A coupling model for quasi-normal modes of photonic resonators

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.

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• Dissipative modes, Purcell factors and directional beta factors in gold bowtie nanoantenna structures
• Connecting classical and quantum mode theories for coupled lossy cavity resonators using quasinormal modes
• Classical Purcell factors and spontaneous emission decay rates in a linear gain medium
• Rigorous theory of coupled resonators
• A normalization approach for scattering modes to be of use in classical and quantum electrodynamics