Eigenequations and compact algorithms for bulk and layered anisotropic optical media: Reflection and refraction at a crystal-crystal interface

Eigenequations leading to compact algorithms for computing the optical properties of anisotropic media that may be stratified in the x-direction are described. For each medium a 4 x 4 matrix (F) over cap of basis field vectors is determined as the eigenvectors of a 4 x 4 matrix form of Fresnel's equation. A minimum sort of the columns of (F) over cap that is necessary for a birefringent cover or substrate separates basis vectors that carry power in the positive and negative x-directions respectively. A sorting procedure is discussed for the most complicated refractive index section in which the outer and inner sheets do not touch and the outer sheet has a well defined cusp. MATLAB code is provided for the implementation of basic routines. (C) 1997 Academic Press.