Analytical model of metasurfaces comprising meta-atoms with anisotropic polarizabilities

TL;DR

This paper introduces a comprehensive analytical model for anisotropic metasurfaces that elucidates electromagnetic resonances and coupling effects, aiding the design of advanced nanophotonic devices under oblique light incidence.

Contribution

It presents a novel analytical approach to analyze anisotropic metasurfaces with electric and magnetic dipoles, including explicit formulas for optical responses and dipole interactions.

Findings

The model accurately characterizes spectral resonances of dielectric metasurfaces.

It reveals the role of electric-magnetic dipole coupling in optical resonances.

The approach is validated against numerical results for silicon nanoprisms.

Abstract

A general analytical approach to the study of electromagnetic resonances of metasurfaces consisting of meta-atoms with anisotropic electric and magnetic dipole polarizabilities and irradiated with obliquely incident light is developed in the direct dipole-moment representation. The presented approach allows us to clearly trace and explain the features of the electromagnetic coupling between electric and magnetic dipole moments in the metasurface and to identify its role in the formation of optical resonances. For these purposes, the dependence of the dipole lattice sums on the angle of illumination is also presented. Expressions for the transmittance and reflectivity corresponding to the specular reflectance are presented with explicit inclusion of the dipole moments of particles in the array, which allows using these expressions for multipole analysis of purely numerical results concerning the optical response of metasurfaces. The developed analytical method is tested to characterize the spectral resonances of dielectric metasurfaces composed of rectangular silicon nanoprisms. In addition, we discuss the relationship and similarity between the results of coupled dipole and coupled dipole-quadrupole methods. Our analytical representation of electromagnetic dipole coupling is an insightful and fast method for the characterization of collective resonances in metasurfaces under illumination at oblique incidence. It could be especially useful for designing planar nanophotonic devices consisting of arbitrary-shaped building blocks and operating under special irradiation conditions.