Yousef Vahabzadeh

Simulation of Metasurfaces in Finite Difference Techniques

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 an FD version of generalized sheet transition conditions. In contrast to previously reported approaches, the proposed method can handle sheets exhibiting both electric and magnetic discontinuities, and represents therefore a fundamental contribution to computational electromagnetics. It is presented here in the framework of the FD frequency domain method, but also applies to the FD time domain scheme. The theory is supported by five illustrative examples.

Spacetime processing metasurfaces: GSTC synthesis and prospective applications

The paper presents the general concept of spacetime processing metasurfaces, synthesized by generalized sheet transition conditions (GSTCs). It is shown that such metasurfaces can perform multiple simultaneous spatio-temporal processing transformations on incident electromagnetic waves. A time-reversal space-generalized-refraction metasurface and a multi-time-space-differentiating metasurfaces are presented as applications of the general spacetime processing metasurface concept.

Mathematical synthesis and analysis of a second-order magneto-electrically nonlinear metasurface

We propose a discussion on the synthesis and scattering analysis of nonlinear metasurfaces. For simplicity, we investigate the case of a second-order nonlinear isotropic metasurface possessing both electric and magnetic linear and nonlinear susceptibility components. We next find the synthesis expressions relating the susceptibilities to the specified fields, which leads to the definition of the nonlinear metasurface conditions for no reflection, themselves revealing the nonreciprocal nature of such structures. Finally, we provide the approximate expressions of the scattered fields based on perturbation theory and compare the corresponding results to finite-difference time-domain simulations.

GSTC-based simulation of metasurfaces in finite difference techniques

We propose a simple and robust method for simulating bi-anisotropic metasurfaces as electromagnetic spatial discontinuity problems in the Finite Difference Frequency Domain (FDFD) scheme. The method consists in embedding a numerical version of the Generalized Sheet Transition Conditions (GSTCs) in the finite difference scheme and straightforwardly applies also to the Finite Difference Frequency Domain (FDTD) scheme. This provides a timely solution to the fundamental problem of scattering from an electromagnetic sheet with simultaneous electric and magnetic discontinuities.

Field moving metasurface

We introduce the concept of field moving metasurface, where the field profile (magnitude and phase) produced by a source at a given distance d0 is moved to a closer (d < d0) or farther (d > d0) distance by placing the properly designed metasurface just above the source. The metasurfaces are designed by specifying the field measured at d0 without the metasurface at the new distance d with the metasurface and applying the surface susceptibility synthesis method [1]. The concept is demonstrated by two full-wave examples, one pulling a far-field profile to the near field (d < d0, magnification) and the other one pushing a near-field profile to the far field (d > d0, contraction). Field moving metasurfaces are expected to find numerous applications across the entire electromagnetic spectrum from microwaves (e.g. field pulling in compact range systems) to optical waves (e.g. field pushing in microscopy). Details and experimental results will be presented at the conference.

Simulation of space-time varying metasurface using finite-difference time-domain technique

An exact and simple method is proposed for the simulation of a space-time varying discontinuity in the Finite-Difference Time-Domain (FDTD) scheme. The method can handle completely general discontinuities (nonuniform bi-anisotropic), that may also be simultaneous electric and magnitude in nature. The effect of the discontinuity is modeled by virtual nodes around the discontinuity, where update equations for the electric and magnetic field nodes are modified using Generalized Sheet Transition Conditions (GSTCs). The method features interesting characteristics for the asymptotic cases of vanishing discontinuity and volume-diluted surface. The applicability of the proposed method is demonstrated by an illustrative example for a 1D time varying problem.

A guided tour in metasurface land: Discontinuity conditions, design and applications

The paper presents an overview of the recent research on metasurfaces performed in the authors group. This covers the introduction of bianistropic Sheet Transition Conditions (STCs), the subsequent elaboration of a general synthesis technique based on surface susceptibility tensors, the complementary elaboration of Finite Difference (FD) and Finite Element (FE) computational schemes for analysis, and, based upon this solid foundation, the development of a host of novel applications across the whole microwave to optical range of the electromagnetic spectrum.