Microscopic model of Purcell enhancement in hyperbolic metamaterials

TL;DR

This paper presents a microscopic model demonstrating how hyperbolic metamaterials can dramatically enhance spontaneous emission, with optimal emitter placement and detailed Green function analysis providing fundamental insights into their behavior.

Contribution

The study introduces a microscopic lattice model for hyperbolic metamaterials, revealing the dependence of Purcell enhancement on emitter position and Green function characteristics.

Findings

Optimal emitter positions are at local field maxima.

Green function exhibits a cross-like spatial pattern.

Significant Purcell factor enhancement is achievable.

Abstract

We study theoretically a dramatic enhancement of spontaneous emission in metamaterials with the hyperbolic dispersion modeled as a cubic lattice of anisotropic resonant dipoles. We analyze the dependence of the Purcell factor on the source position in the lattice unit cell and demonstrate that the optimal emitter position to achieve large Purcell factors and Lamb shifts are in the local field maxima. We show that the calculated Green function has a characteristic cross-like shape, spatially modulated due to structure discreteness. Our basic microscopic theory provides fundamental insights into the rapidly developing field of hyperbolic metamaterials.