An algorithm for solving the optical problem for stratified anisotropic media

Abstract

An algorithm for solving the Maxwell equations for propagation of light through anisotropic stratified media is considered. The algorithm uses the Berreman matrices of order 4 × 4. In contrast to the numerical methods suggested by Berreman, the new method is exact. The Sylvester theorem for calculating functions of a matrix and the Laguerre method for determining eigenvalues provide the basis for an algorithm with an efficiency comparable to that of the algorithms based on analytic solutions, which exist only in the case of uniaxial media. The method suggested in this paper allows for the analysis of complex optical systems where the effects of biaxiality, magnetic anisotropy, and optical activity play an important role.