Generation of multiple bound states in the continuum through doubly degenerate quasi-guided modes

TL;DR

This paper theoretically analyzes how multiple bound states in the continuum (BICs) can be generated in two-dimensional dielectric sphere arrays with high symmetry, involving doubly degenerate modes and their tunable interactions.

Contribution

It introduces a novel mechanism for generating multiple BICs via doubly degenerate quasi-guided modes in symmetric dielectric arrays, with detailed theoretical insights.

Findings

Multiple BICs can be generated at high-symmetry points in dielectric arrays.

Tuning system parameters leads to accidental BICs and BIC annihilation.

A ring-like high-Q channel with multiple BICs emerges in certain lattice symmetries.

Abstract

We present a detailed theoretical analysis of a peculiar generation of multiple bound states in the continuum (BICs) in two-dimensional periodic arrays of dielectric spheres. They emerge in high-symmetry lattices with the $C_{6v}$ and $C_{4v}$ point groups and involve doubly degenerate quasi-guided modes at the $\Gamma$ point that can couple to external radiation. By tuning a system parameter, the doubly degenerate modes can exhibit accidental BICs at a critical parameter. In the vicinity of the critical parameter, the two bands originating from the degenerate mode exhibit multiple off-$\Gamma$ BICs. They move and annihilate across the two bands by changing the parameter around the critical one. A ring-like high $Q$ channel pinned with multiple BICs emerges particularly for the $C_{6v}$ case. Across the critical coupling, the total vorticity of the multiple BICs is conserved. The $\vb*{k}\cdot\vb*{p}$ perturbation theory explains some features of the phenomena reasonably well.