Modal Analysis of photonic and plasmonic resonators

TL;DR

This paper introduces a method leveraging Maxwell's equations to efficiently compute quasi-normal modes in photonic and plasmonic resonators, enabling accurate predictions of resonator behavior and emitter decay rates.

Contribution

It presents a novel approach using Maxwell's equation structure and Lanczos reduction to compute QNMs and a closed-form model for spontaneous decay rates without prior QNM expansions.

Findings

Accurately predicts QNMs of open resonators.

Provides a closed-form model for spontaneous decay rate.

Validates the approach with numerical examples.

Abstract

Quasi-normal modes (QNMs) are ubiquitous throughout photonics and are utilized in a wide variety of applications, but determining these modes remains a formidable task in general. Here we show that by exploiting the structure of Maxwell's equations it is possible to effectively compute QNMs of photonic and plasmonic nanoresonators. The symmetry of Maxwell's equations allows for a reduction to a system of small order via a Lanczos reduction process through which dominant QNMs can be identified. A closed-form reduced-order model for the spontaneous decay (SD) rate of a quantum emitter is also obtained, which does not require an a priori QNM expansion of the fields. The model is parametric in wavelength and field expansions in dominant QNMs are determined a posteriori. We demonstrate and validate that QNMs of open resonators and the SD rate of a quantum emitter are accurately predicted.