Rigorous theory of coupled resonators

TL;DR

This paper reveals the limitations of traditional tight binding models for coupled resonators and introduces a rigorous, general theory for accurately calculating eigenmodes of complex three-dimensional dispersive resonators.

Contribution

It provides a new, comprehensive theoretical framework that correctly describes mode hybridization in coupled resonators, surpassing the inaccuracies of existing models.

Findings

Traditional tight binding models fail for planar resonators.

The new theory accurately predicts eigenmodes of 3D dispersive resonators.

Verification with planar optical resonators confirms the theory's validity.

Abstract

We demonstrate the general failure of the famous concept of tight binding and mode hybridization underlying modern theories of coupled open resonators. In spite of sophisticated examples in the literature, successfully illustrating these theories, the latter fail to describe any planar systems. This includes the simplest possible case of two dielectric slabs placed next to each other or separated by a distance, which is straightforward for verification, due to its analytical solvability. We present a rigorous theory capable of calculating correctly the eigenmodes of arbitrary three-dimensional dispersive coupled resonators in terms of their individual modes, providing insight into the proper mode hybridization and formation of bonding and antibonding supermodes. Planar optical resonators, such as coupled slabs and Bragg-mirror microcavities, are used for illustrative purposes as they allow precise and reliable verification of the theory.