Transfer Relations for Electromagnetic Wave Scattering From Periodic Dielectric One-Dimensional Interface: Te Polarization

Abstract

Some general statements for theory of wave multiple scattering in a three-dimensional inhomogeneous layered dielectric medium are established using the composition rule of the scattering (T-matrix) operators to show that the problem of wave scattering from dielectric interface may be studied similar to the problem of volume wave scattering. The medium is thought as being a stack of n layers, each of them is confined by perpendicular to the z axis planes and consists of a three-dimensional discrete or continuous inhomogeneous medium. The layers do not intersect between them and are embedded into a homogeneous background. A result of the paper is a mixed system of exact operator equations (transfer relations) for the operator wave reflection and transmission coefficients of the medium and the operator wave amplitudes of waves in splits between layers. It is shown that the transfer relations lead to a separate recurrent system of operator equations, which describe the incremental change of the operator wave reflection and transmission coefficients of stack of n - 1 layers upon attachment of a n's layer to the stack. We derive from this recurrent equations a generalized Riccati equation for the operator wave reflection coefficient of the medium and an corresponding equation for the operator wave transmission coefficient of the medium, the coefficients of the Riccati equation and the corresponding equation being expressed in terms of the operator wave reflection and transmission coefficients of a thin slice of the medium and embedding parameter being taken along the z axis. The derived Riccati equation is applied to the problem of electromagnetic wave reflection from a periodic one-dimensional interface of two dielectric half-spaces, the interface being varied in the x axis direction and the wave electric field vector being parallel to the y axis. A solution to the Riccati equation for this problem is found numerically, taking into account with the aid of the Bloch (Floquet) theorem both the propagating and evanescent waves and not invoking the Rayleigh hypothesis. A resonant effect related to the Wood anomalies is discussed.