A Semianalytical Method for Electromagnetic Scattering by Infinitely Long Arbitrary Shaped Multilayer Cylinders at Oblique Incidence

Abstract

A simple and fast method for determining the field scattered from an infinite, arbitrary-shaped multilayer cylinder that is obliquely illuminated by a TMz plane wave is presented. The proposed method is a generalization of the meshless method that was previously introduced for the normal incidence case. The main structure of the procedure is similar to the one given for the normal incidence case. However, in the oblique incidence case, the problem cannot be handled as a scalar problem by considering only one field component, namely, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E_{\text {z}}$ </tex-math></inline-formula> for a TMz plane wave. Accordingly, all components of both the electric and magnetic field vectors are involved in the procedure and at each layer, and they are expressed as series of cylindrical functions with unknown coefficients. These coefficients are determined through the solution of a linear system of equations, which is constructed by first enforcing the continuity of the tangential components of the electric and magnetic field vectors on each boundary between the layers, then expressing the cylindrical functions in these continuity relations as Fourier series, and using the orthogonality of complex exponentials. After determining the coefficients, all field components at any point can be easily computed through the series representations.