Method of integral functionals for electromagnetic wave scattering from a double-periodic magnetodielectric layer

Abstract

A numerical method in the frequency domain is developed for analyzing three-dimensional gratings using the concept of a double-periodic magnetodielectric layer. The method is based on the three-dimensional volume integral equations for the equivalent electric and magnetic polarization currents of the assumed periodic medium. The integral equations are solved by using the integral functionals related to the polarization current distributions and the technique of double Floquet-Fourier series expansion. Once the integral functionals are determined, the scattered fields outside the layer are calculated accordingly. The unit cell of the layer comprises several parallelepiped segments of materials characterized by the complex-valued relative permittivity and permeability of step function profiles. The arbitrary profiles of three-dimensional dielectric or metallic gratings can be flexibly modeled by adjusting the material parameters and sizes or locations of the parallelepiped segments in the unit cell. Numerical examples for various grating geometries and their comparisons with those presented in the literature demonstrate the accuracy and usefulness of the proposed method.

A hybrid finite element/rigorous coupled wave analysis for electromagnetic scattering from periodic structures

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3-D Gaussian beam scattering from a gyromagnetic perforated layer: Quasi-static approach

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An adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures

“…Scattering theory in biperiodic structures has many important applications in micro-optics, where the biperiodic structures are also termed as 2D gratings or crossed gratings. We refer to Dobson and Friedman [27], Abboud [1], Bao [7], Bao, Dobson, and Cox [11], Bao and Dobson [10], Bao and Zhou [13], Li [33], Yachin and Yasumoto [49], and Chang, Li, Chu, and Opsal [20] for the existence, uniqueness, and numerical approximations of solutions to 2D grating problems. An introduction to grating problems can be found in Petit [41].…”