The local density of optical states of a metasurface

TL;DR

This paper presents a semi-analytical method to evaluate the local density of states near 2D metasurfaces of magnetic scatterers, revealing their optical response, oscillations, and mode coupling effects.

Contribution

It introduces a swift, semi-analytical approach for calculating LDOS near magnetic metasurfaces, accounting for all electrodynamic interactions and radiation damping.

Findings

Magnetic scatterer lattices show Drexhage oscillations with phase shifts.

The metasurface's effective homogeneity depends on source-surface separation.

Strong frequency and position dependence indicates coupling to guided modes.

Abstract

While metamaterials are often desirable for near-field functions, such as perfect lensing, or cloaking, they are often quantified by their response to plane waves from the far field. Here, we present a theoretical analysis of the local density of states near lattices of discrete magnetic scatterers, i.e., the response to near field excitation by a point source. Based on a point-dipole theory using Ewald summation and an array scanning method, we can swiftly and semi-analytically evaluate the local density of states (LDOS) for magnetoelectric point sources in front of an infinite two-dimensional (2D) lattice composed of arbitrary magnetoelectric dipole scatterers. The method takes into account radiation damping as well as all retarded electrodynamic interactions in a self-consistent manner. We show that a lattice of magnetic scatterers evidences characteristic Drexhage oscillations. However, the oscillations are phase shifted relative to the electrically scattering lattice consistent with the difference expected for reflection off homogeneous magnetic respectively electric mirrors. Furthermore, we identify in which source-surface separation regimes the metasurface may be treated as a homogeneous interface, and in which homogenization fails. A strong frequency and in-plane position dependence of the LDOS close to the lattice reveals coupling to guided modes supported by the lattice.