Analytical Regularization of the Problem of Wave Diffraction by a Strip Grating Upon Ferromagnetic Medium Interface

А. V. Brovenko, P. N. Melezhik, A. Ye. Poyedinchuk, and А. S. Troschylo

In the paper, a numerical analytical method is developed for solving problems of the wave diffraction by strip gratings placed on the interface of a half-space filled with a homogeneous gyrotropic medium. The initial boundary value problem is reduced to the system of dual series equations of the first kind. The analytical regularization idea is consistently realized, and a closed-form regularizer for the mentioned equations is obtained based on the explicit solution of the corresponding Riemann-Hilbert problem in theory of analytic functions. Finally the infinite system of linear algebraic equations of the second kind is available, which allows effective numerical algorithms for solving the initial diffraction problem. The suggested analytical regularization method is illustrated by the solution of the E-polarized monochromatic wave diffraction from a strip grating put on the interface of a ferrite half-space in a constant magnetic field parallel to the grating strips. The reflection coefficient behavior is examined over a wide range of frequencies and geometrical and constitutive parameters of the grating with the ferromagnetic medium. Emphasis is placed on the regions where the reflection coefficient has resonant character.