A coupling model for quasi-normal modes of photonic resonators

TL;DR

This paper introduces a coupling model for quasi-normal modes in open photonic resonators, enabling efficient analysis and design of complex systems with applications in sensing and filtering.

Contribution

A new linear combination-based coupling model for quasi-normal modes in open photonic systems, validated against full-wave simulations and applicable to complex resonator arrangements.

Findings

Model shows excellent agreement with finite element simulations.

Provides convergence analysis and simplified mode-based models.

Offers physical insights into resonator coupling mechanisms.

Abstract

We develop a model for the coupling of quasi-normal modes in open photonic systems consisting of two resonators. By expressing the modes of the coupled system as a linear combination of the modes of the individual particles, we obtain a generalized eigenvalue problem involving small size dense matrices. We apply this technique to dielectric rod dimmer of rectangular cross section for Transverse Electric (TE) polarization in a two-dimensional (2D) setup. The results of our model show excellent agreement with full-wave finite element simulations. We provide a convergence analysis, and a simplified model with a few modes to study the influence of the relative position of the two resonators. This model provides interesting physical insights on the coupling scheme at stake in such systems and pave the way for systematic and efficient design and optimization of resonances in more complicated systems, for applications including sensing, antennae and spectral filtering.