Investigation of Problems of Electromagnetic Wave Scattering by Conductive Strip Gratings Using Integral Equation Method

Abstract

A detailed study of the problem of scattering of a plane-polarized electromagnetic wave by systems of conductive strips with impedance forming a plane grating is carried out. Two correct general mathematical models of scattering by conductive gratings were developed in a system of singular integral equations. The first modification of the method of integral equations is related to the simpler case of scattering of an E-polarized wave by a conducting strip grating. A simple and correct mathematical model of scattering in the form of a system of singular integral equations was obtained. The diagonal kernel functions of this system have a logarithmic feature, which is considered weak. The second modification is developed for the more complicated case of H-polarized wave scattering by a conducting strip grating. A more complex mathematical model of scattering in the form of a system of integral equations was obtained. The diagonal kernel functions of this system have a strong or Cauchy-type singularity. In this polarization case, two sets of additional conditions arise to ensure the correctness of the mathematical model. In order to check the correctness of the solution of electromagnetic wave scattering problems, it is important to obtain it in an explicit analytical form, even under certain assumptions that narrow the frequency range of the application of mathematical models. The asymptotic models of wave scattering by a single narrow strip with impedance and a weakly filled grating were developed. To show the asymptotic model effectiveness, the algorithms for calculating the directional characteristics are developed and simulations were performed.