Abstract

The propagation of electromagnetic radiation in birefringent layered media is considered. A general formulation of the plane-wave propagation in an arbitrarily birefringent layered medium is presented. The concepts of dynamical matrix and propagation matrix are introduced. A 4 × 4 transfer matrix method is used to relate the field amplitudes in different layers. Our general theory is then applied to the special case of periodic birefringent layered media, especially the Šolc birefringent layered media [ I. Šolc, Cesk. Casopis Fys. 3, 366 (1953);10, 16 (1960)]. The unit cell translation operator is derived. The band structures as well as the Bloch waves are obtained by diagonalizing the translation operator. Coupled mode theory is extended to the case of birefringent periodic perturbation to explain the exchange Bragg scattering. A general mode dispersion relation for guided waves is also obtained in terms of the transfer matrix elements.

© 1979 Optical Society of America

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  1. P. Yeh, A. Yariv, and C. S. Hong, J. Opt. Soc. Am. 67, 423 (1977); 67, 438 (1977).
  2. A. Wunsche, Ann. Phys. (Leipz.) 25, 201 (1970).
  3. J. Schesser and G. Eichmann, J. Opt. Soc. Am. 62, 786 (1972).
  4. C. E. Curry, Electromagnetic Theory of Light, (MacMillan, London, 1950), pp. 356–369.
  5. H. Schopper, Z. Phsik 132, 146 (1952).
  6. A. B. Winterbottom, Kgl. Norske Videnskab. Selskab, Skrifter 1, 27 (1955); 1, 37 (1955).
  7. A. M. Goncharenko and F. J. Federov, Opt. Spectrosk. 14, 94 (1962) [Opt. Spectrosc. (USSR) 14, 48 (1963)].
  8. J. Schesser and G. Eichmann, J. Opt. Soc. Am. 62, 786 (1972).
  9. D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 56, 1763 (1966).
  10. J. J. Stamnes and G. C. Sherman, J. Opt. Soc. Am. 67, 683 (1977).
  11. M.Born and E. Wolf, Principles of Optics, (Macmillan, New York, 1964).
  12. See for example, H. Goldstein, Classical Mechanics, (Addison-Wesley, Reading, 1965).
  13. See for example, J. M. Stone, Radiation and Optics, (McGraw-Hill, New York, 1963), Sec. 17–5.
  14. E. O. Ammann, Progress in Optics, IX, edited by E. Wolf (North-Holland, Amsterdam, 1971), pp. 125–177.
  15. This is a generalized Šolc layered medium with alternating layer thicknesses as well as azimuths.
  16. F. Bloch, Z. Phys. 52, 555 (1928).
  17. H. Kogelnik, Bell. Syst. Tech. J. 55, 109–126 (1976).
  18. A. Yariv, IEEE J. Quant. Electron. QE-9, 919 (1973).
  19. 2A/∂z2kA/∂z.
  20. This periodic function is the first term of the Fourier sines expansion of a unit alternating square wave perturbation.
  21. See, for example, A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), p. 523.
  22. I. Šolc, J. Opt. Soc. Am. 55, 621 (1965).
  23. L. Brillouin, Wave Propagation and Group Velocity, (Academic, New York, 1960).
  24. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).
  25. J. W. Evans, J. Opt. Soc. Am. 48, 142 (1958).
  26. I. P. Kaminow and J. R. Carruthers, Appl. Phys. Lett. 22, 326 (1973).
  27. R. V. Schmidt and I. P. Kaminow, Appl. Phys. Lett. 25, 458 (1974).
  28. S. C. Frautschi, Regge Poles and S-Matrix Theory, (Benjamin, New York, 1963).
  29. T. Regge, Nuov. Cim. 14, 951 (1959).∂
  30. M. J. Lighthill, J. Inst. Maths. Applic. 1, 1 (1965).

Ammann, E. O.

E. O. Ammann, Progress in Optics, IX, edited by E. Wolf (North-Holland, Amsterdam, 1971), pp. 125–177.

Bloch, F.

F. Bloch, Z. Phys. 52, 555 (1928).

Born, M.

M.Born and E. Wolf, Principles of Optics, (Macmillan, New York, 1964).

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity, (Academic, New York, 1960).

Carruthers, J. R.

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

Curry, C. E.

C. E. Curry, Electromagnetic Theory of Light, (MacMillan, London, 1950), pp. 356–369.

Eichmann, G.

J. Schesser and G. Eichmann, J. Opt. Soc. Am. 62, 786 (1972).

J. Schesser and G. Eichmann, J. Opt. Soc. Am. 62, 786 (1972).

Evans, J. W.

J. W. Evans, J. Opt. Soc. Am. 48, 142 (1958).

Federov, F. J.

A. M. Goncharenko and F. J. Federov, Opt. Spectrosk. 14, 94 (1962) [Opt. Spectrosc. (USSR) 14, 48 (1963)].

Feucht, D. L.

D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 56, 1763 (1966).

Frautschi, S. C.

S. C. Frautschi, Regge Poles and S-Matrix Theory, (Benjamin, New York, 1963).

Goldstein, H.

See for example, H. Goldstein, Classical Mechanics, (Addison-Wesley, Reading, 1965).

Goncharenko, A. M.

A. M. Goncharenko and F. J. Federov, Opt. Spectrosk. 14, 94 (1962) [Opt. Spectrosc. (USSR) 14, 48 (1963)].

Holmes, D. A.

D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 56, 1763 (1966).

Hong, C. S.

P. Yeh, A. Yariv, and C. S. Hong, J. Opt. Soc. Am. 67, 423 (1977); 67, 438 (1977).

Jones, R. C.

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

Kaminow, I. P.

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

R. V. Schmidt and I. P. Kaminow, Appl. Phys. Lett. 25, 458 (1974).

Kogelnik, H.

H. Kogelnik, Bell. Syst. Tech. J. 55, 109–126 (1976).

Lighthill, M. J.

M. J. Lighthill, J. Inst. Maths. Applic. 1, 1 (1965).

Regge, T.

T. Regge, Nuov. Cim. 14, 951 (1959).∂

Schesser, J.

J. Schesser and G. Eichmann, J. Opt. Soc. Am. 62, 786 (1972).

J. Schesser and G. Eichmann, J. Opt. Soc. Am. 62, 786 (1972).

Schmidt, R. V.

R. V. Schmidt and I. P. Kaminow, Appl. Phys. Lett. 25, 458 (1974).

Schopper, H.

H. Schopper, Z. Phsik 132, 146 (1952).

Sherman, G. C.

J. J. Stamnes and G. C. Sherman, J. Opt. Soc. Am. 67, 683 (1977).

Šolc, I

I. Šolc, J. Opt. Soc. Am. 55, 621 (1965).

Stamnes, J. J.

J. J. Stamnes and G. C. Sherman, J. Opt. Soc. Am. 67, 683 (1977).

Stone, J. M.

See for example, J. M. Stone, Radiation and Optics, (McGraw-Hill, New York, 1963), Sec. 17–5.

Winterbottom, A. B.

A. B. Winterbottom, Kgl. Norske Videnskab. Selskab, Skrifter 1, 27 (1955); 1, 37 (1955).

Wolf, E.

M.Born and E. Wolf, Principles of Optics, (Macmillan, New York, 1964).

Wunsche, A.

A. Wunsche, Ann. Phys. (Leipz.) 25, 201 (1970).

Yariv, A.

See, for example, A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), p. 523.

P. Yeh, A. Yariv, and C. S. Hong, J. Opt. Soc. Am. 67, 423 (1977); 67, 438 (1977).

A. Yariv, IEEE J. Quant. Electron. QE-9, 919 (1973).

Yeh, P.

P. Yeh, A. Yariv, and C. S. Hong, J. Opt. Soc. Am. 67, 423 (1977); 67, 438 (1977).

Other (30)

P. Yeh, A. Yariv, and C. S. Hong, J. Opt. Soc. Am. 67, 423 (1977); 67, 438 (1977).

A. Wunsche, Ann. Phys. (Leipz.) 25, 201 (1970).

J. Schesser and G. Eichmann, J. Opt. Soc. Am. 62, 786 (1972).

C. E. Curry, Electromagnetic Theory of Light, (MacMillan, London, 1950), pp. 356–369.

H. Schopper, Z. Phsik 132, 146 (1952).

A. B. Winterbottom, Kgl. Norske Videnskab. Selskab, Skrifter 1, 27 (1955); 1, 37 (1955).

A. M. Goncharenko and F. J. Federov, Opt. Spectrosk. 14, 94 (1962) [Opt. Spectrosc. (USSR) 14, 48 (1963)].

J. Schesser and G. Eichmann, J. Opt. Soc. Am. 62, 786 (1972).

D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 56, 1763 (1966).

J. J. Stamnes and G. C. Sherman, J. Opt. Soc. Am. 67, 683 (1977).

M.Born and E. Wolf, Principles of Optics, (Macmillan, New York, 1964).

See for example, H. Goldstein, Classical Mechanics, (Addison-Wesley, Reading, 1965).

See for example, J. M. Stone, Radiation and Optics, (McGraw-Hill, New York, 1963), Sec. 17–5.

E. O. Ammann, Progress in Optics, IX, edited by E. Wolf (North-Holland, Amsterdam, 1971), pp. 125–177.

This is a generalized Šolc layered medium with alternating layer thicknesses as well as azimuths.

F. Bloch, Z. Phys. 52, 555 (1928).

H. Kogelnik, Bell. Syst. Tech. J. 55, 109–126 (1976).

A. Yariv, IEEE J. Quant. Electron. QE-9, 919 (1973).

2A/∂z2kA/∂z.

This periodic function is the first term of the Fourier sines expansion of a unit alternating square wave perturbation.

See, for example, A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), p. 523.

I. Šolc, J. Opt. Soc. Am. 55, 621 (1965).

L. Brillouin, Wave Propagation and Group Velocity, (Academic, New York, 1960).

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

J. W. Evans, J. Opt. Soc. Am. 48, 142 (1958).

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

R. V. Schmidt and I. P. Kaminow, Appl. Phys. Lett. 25, 458 (1974).

S. C. Frautschi, Regge Poles and S-Matrix Theory, (Benjamin, New York, 1963).

T. Regge, Nuov. Cim. 14, 951 (1959).∂

M. J. Lighthill, J. Inst. Maths. Applic. 1, 1 (1965).

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