Finding Solutions to Equations for the Longitudinal Components of an Electromagnetic Field in a Biisotropic Medium in the Neighborhood of a Regular Singular Point as Generalized Power Series

Abstract

For a system of equations that describe electromagnetic fields in a biisotropic medium, particular solutions have been constructed in the neighborhood of a regular singular point. The solutions are written in the form of generalized power series. For the coefficients of the power series, exponents and recursion relations have been found. It has been shown that the solutions of the wave equations are generalizations of well-known special cylindrical functions. The behavior of the particular solutions have been examined for varied material parameters of the medium. The solutions obtained allow one to formulate mathematical models which could be used to calculate and optimize the parameters of a wide spectrum of functional devices based on waveguide structures with biisotropic inserts.