Electromagnetic propagation in birefringent layered media

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 Fẏs.3, 366 ( 1953);Cesk. Casopis Fẏs.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.