Amplified and directional spontaneous emission from arbitrary composite bodies: self-consistent treatment of Purcell effect below threshold

TL;DR

This paper presents a self-consistent electromagnetic model for amplified spontaneous emission in complex composite bodies, accounting for Purcell effects and enabling directional, tunable radiation predictions based on active and passive media configurations.

Contribution

It introduces a novel fluctuating volume-current formulation that incorporates Purcell effects into linear ASE modeling through a self-consistent gain renormalization approach.

Findings

Directional emission patterns depend on gain distribution and shape.

The model captures Purcell effect influences on gain and emission.

Predictions include tunable radiation characteristics in composite bodies.

Abstract

We study amplified spontaneous emission (ASE) from wavelength-scale composite bodies--complicated arrangements of active and passive media--demonstrating highly directional and tunable radiation patterns, depending strongly on pump conditions, materials, and object shapes. For instance, we show that under large enough gain, $\mathcal{PT}$ symmetric dielectric spheres radiate mostly along either active or passive regions, depending on the gain distribution. Our predictions are based on a recently proposed fluctuating volume--current (FVC) formulation of electromagnetic radiation that can handle inhomogeneities in the dielectric and fluctuation statistics of active media, e.g. arising from the presence of non-uniform pump or material properties, which we exploit to demonstrate an approach to modelling ASE in regimes where Purcell effect (PE) has a significant impact on the gain, leading to spatial dispersion and/or changes in power requirements. The nonlinear feedback of PE on the active medium, captured by the Maxwell--Bloch equations but often ignored in linear formulations of ASE, is introduced into our linear framework by a self-consistent renormalization of the (dressed) gain parameters, requiring the solution of a large system of nonlinear equations involving many linear scattering calculations.