2 × 2 propagation matrix for electromagnetic waves propagating obliquely in layered inhomogeneous uniaxial media

Abstract

A 2 × 2 propagation-matrix formalism for finding the obliquely propagating electromagnetic fields in layered inhomogeneous uniaxial structures is presented. The 2 × 2 propagation matrix was produced by our generalized geometrical-optics approximation method. A 2 × 1 field vector for the transverse electric field is defined together with a 2 × 2 propagation matrix, which describes the spatial propagation of the 2 × 1 field vector. Eight different equivalent forms for the propagation matrix are presented. The propagation matrix depends on the dielectric parameter and other optical parameters of the medium, the thickness of the medium, and the propagation vector of the incident light. The inhomogeneous medium is divided into sublayers, and the problem is then solved as if each layer has spatially invariant optical parameters. The propagation matrix for the inhomogeneous medium is equal to the matrix product of the propagation matrices for any complete series of layers that subdivide the inhomogeneous medium. The 2 × 2 propagation matrix reduces to the conventional Jones matrix for the case of normally incident light. The results are applied in studying the electro-optics of various liquid-crystal displays. The computation results are the same as those produced by the generalized geometrical-optics approximation and are in good agreement with those computed by the 4 × 4 propagation matrix and with experimental results.