Rigorous Theory of Coupled Resonators

We demonstrate the general failure of the famous concept of tight binding and mode hybridization underlying modern theories of coupled open resonators. Despite sophisticated examples in the literature illustrating these theories, they fail to describe planar systems. This includes even the simplest case of two dielectric slabs placed next to each other or separated by a distance, which is straightforward to verify analytically. We present a rigorous theory capable of calculating correctly the eigenmodes of arbitrary three-dimensional dispersive coupled resonators in terms of their individual modes, revealing proper mode hybridization and formation of bonding and antibonding supermodes. Planar optical resonators, such as coupled slabs and Bragg-mirror microcavities, are used for illustration since they allow reliable verification of the theory.