptions of anisotropic film waveguides that consist of three-layered biaxial materials with one of the principal axes of the crystal in each of the three media oriented in the direction of propagation and the other two parallel and perpendicular to the plane of the film. We show that the Burke-Kogelnik-Weber (BKW) ray model provides a complete description of energy flow in such anisotropic structures. Expressions for the ray shift, group velocity, power flow, and stored energy, applicable to both TE and TM modes, are presented.

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  1. G. B. Airy, Philos. Mag. 2, 20 (1833).
  2. A. Sommerfeld, Optics, (Academic, New York, 1954), p. 47 ff.
  3. H. K. V. Lotsch, Optik 27, 239 (1968).
  4. P. K. Tien and R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
  5. J. J. Burke, J. Opt. Soc. Am. 61, 676 (1971); Opt. Sci. Newsletter (U. Arizona) 5, 66 (1971).
  6. N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), p. 79.
  7. H. Kogelnik and V. Ramaswamy, Appl. Opt. 13, 1857 (1974).
  8. H. Kogelnik and H. P. Weber, J. Opt. Soc. Am. 64, 174 (1974).
  9. V. Ramaswamy, Appl. Phys. Lett. 21, 183 (1972).
  10. D. Hall, A. Yariv, and E. Garmire, Opt. Commun. 1, 403 (1970).
  11. I. P. Kaminow and J. R. Carruthers, Appl. Phys. Lett. 22, 326 (1973).
  12. J. M. Hammer and W. Phillips, Appl. Phys. Lett. 24, 545 (1974).
  13. P. K. Tien, R. J. Martin, S. L. Blank, S. H. Wemple, and L. J. Varnerin, Appl. Phys. Lett. 21, 207 (1972).
  14. S. Yamamoto, Y. Koyamada, and T. Makimoto, J. Appl. Phys. 43, 5090 (1972).
  15. D. P. GiaRusso and J. H. Harris, J. Opt. Soc. Am. 63, 138 (1973).
  16. V. Ramaswamy, Appl. Opt. 13, 1363 (1974).
  17. M. S. Kharusi, J. Opt. Soc. Am. 64, 27 (1974).
  18. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1958), p. 670, Eq. (41); p. 678, Eq. (6).
  19. Reference 18, p. 666, Eq. (9).
  20. H. L. Bertoni and A. Hessel, IEEE Trans. Antennas Propag. 14, 344 (1966).
  21. J. A. Arnaud and A. A. M. Saleh, Proc. IEEE Lett. 60, 639 (1972).

1974 (5)

H. Kogelnik and V. Ramaswamy, Appl. Opt. 13, 1857 (1974).

H. Kogelnik and H. P. Weber, J. Opt. Soc. Am. 64, 174 (1974).

J. M. Hammer and W. Phillips, Appl. Phys. Lett. 24, 545 (1974).

V. Ramaswamy, Appl. Opt. 13, 1363 (1974).

M. S. Kharusi, J. Opt. Soc. Am. 64, 27 (1974).

1973 (2)

I. P. Kaminow and J. R. Carruthers, Appl. Phys. Lett. 22, 326 (1973).

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

1972 (4)

P. K. Tien, R. J. Martin, S. L. Blank, S. H. Wemple, and L. J. Varnerin, Appl. Phys. Lett. 21, 207 (1972).

S. Yamamoto, Y. Koyamada, and T. Makimoto, J. Appl. Phys. 43, 5090 (1972).

J. A. Arnaud and A. A. M. Saleh, Proc. IEEE Lett. 60, 639 (1972).

V. Ramaswamy, Appl. Phys. Lett. 21, 183 (1972).

1971 (1)

J. J. Burke, J. Opt. Soc. Am. 61, 676 (1971); Opt. Sci. Newsletter (U. Arizona) 5, 66 (1971).

1970 (2)

P. K. Tien and R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).

D. Hall, A. Yariv, and E. Garmire, Opt. Commun. 1, 403 (1970).

1968 (1)

H. K. V. Lotsch, Optik 27, 239 (1968).

1966 (1)

H. L. Bertoni and A. Hessel, IEEE Trans. Antennas Propag. 14, 344 (1966).

1833 (1)

G. B. Airy, Philos. Mag. 2, 20 (1833).

Airy, G. B.

G. B. Airy, Philos. Mag. 2, 20 (1833).

Arnaud, J. A.

J. A. Arnaud and A. A. M. Saleh, Proc. IEEE Lett. 60, 639 (1972).

Bertoni, H. L.

H. L. Bertoni and A. Hessel, IEEE Trans. Antennas Propag. 14, 344 (1966).

Blank, S. L.

P. K. Tien, R. J. Martin, S. L. Blank, S. H. Wemple, and L. J. Varnerin, Appl. Phys. Lett. 21, 207 (1972).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1958), p. 670, Eq. (41); p. 678, Eq. (6).

Burke, J. J.

J. J. Burke, J. Opt. Soc. Am. 61, 676 (1971); Opt. Sci. Newsletter (U. Arizona) 5, 66 (1971).

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), p. 79.

Carruthers, J. R.

I. P. Kaminow and J. R. Carruthers, Appl. Phys. Lett. 22, 326 (1973).

Garmire, E.

D. Hall, A. Yariv, and E. Garmire, Opt. Commun. 1, 403 (1970).

GiaRusso, D. P.

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

Hall, D.

D. Hall, A. Yariv, and E. Garmire, Opt. Commun. 1, 403 (1970).

Hammer, J. M.

J. M. Hammer and W. Phillips, Appl. Phys. Lett. 24, 545 (1974).

Harris, J. H.

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

Hessel, A.

H. L. Bertoni and A. Hessel, IEEE Trans. Antennas Propag. 14, 344 (1966).

Kaminow, I. P.

I. P. Kaminow and J. R. Carruthers, Appl. Phys. Lett. 22, 326 (1973).

Kapany, N. S.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), p. 79.

Kharusi, M. S.

M. S. Kharusi, J. Opt. Soc. Am. 64, 27 (1974).

Kogelnik, H.

H. Kogelnik and H. P. Weber, J. Opt. Soc. Am. 64, 174 (1974).

H. Kogelnik and V. Ramaswamy, Appl. Opt. 13, 1857 (1974).

Koyamada, Y.

S. Yamamoto, Y. Koyamada, and T. Makimoto, J. Appl. Phys. 43, 5090 (1972).

Lotsch, H. K. V.

H. K. V. Lotsch, Optik 27, 239 (1968).

Makimoto, T.

S. Yamamoto, Y. Koyamada, and T. Makimoto, J. Appl. Phys. 43, 5090 (1972).

Martin, R. J.

P. K. Tien, R. J. Martin, S. L. Blank, S. H. Wemple, and L. J. Varnerin, Appl. Phys. Lett. 21, 207 (1972).

Phillips, W.

J. M. Hammer and W. Phillips, Appl. Phys. Lett. 24, 545 (1974).

Ramaswamy, V.

H. Kogelnik and V. Ramaswamy, Appl. Opt. 13, 1857 (1974).

V. Ramaswamy, Appl. Opt. 13, 1363 (1974).

V. Ramaswamy, Appl. Phys. Lett. 21, 183 (1972).

Saleh, A. A. M.

J. A. Arnaud and A. A. M. Saleh, Proc. IEEE Lett. 60, 639 (1972).

Sommerfeld, A.

A. Sommerfeld, Optics, (Academic, New York, 1954), p. 47 ff.

Tien, P. K.

P. K. Tien, R. J. Martin, S. L. Blank, S. H. Wemple, and L. J. Varnerin, Appl. Phys. Lett. 21, 207 (1972).

P. K. Tien and R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).

Ulrich, R.

P. K. Tien and R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).

Varnerin, L. J.

P. K. Tien, R. J. Martin, S. L. Blank, S. H. Wemple, and L. J. Varnerin, Appl. Phys. Lett. 21, 207 (1972).

Weber, H. P.

H. Kogelnik and H. P. Weber, J. Opt. Soc. Am. 64, 174 (1974).

Wemple, S. H.

P. K. Tien, R. J. Martin, S. L. Blank, S. H. Wemple, and L. J. Varnerin, Appl. Phys. Lett. 21, 207 (1972).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1958), p. 670, Eq. (41); p. 678, Eq. (6).

Yamamoto, S.

S. Yamamoto, Y. Koyamada, and T. Makimoto, J. Appl. Phys. 43, 5090 (1972).

Yariv, A.

D. Hall, A. Yariv, and E. Garmire, Opt. Commun. 1, 403 (1970).

Other (21)

G. B. Airy, Philos. Mag. 2, 20 (1833).

A. Sommerfeld, Optics, (Academic, New York, 1954), p. 47 ff.

H. K. V. Lotsch, Optik 27, 239 (1968).

P. K. Tien and R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).

J. J. Burke, J. Opt. Soc. Am. 61, 676 (1971); Opt. Sci. Newsletter (U. Arizona) 5, 66 (1971).

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, New York, 1972), p. 79.

H. Kogelnik and V. Ramaswamy, Appl. Opt. 13, 1857 (1974).

H. Kogelnik and H. P. Weber, J. Opt. Soc. Am. 64, 174 (1974).

V. Ramaswamy, Appl. Phys. Lett. 21, 183 (1972).

D. Hall, A. Yariv, and E. Garmire, Opt. Commun. 1, 403 (1970).

I. P. Kaminow and J. R. Carruthers, Appl. Phys. Lett. 22, 326 (1973).

J. M. Hammer and W. Phillips, Appl. Phys. Lett. 24, 545 (1974).

P. K. Tien, R. J. Martin, S. L. Blank, S. H. Wemple, and L. J. Varnerin, Appl. Phys. Lett. 21, 207 (1972).

S. Yamamoto, Y. Koyamada, and T. Makimoto, J. Appl. Phys. 43, 5090 (1972).

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

V. Ramaswamy, Appl. Opt. 13, 1363 (1974).

M. S. Kharusi, J. Opt. Soc. Am. 64, 27 (1974).

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1958), p. 670, Eq. (41); p. 678, Eq. (6).

Reference 18, p. 666, Eq. (9).

H. L. Bertoni and A. Hessel, IEEE Trans. Antennas Propag. 14, 344 (1966).

J. A. Arnaud and A. A. M. Saleh, Proc. IEEE Lett. 60, 639 (1972).

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