A scalar product for the radiation of resonant modes

Abstract

We introduce the conformally-invariant scalar product, originally devised for radiation fields, to the study of the modes of optical resonators. This scalar product allows one to normalize and compare resonant modes using their corresponding radiation fields. Such fields are polychromatic fields free of divergences, which are determined from the complex frequencies and the modal fields on the surface of the resonator. The scalar product is expressed as surface integrals involving the modal fields, multiplied by closed-form factors incorporating the complex frequencies. In a practical application, we study the modes of disk-shaped whispering gallery resonators, and show that the proposed scalar product accurately predicts the geometry-dependent crossings and anti-crossings between modes.

References in corpus (21)

• MNPBEM - A Matlab toolbox for the simulation of plasmonic nanoparticles
• Light interaction with photonic and plasmonic resonances
• Effective mode volumes and Purcell factors for leaky optical cavities
• Quantization of quasinormal modes for open cavities and plasmonic cavity-QED
• Quasinormal mode solvers for resonators with dispersive materials
• Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics
• Normalization, orthogonality and completeness of quasinormal modes of open systems: the case of electromagnetism
• Resonant-state expansion for open optical systems: Generalization to magnetic, chiral, and bi-anisotropic materials
• Quantum Optics Model of Surface Enhanced Raman Spectroscopy for Arbitrarily Shaped Plasmonic Resonators
• Quantum dynamics of two quantum dots coupled through localized plasmons: An intuitive and accurate quantum optics approach using quasinormal modes
• Modal Expansion of the Scattered Field: Causality, Non-Divergence and Non-Resonant Contribution
• Regularized quasinormal modes for plasmonic resonators and open cavities
• Quasinormal mode expansion of optical far-field quantities
• Substrate-induced maximum optical chirality of planar dielectric structures
• Completeness and divergence-free behavior of the quasi-normal modes using causality principle
• Nanophotonic resonance modes with the nanobem toolbox
• Connecting classical and quantum mode theories for coupled lossy cavity resonators using quasinormal modes
• Exact Maxwell evolution equation of resonators dynamics: temporal coupled-mode theory revisited
• Efficient rational approximation of optical response functions with the AAA algorithm
• A scalar product for computing fundamental quantities in matter
• The electromagnetic scalar product in spatially-bounded domains