OPERATOR METHOD IN THE PROBLEM OF AN H-POLARIZED PLANE WAVE DIFFRACTION BY A DOUBLE-LAYER INFINITE PERIODIC STRIP GRATING IN THE ABSENCE OF ONE STRIP IN EVERY LAYER

Abstract

Purpose: The problem of an H-polarized plane wave diffraction by the infinite double-layer non-ideally periodic strip grating is considered. The grating is obtained from the ideally-periodic one by excluding of a single strip in each layer. The purpose of this paper is to build the rigorous mathematical model based on the operator method, the study of the fields scattered by the structure. Design/methodology/approach: The field scattered by the grating is found as a sum of three summands. The first one is the field scattered by the ideally periodic grating. The second one is the field of currents on the two strips being absent in the structure under consideration (with the minus sign). The third one is the correction field caused by the absence of the strips. The operator equations with respect to the Fourier amplitudes are obtained for every field. In these equations, the scattering operators of a single layer are used. A short-form algorithm of their determination based on the method of singular integral equations is represented. Findings: The obtained numerical results allow to make a conclusion about the behavior of the field scattered by the grating. The numerical study of convergence is made. The stop bands and pass bands can appear at the double-layer gratings. In the case of strips being absent in each layer, the waveguide channel can be formed; the incident wave can transmit through this channel even when the parameters correspond to the stop band. The dependences of the reflection and transmission coefficients on the frequency, which allow to determine the position of the stop bands and pass bands are given. The diffraction patterns of the transmitted field and near field distribution are built. Conclusions: An effective algorithm for studying the field scattered by the double-layer infinite grating in the absence of strips in each layer is suggested. The obtained results indicate a significant dependence of the width of the transmitted field main lobe vs. frequency. The developed approach can be effective in solving of a number of antenna technique and microwave electronics problems.

Keywords

• strip grating
• non-ideally periodic grating
• operator method
• wave diffraction