Scattering of the plane waves from the layered multielements periodic grating of circular dielectric cylinders

The purpose of this paper is to present an accurate formulation for the two-dimensional diffraction of electromagnetic waves by the layered multielements periodic grating of the dielectric circular cylinders having different radii and geometrical locations per unit cell. In the formulation, the scattered fields are expressed in terms of the expansion into multipole and diffracted spectra. Then the addition theorem for the cylindrical functions and the projection method are used to obtain an infinite system of linear equations for the unknown coefficients of the multipole spectra. The system of equations is solved using the reduction method. The convergence and stability of the solutions are numerically tested by analyzing the dependence of the reflection coefficient on the truncation order of the scattered fields. Numerical examples for the reflection coefficient of the fundamental space harmonic are presented.