Analysis of lossy dielectric gratings using pseudo‐periodic green's function

Abstract

Differential equation methods often are used for the analysis of the waves scattered by a dielectric grating. It is known that accurate numerical solutions can be obtained if the number of expansion terms of the spatial harmonics is increased. However, when the differential equation method is applied to a dielectric grating with an extremely large permittivity, the convergence speed of the solution becomes excessively slow in the TM wave analysis. Because of the increase of the computation time and the memory capacity, an analysis based on the differential equation method becomes difficult in practice. In this paper, it is shown that a boundary element method using Green's function satisfying the periodic condition is effective for the analysis. By introduction of pseudo‐periodic Green's function, the definition region for the integral equation is limited to the grating surface. In comparison to the boundary element method using the Hankel function, the number of linear equations is reduced. By means of numerical examples, it is shown that the convergence speed of the solution by the present method is faster and the computation time is significantly shorter than the solution by the differential equation method even in the TM wave analysis of a dielectric grating with a large loss.

Effectiveness of resistive boundary conditions for plane gratings

“…For the details of this numerical approach, the reader is referred to Ref. 6. In contrast with spectral Galerkin procedure mentioned later, this approach is repeated in this section for clarity.…”

“…In the analysis of dielectric gratings, mode matching methods [1,2], Fourier series expansion methods [3,4], finite element methods [5], boundary element methods [6], eigen-mode expansion methods, differential equation methods, and integral equation methods [8] have been applied. Lossy, anisotropic, chiral and slanted gratings have been analyzed [9].…”

Analysis of infinitely thin dielectric gratings with surface relief

“…1(a) [14]. (1) (2) Since the structure is periodic, the relative permittivity H 2 (x, z) in the grating layer is expanded as a Fourier series of N f terms with Fourier coefficients b m (x):…”

“…Many authors have reported analyses of resistive gratings in addition to perfectly conducting gratings [14].…”