General Theory of Spontaneous Emission Near Exceptional Points

TL;DR

This paper develops a comprehensive theory for spontaneous emission at exceptional points in non-Hermitian systems, revealing finite bounds on emission enhancement and contrasting non-Lorentzian emission profiles with traditional Lorentzian resonances.

Contribution

It extends spontaneous emission theory to exceptional points, providing finite enhancement bounds and analyzing non-Lorentzian emission behaviors in non-Hermitian systems.

Findings

Maximum enhancement of 4 in passive second-order EPs

Enhancements exceeding 400 times in gain-aided and higher-order EPs

Enhancement scales polynomially with resonance quality factor

Abstract

We present a general theory of spontaneous emission at exceptional points (EPs)---exotic degeneracies in non-Hermitian systems. Our theory extends beyond spontaneous emission to any light--matter interaction described by the local density of states (e.g., absorption, thermal emission, and nonlinear frequency conversion). Whereas traditional spontaneous-emission theories imply infinite enhancement factors at EPs, we derive finite bounds on the enhancement, proving maximum enhancement of 4 in passive systems with second-order EPs and significantly larger enhancements (exceeding $400\times$) in gain-aided and higher-order EP systems. In contrast to non-degenerate resonances, EPs are associated with non-Lorentzian emission curves, leading to enhancements that scale polynomially with the resonance quality factor.