PROPAGATION AND ATTENUATION OF ELECTROMAGNETIC WAVES IN INHOMOGENEOUS MEDIA: NUMERICAL MODELING USING LAGUERRE TRANSFORM

Abstract

One-dimensional Maxwell's equations with relaxation are solved using the Laguerre time series. Space derivatives are obtained by difference approximation of the fourth order of accuracy. The equations reduce to a harmonic series of linear algebraic equations, in which each harmonic is obtained by multiplication of the matrix by the right term. The matrix is universal and is the same for all harmonics. The algorithm shows a high efficiency. With the optimum choice of parameters, the Laguerre transform is advantageous over the finite-difference and Fourier methods. It is more precise than the second order approximation of the finite-difference solution, and uncertainty grows at a lower rate. The method is applicable to two- and three-dimensional Maxwell's equations, without significant limitations.