The Carleman regularization technique in the modelling of the plane E‐polarized electromagnetic wave scattering by a flat system of impedance strips

Abstract

Abstract The Carleman method of analytical regularization is used to model the plane E‐polarized electromagnetic wave scattering by flat grating of a finite number of impedance strips. It is based on a modification of the singular integral equation technique, the perturbation method and the Carleman inversion formula for the simplest logarithmically singular integral equation. Attention is focussed on the asymptotic model of the plane E‐polarized electromagnetic wave scattering by a sparsely filled impedance strip grating. In this case, the corresponding singular integral equation system has an explicit solution. This result is important to verify direct numerical methods. The scattered electromagnetic field in the far zone is successfully analysed with the aid of the asymptotic solution derived for electrically narrow strips.

Keywords

• diffraction gratings
• electromagnetic fields
• electromagnetic wave polarisation
• electromagnetic wave scattering
• integral equations
• numerical analysis