Abstract
We present a quasinormal-mode (QNM) theory for coupled loss and gain resonators working in the vicinity of an exceptional point. Assuming linear media, which can be fully quantified using the complex pole properties of the QNMs, we show how the QNMs yield a quantitatively accurate model to a full classical dipole spontaneous-emission response in Maxwell’s equations at a variety of spatial positions and frequencies (under linear response). We also develop an intuitive QNM coupled-mode theory, which can be used to accurately model such systems using only the QNMs of the bare resonators, where the hybrid QNMs of the complete system are automatically obtained. Near a lossy exceptional point, whose general properties are broadened and corrected through use of QNM theory, we analytically show how the QNMs yield a Lorentzian-like and a Lorentzian-squared-like response for the spontaneous-emission line shape consistent with other works. However, using rigorous analytical and numerical solutions for microdisk resonators, we demonstrate that the general line shapes are far richer than what has been previously predicted. Indeed, the classical picture of spontaneous emission can take on a wide range of positive and negative Purcell factors from the hybrid modes of the coupled loss-gain system. The negative Purcell factors are unphysical and signal a clear breakdown of the classical dipole picture of spontaneous emission in such media, though the concept of a negative local density of states is correct. This finding has enabled a quantum fix to the decay of a two-level-system dipole emitter in amplifying and lossy media [Franke et al., Phys. Rev. Lett. 127, 013602 (2021)], and we further show and discuss the impact of this fix using the QNMs of the microdisk resonators. We also show the rich spectral features of the Green’s function propagators, which can be used to model various physical observables, such as photon detection.
- Received 18 January 2021
- Revised 31 May 2021
- Accepted 17 August 2021
DOI:https://doi.org/10.1103/PhysRevX.11.041020
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Optical resonators—in which photonic cavity structures are used to trap light waves—are a central component of many technologies such as lasers, filters, and interferometers. However, the performance of resonators is limited in part by dissipation via material absorption and/or radiation. One way to reduce such losses is through gain compensation, where a controllable medium amplifies the light. To that end, coupled loss and gain structures have been under intense investigation recently for applications in sensing and quantum optics. Here, we present a crucial step for rigorously describing such systems based on a quantitative mode theory using quasinormal modes, which are the correct cavity modes of open-cavity resonators.
The analytical nature of our theory enables researchers to construct accurate and intuitive descriptions of coupled loss-gain resonators using only the properties of the bare modes. Near a lossy exceptional point, where the coupled modes are very close together, we demonstrate both analytically and numerically far richer spectral line shapes and Purcell factors (which quantify how the environment enhances a dipole emitter’s spontaneous emission) than what has been previously predicted. Our theory quantitatively explains how a negative local density of states (where the net classical power flow surrounding a small dipole flows inward instead of outward) is possible, even in a linear gain-loss system, and demonstrates a clear breakdown of the classical Purcell factor in such media, which is shown to take on a wide range of positive and negative values.
Our formalism gives a solid and accurate understanding of how cavity modes hybridize in coupled loss-gain systems, and paves the way toward a complete quantum description of active cavity resonators.
