The snell and fresnel relationships for electromagnetic waves with the constant linear polarization

Abstract

General conditions for the existence of plane electromagnetic waves with a single nonzero electric-field component (TE waves) in an anisotropic medium are established. A transformation that makes it possible to derive similar formulas for TM waves (plane electromagnetic waves with a single nonzero magnetic-field component) from the formulas expressing the properties of TE waves is considered. A general numerical algorithm is developed for calculating the amplitudes (with allowance for phases) of the TE waves formed when an external TE wave propagates through a system of plane-parallel plates consisting of media supporting TE waves. Formulas are obtained for the solution of the particular problem on the transmission of a TE wave through a plane interface between two media supporting TE waves. A series of relationships that can be interpreted as generalizations of the Snell and Fresnel relationships for media of the considered type are derived. Formulas for the transmission, reflection, and refraction coefficients are obtained. The existence conditions for TE (TM) surface waves are derived. A numerical method is proposed for computing the spectra of such surface waves formed on the interface between two media. For isotropic media, analytic expressions for the spectra of surface waves are derived. It is shown that the obtained formulas are similar to the known formulas for surface TM waves in dielectrics but, in addition, make it possible to take into account both the permittivities and permeabilities of the media.