Bound States in the Continuum in a Double Whispering Gallery Resonator

TL;DR

This paper explores bound states in the continuum within a double whispering gallery resonator system, analyzing their formation, properties, and potential for photon storage using Green's function formalism.

Contribution

It introduces the concept of symmetry-protected and Fabry-Perot type BICs in coupled WGRs and studies their effects on photon transport and storage.

Findings

Identification of two types of BICs in coupled WGRs.

Demonstration of sharp resonances due to quasi-BICs.

Analysis of photon storage mechanisms in the resonator system.

Abstract

In this work, we investigate the single-photon transport through two whispering gallery resonators (WGRs) coupled to a one-dimensional waveguide. Using Green's function formalism, we compute the transmission spectra and the photonic density of states (DOS) for the stationary states. We also obtain the formation of two types of bound states in the continuum (BICs). The first kind is localized into the WGR and are symmetry-protected BICs. In contrast, the second depends on the distance between resonators through the waveguide and is of the Fabry-Perot kind. These BICs are represented as Dirac delta functions in the local density of states. Additionally, we show that quasi-BICs manifest as sharp resonances in photonic transmission due to small symmetry-breaking perturbations. Furthermore, we investigate the dynamics of a single-photon wave packet interacting with the WGRs and analyze the mechanism for storing the wave packet in the structure formed by the WGRs and the finite waveguide between them.