Diffraction of an electromagnetic wave by a three-dimensional planar lattice

Two approaches to the solution of the problem of diffraction by a plane grating of dielectric bodies of revolution

“…This work substantially differs from the paper [4] by the method of algebraization of the problem. To be more exact, we consider two approaches of reducing the system of integral equations to the corresponding algebraic system.…”

“…OF INTEGRAL EQUATIONS We solve the formulated problem using the auxil iary current method that hereinafter is reduced to the MMDS [1][2][3][4][5][6]. To this end, we represent the wave field outside the region of the grating and inside the central elements of the grating as …”

“…In contrast to the work [4], we solve the system of integral equations (23) and (24) immediately, i.e., without decomposing the unknown currents in the Fourier series. Let us apply the collocation method.…”

“…The problem is solved here using the modified method of discrete sources (MMDS) [1][2][3][4][5][6]. The close problem of diffraction of a plane wave by a plane grating of impedance bodies of revolution was earlier considered in [4]. In this study, the problem is generalized to the case when the grating elements are dielectric bodies of revolution.…”

“…Note that the con sidered method of finding the periodic GF in the 2D case is described in [7]. The second approach is similar to the algorithm proposed in [4] where the problem is reduced to an algebraic system with the use of the axial symmetry of grating elements. The system of surface integral equations is solved using the decompositions of the unknown currents and kernels in the Fourier series in the angular coordinate and the subsequent application of the collocation method.…”