Fresnel's reflection and transmission operators for stratified gyroanisotropic media

Abstract

For the general case of an inhomogeneous anisotropic and gyrotropic medium a differential tensor equation, expressing the evolution of the tangential component of the field vectors of an electromagnetic wave is obtained. A fundamental solution of this equation is given by a multiplicative integral. A plane-stratified system of anisotropic and gyrotropic layers is considered. By means of the characteristic matrix of such a medium Fresnel's reflection and transmission operators are derived. These operators have wide utility because they describe exactly the interaction of light with any plane-stratified gyroanisotropic structure. The conservation of the normal component of the Poynting vector in such a structure allows the authors to find a correlation between the operators of reflection and transmission. The operator dispersion equation of the multilayer gyroanisotropic waveguide is presented. All the calculations in this paper are based on the direct manipulation of tensors and their invariants, eliminating the use of coordinate systems. This facilitates solutions and provides results of great generality which are suitable for computer use.