Homogenization of bi-anisotropic metasurfaces

Amr Shaltout,Vladimir Shalaev,Alexander Kildishev

doi:10.1364/oe.21.021941

Abstract

Ultrathin metamaterial layers are modeled by a homogeneous bi-anisotropic film to represent various kinds of broken symmetries in photonic nanostructures, and specifically in optical metamaterials and metasurfaces. Two algorithms were developed to obtain the electromagnetic (EM) wave response from a metasurface (direct solver) or the metasurface parameters from the EM wave response (inverse solver) for a bi-anisotropic, subwavelength-thick nanostructured film. The algorithm is applied to two different metasurfaces to retrieve their effective homogeneous bi-anisotropic parameters. The effective layer of the same physical thickness is shown to produce the same response to plane wave excitation as the original metasurface.

Highlights

Metamaterials have been used for manipulating light in a controllable manner, and they were able to achieve optical properties not existing in nature including negative index of refraction [1, 2], optical magnetism [3], invisibility cloaking [4] and superlensing [5, 6]
Metasurfaces have been used to implement important applications such as light bending [8, 9], flat lenses [10], circular polarizers [11], half-wave plates [12, 13], and quarter wave plates [14, 15]. Those metasurfaces provide their intended functionality by changing the phase and/or polarization of light transmitted through the layer
One major advantage of this direct solver is that it depends on simple matrix operations, which are reversible. This makes the development of the inverse solver straightforward as described

Summary

Introduction

Metamaterials have been used for manipulating light in a controllable manner, and they were able to achieve optical properties not existing in nature including negative index of refraction [1, 2], optical magnetism [3], invisibility cloaking [4] and superlensing [5, 6]. Metasurfaces have been used to implement important applications such as light bending [8, 9], flat lenses [10], circular polarizers [11], half-wave plates [12, 13], and quarter wave plates [14, 15] Those metasurfaces provide their intended functionality by changing the phase and/or polarization of light transmitted through the layer. We have developed a model for metasurface layers with a thin, homogeneous, equivalent film Using this framework, metasurface designers can obtain insight on how best to use the unit-cell structures. The goal is to obtain a homogenous bi-anisotropic film that will generate the same values of the complex coefficients for reflection and transmission as those obtained by the real metamaterial structure. After explaining the details of the process, the algorithm is implemented to homogenize two specific structures that are commonly used in metasurface applications

Direct solver

Inverse problem

Application of algorithm to metasurfaces

Summary