Simulation of Metasurfaces in Finite Difference Techniques

Abstract

Abstract-We introduce a rigorous and simple method for analyzing metasurfaces, modeled as zero-thickness electromagnetic sheets, in Finite Difference (FD) techniques. The method consists in describing the spatial discontinuity induced by the metasurface as a virtual structure, located between nodal rows of the Yee grid, using a finite difference version of Generalized Sheet Transition Conditions (GSTCs). In contrast to previously reported approaches, the proposed method can handle sheets exhibiting both electric and magnetic discontinuities, and represents therefore a fundamental contribution in computational electromagnetics. It is presented here in the framework of the FD Frequency Domain (FDFD) method but also applies to the FD Time Domain (FDTD) scheme. The theory is supported by five illustrative examples.Index Terms-Metasurface, electromagnetic sheet, spatial discontinuity, generalized sheet transition conditions (GSTCs), finite difference frequency domain (FDFD), finite difference time domain (FDTD), diffraction orders.

On the Use of Electromagnetic Inversion for Metasurface Design

“…where 0 and µ 0 are the permittivity and permeability of free space, respectively, and χ ee , χ mm , χ em , and χ me represent the electric/magnetic (first subscript) surface susceptibility tensors describing the response to electric/magnetic (second subscript) field excitations [40]. The average fields on the surface Σ of the metasurface are defined as…”

“…Since all fields are TE z , the system in (3) can be simplified and the metasurface can be represented by only four unknown susceptibility terms. Furthermore, we stipulate that there is no magnetoelectric coupling for simplicity, resulting in χ em = χ me = 0 [40]. With this choice, the unknown susceptibility tensors reduce to…”

Nonreciprocal Phase Gradient Metasurface: Principle and Transistor Implementation

“…where the symbol ∆ and the subscript 'av' represent the differences and averages of the tangential electric or magnetic fields at both sides of the metasurface, and χ ee , χ mm , χ em , χ me are the bianisotropic susceptibility tensors characterizing the metasurface. Figure 1(b) plots the FDFD-simulated [9] fields propagating across a uniform nonreciprocal phase shifting metasurface with phase difference ∆φ = 180 • , corresponding to a spatial gyrator. The corresponding susceptiblities for an x-polarized incident wave are obtained from (1) as…”

Simultaneous enhancement of light extraction and spontaneous emission using a partially reflecting metasurface cavity

“…to maximize the overall LED PCE. The full-wave simulations will be performed using the COMSOL finite element method (FEM) commercial software, where the metasurface is modeled as a deeply sub-wavelength slab with volume susceptibilityχ vol =χ/δ , where δ is the thickness of the slab [21]. Given the high density of the FEM mesh required in the metasurface-modeling slab and around the (point) dipole, the actual 3D problem is not tractable on a standard computer.…”