Dispersion of guided modes in two-dimensional split ring lattices

TL;DR

This paper introduces a semi-analytical method to analyze the dispersion relations of guided modes in 2D metasurfaces with complex scatterers, accounting for all electrodynamic interactions and radiation damping.

Contribution

It develops a comprehensive point-dipole approach using Ewald summation to study guided plasmonic modes in 2D split ring lattices, including effects of bianisotropy.

Findings

Supported transverse and longitudinal electric modes in plasmon nanorod lattices.

Bianisotropy influences mode band structure and coupling.

Strong bi-anisotropy enhances magnetoelectric character of Bloch modes.

Abstract

We present a semi-analytical point-dipole method that uses Ewald lattice summation to find the dispersion relation of guided plasmonic and bianisotropic modes in metasurfaces composed of 2D periodic lattices of arbitrarily strongly scattering magneto-electric dipole scatterers. This method takes into account all retarded electrodynamic interactions as well as radiation damping selfconsistently. As illustration we analyze the dispersion of plasmon nanorod lattices, and of 2D split ring resonator lattices. Plasmon nanorod lattices support transverse and longitudinal in-plane electric modes. Scatterers that have an in-plane electric and out-of-plane magnetic polarizability, but without intrinsic magnetoelectric coupling, result in two bands that are mixtures of the bands of electric-only and magnetic-only lattices. Thereby bianisotropy through mutual coupling, in absence of building-block bianisotropy, is evident. Once strong bi-anisotropy is included in each building block, the Bloch modes become even more strongly magnetoelectric. Our results are important to understand spatial dispersion and bianisotropy of metasurface and metamaterial designs.