Optical degeneracies in anisotropic layered media: Treatment of singularities in a 4×4 matrix formalism

Abstract

4\ifmmode\times\else\texttimes\fi{}4 matrices have been used extensively to study the propagation of light in anisotropic layered systems whose principal optic axes have arbitrary orientation. We present a general theory for the propagation of light in arbitrarily anisotropic layered systems that is particularly suited for treating optical degeneracies that arise (1) when light propagates in an isotropic medium embedded within the anisotropic layers or (2) when light propagates along one of the optic axes in an anisotropic layer. Boundary conditions are applied explicitly to the electric and magnetic fields at each interface, and transfer matrices that relate the transmitted and reflected fields to the optical properties of the system are developed. Criteria are given for identifying the mathematical singularities caused by the degeneracies described above, and a method for treating the singularities in the relevant expressions is presented.