Simulation of Electromagnetic Fields in Layered Media Based on Semi-Analytical Integral Transformations

Calculation of electromagnetic fields in layered models of the medium leads to the need to calculate the direct and inverse Fourier-Bessel (Hankel) transformations. The calculation of such improper integrals is complicated by the oscillating nature of the integrand. As a rule, it is the product of a smooth function of bounded variation by a Bessel function of the first kind. This circumstance allows the first function to be approximated in such a way that the integral of its product by the Bessel function is calculated analytically. We have analyzed two calculation algorithms. One of them is based on the expansion in terms of eigenfunctions of the Hankel integral operator, the second is based on approximation by a linear combination of exponentials. Both approaches make it possible to present the results of calculating integrals in an analytical form that allows their further mathematical analysis.