Symmetry Analysis And Multipole Classification Of Eigenmodes In Electromagnetic Resonators For Engineering Their Optical Properties

The resonator is one of the main building blocks of a plethora of photonic and microwave devices from nanolasers to compact biosensors and magnetic resonance scanners. The symmetry of the resonators is tightly related to their mode structure and multipole content which determines the linear and nonlinear response of the resonator. Here, we develop the algorithm for the classification of eigenmodes in resonators of the simplest shapes depending on their symmetry group. For each type of mode, we find its multipole content bridging the gap between the modal and multipolar descriptions. As an illustrative example, we apply the developed formalism to the analysis of a dielectric triangular prism and demonstrate the formation of high-Q resonances originating due to the suppression of scattering through the main multipole channel. The developed approach allows one to engineer, predict, and explain scattering phenomena and optical properties of resonators and meta-atoms based only on their symmetry without the need for numerical simulations, and it can be used for the design of photonic and microwave devices.