Analysis of Doubly Periodic Inhomogeneous Dielectric Structures by a Hybrid Projective Method

Abstract

The problem of plane electromagnetic wave scattering by doubly periodic structures with both homogeneous and inhomogeneous dielectric elements arranged on a homogeneous dielectric substrate is considered. A hybrid projective method involving the method of coupled waves, method of projective matching of fields on the boundaries of partial regions, and one-dimensional finite elements method, is proposed. The method avoids using excessive number of unknown coefficients of expansion taking place in the previous versions. The effectiveness of the method is validated by a few tests including convergence of the results with increasing the number the expansion coefficients and comparison with appropriate data available in literature. The capabilities of homogeneous lossless matching dielectric elements of various shape and some properties of ultra-wideband absorbing structures with pyramidal elements are studied. The potential advantage of using inhomogeneous absorbing elements is also demonstrated.

Reformulated Fourier Modal Method with improved near field computations

“…K. Edee developed an alternative method using Gegenbauer polynomials instead of plane-wave decomposition [31]. This approach eliminates the Gibbs effect problem by a cost of partial loss of method's flexibility in terms of coupling multilayer structures and potential applications of fast numerical schemes (e.g., [32,33]). In addition, the convergence of the near field, which is important for certain applications like sensing and non-linear optics, was outside the scope of the review for a long time.…”

Curvilinear coordinate generalized source method for gratings with sharp edges

“…Fourier space methods are good candidates for the purpose of large scale optimization of periodic dielectric structures being versatile in terms of structure geometries and offering a reliable convergence error analysis [5,6]. There were proposed several fast numerical schemes exhibiting an O (N log N ) numerical complexity and O (N ) computational memory resort [7,8,9,10,11], and providing a large room for parallelization on vector processors. This asymptotic behaviour is due to a specific structure of the scattering operator, which factorizes into blockdiagonal and block-Toeplitz components, and due to the possibility to multiply Towplitz matrices by vectors by means of the Fast Fourier Transform (FFT).…”

Numerical modelling of diffraction of electromagnetic field on pyramidal radio-absorber on the side walls of the compact range.

“…В работах [4,5] вместо коллиматора используются более простые модели, например точечный излучатель с заданной диаграммой направленности, а радиопоглощающий материал заменяется на однородную эффективную среду, для вычисления электромагнитных характеристик которой предлагаются различные способы. В работах [6,7] рассматривается рассеяние от периодических структур с учетом высших гармоник, однако в качестве падающего поля выступает не поле коллиматора, а плоская волна. В работе [8] изложен метод расчета поля в рабочей зоне, учитывающий зеркальное отражение от боковых стенок, потолка и пола и рассеяние на задней стенке.…”