Analysis of wave scattering from 2D curved metasurfaces using Floquet and Fourier series expansions

Abstract

An efficient technique for calculating the scattering from curved metasurfaces using the extinction theorem in conjunction with the Floquet and Fourier series expansions is presented. Here, we treat the two-dimensional metasurfaces that have transversal polarizabilities with no variation along the y-axis. The boundary conditions at the metasurface are given by the generalized sheet transition conditions (GSTCs) whose susceptibilities are given in an arbitrary local coordinate system. First, we use the extinction theorem to provide integral equations of the scattering problem. The integral equations involve the Green's functions, tangential electric and magnetic fields and their normal derivatives in regions above and below the metasurface. Then, we employ the Floquet theorem that gives us the analytical periodic Green's functions of each region. Next, we employ the Fourier theorem to expand the tangential fields in terms of unknown Fourier coefficients. The GSTCs and the integral equations provide equations to be solved for the unknowns. The method can calculate scattering from both periodic and non-periodic metasurfaces. The technique is used to analyse different applied problems such as carpet cloaking, illusion, and radar echo width reduction. The method is fast and accurate and can efficiently treat metasurfaces with electrically large curved geometries with dimensions as large as 120 times the wavelength.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

A theoretical approach to zero-reflection toroidal curved metasurfaces

“…Approaches for calculating scattered electromagnetic fields of metasurfaces have been proposed in the past, such as using periodic Green’s function (Floquet-Bloch) or the GSTC method 1 , but the fundamental issue with applying these methods is that the structures must have a minimum of periodicity in order to be employed and they are unsuitable for calculating near-field responses.…”