Modal Analysis of photonic and plasmonic resonators

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.