Scattering Field Solutions of Metasurfaces Based on the Boundary Element Method for Interconnected Regions in 2-D

Abstract

A methodology for determining the scattered Electromagnetic (EM) fields present for interconnected regions with common metasurface boundaries is presented. The method uses a Boundary Element Method (BEM) formulation of the frequency domain version of Maxwell's equations -which expresses the fields present in a region due to surface currents on the boundaries. Metasurface boundaries are represented in terms of surface susceptibilities which when integrated with the Generalized Sheet Transition Conditions (GSTCs), gave rise to an equivalent configuration in terms of electric and magnetic currents. Such a representation is then naturally incorporated into the BEM methodology. Two examples are presented for EM scattering of a Gaussian beam to illustrate the proposed method. In the first example, metasurface is excited with a diverging Gaussian beam, and the scattered fields are validated using a semi-analytical method. Second example concerned with a non-uniform metasurface modeling a diffraction grating, whose results were confirmed with conventional Finite Difference Frequency Domain (FDFD) method.

FDTD Simulation of Dispersive Metasurfaces With Lorentzian Surface Susceptibilities

“…Such space-discontinuities can be rigorously modeled using Generalized Sheet Transition Conditions (GSTCs). Various numerical approaches have been recently presented, where the GSTC conditions are incorporated into bulk Maxwell's equations [21]- [23], including finite-difference formulations in the frequency domain to accurately analyze the transmitted and reflected fields of a general zero-thickness metasurface [24]- [27].…”

Surface Susceptibility Synthesis of Metasurface Holograms for Creating Electromagnetic Illusions

“…where ∆ψ T = ψ(r m+ ) − ψ(r m− ), and ψ av = {ψ(r m+ ) + ψ(r m− )}/2, are expressed in terms of total fields just before and after the metasurface (this implies for a closed object that − indicates the region or field external to the object and + internal quantities). These equations can be incorporated into the IE infrastructure [20] to provide a complete simulation environment for creating metasurface based illusion and camouflage as will be described in following sections.…”

“…Many metasurface synthesis and analysis problems using surface susceptibilities have been reported in the literature, where for planar surfaces, metasurface susceptibilities can be analytically computed, for instance [11], [16]. On the other hand, metasurface analysis typically involves integrating GSTCs into bulk Maxwell's equations using a variety of standard numerical techniques based on Finite-Difference and Finite Element methods [17]- [19], and Integral-Equation (IE) techniques [16], [20]- [24]. Given that the field scattering from a metasurface hologram may need to be evaluated for electrically large domains, IE-GSTC methods are a computationally efficient choice and, as will be shown later and in [15], are well suited for analysis of both closed and open metasurface holograms.…”

Surface Susceptibility Synthesis of Metasurface Skins/Holograms for Electromagnetic Camouflage/Illusions

“…where ∆ψ T = ψ(r m+ ) − ψ(r m− ), and ψ av = {ψ(r m+ ) + ψ(r m− )}/2, are expressed in terms of total fields just before and after the metasurface (this implies for a closed object that − indicates the region or field external to the object and + internal quantities). These equations can be incorporated into the IE infrastructure [29] to provide a complete simulation environment for creating metasurface based illusion and camouflage as will be described in following sections.…”

“…Many metasurface synthesis and analysis problems using surface susceptibilities have been reported in the literature, where for planar surfaces, metasurface susceptibilities can be analytically computed, for instance [20], [25]. On the other hand, metasurface analysis typically involves integrating GSTCs into bulk Maxwell's equations using a variety of standard numerical techniques based on Finite-Difference and Finite Element methods [26]- [28], and Integral-Equation (IE) techniques [25], [29]- [33]. Given that the field scattering from a metasurface hologram may need to be evaluated for electrically large domains, IE-GSTC methods are a computationally efficient choice and, as will be shown later and in [24], are well suited for analysis of both closed and open metasurface holograms.…”