Jones matrix treatment of electromagnetic wave propagation in anisotropic stratified media

Abstract

Light propagation in anisotropic stratified media may be conveniently described, in the quasi-adiabatic limit, by the so-called Jones matrix formalism. In systems like liquid crystals, the quasi adiabatic limit occurs when the director rotates very slightly over distances of the order of the light wavelength. This limit is of relevant interest in many optical devices. As known, the general solution of the Maxwell's equations in anisotropic stratified media may be obtained by using the 4 × 4 Berreman's matrix method. However, as long as the polarization properties of the light transmitted through the medium are concerned, a much simpler approach is possible, which consists in completely neglecting the solutions of the Berreman's equations corresponding to the waves propagating in the backward direction. In this case, the number of differential equations describing light propagation is reduced from 4 to 2. The 2 × 2 matrix introduced in this approximated fromalism is termed the Jones matrix of the problem. In this paper, we show that in general case of oblique incidence of light is possible to properly transform the original Berreman's matrix into a form suitable for reduction to a 2 × 2 Jones matrix.