A coupling model for quasi-normal modes of photonic resonators

Abstract

We develop a model for the coupling of quasinormal 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.

Light Interaction with Photonic and Plasmonic Resonances

“…Will it be possible to derive a simple and general formalism to hybridize resonances of different natures, similar to what has been done for spontaneous emission in the strong coupling regime? QNM formulations with correct normalization have the potential to bring major consistency to coupled‐mode theory, but current literature contains scarce studies for very simple cases, e.g., 2D dielectric resonators or 3D spheres . Increasingly important applications of nanoresonators rely on the cross‐action of Maxwell's resonant fields with other equations of physics, e.g., optomechanical cooling, plasmonic trapping, photonic switching, plasmon‐enhanced Raman scattering… Traditional modeling tools are not effective, as the full photon Green function needs to be repeatedly computed to iteratively model the nonlinear dynamics.…”

“…, it is possible to remove the mistake brought by the energy normalization. In general, all the perturbed QNMs of the perturbed resonators can be expanded into the complete set of the unpertubed QNMs, and the expansion coefficients can be computed by solving a linear matrix eigenvalue problem . This rigorous expansion approach works well provided that the basis is complete and remains valid well beyond the perturbation regime.…”

A physical interpretation of coupling chiral metaatoms

“…Finally, we evaluated the near field coupling coefficient < ω37 ð Þ ¼ Àω 15 þ ω 17 and ω38 ¼ ω 16 À ω 18 . The interaction between subwavelength nanorods can be directly calculated from the field overlapping integral among nanocavities, which is defined as, 37,60…”

“…We should stress that, although CMT is well-accepted as a phenomenological model, recent developments in the QNM have unveiled its solid physical foundations, where the parameters in CMT can be directly deduced from QNM information. 36,[60][61][62][63][64][65][66][67] An important implication of the foregoing analysis is the rational design of zero transmission points for circularly polarized light. Generally speaking, the optimal CD response, defined by CD = ±1, corresponds to the zero transmission point upon either LCP or RCP excitation.…”

Normalization approach for scattering modes in classical and quantum electrodynamics

“…where the polarization vectorsê k,σ are normalized. This means that in order to achieve correct field orthonormalization in any case where a plane wave is incident on a localized scatterer one simply has to fix the amplitude of the plane wave according to (35). The result (35) might be surprising at first, since the normalization does not depend on the scattered field.…”