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 pointdipole 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.
Highlights
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
The primary motivation to tackle this problem was to assess in how far analyzing a metamaterial as effectively homogeneous is reasonable in an actual scenario where it interacts with a localized object in its near field
We found that a lattice of magnetic scatterers shows characteristic oscillations of the local density of states (LDOS) as a function of distance, shifted in phase compared to those at an electric scattering lattice
Summary
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. 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. Since an emitter is a point-like probe, approaching it to a metamaterial while measuring the lifetime is a direct method to probe at which source-material separations the effective medium approximation holds despite the inherently discrete geometry of metamaterials. These questions have, to the best of our knowledge, not been addressed previously. We spectrally resolve the LDOS in regions in the lattice plane, revealing an increased LDOS by coupling to guided lattice modes
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