Optical response induced by bound states in the continuum in arrays of dielectric spheres

TL;DR

This paper develops an analytical theory combining quasi-mode expansion and coupled mode theory to describe the optical response near bound states in the continuum in arrays of dielectric spheres, validated against numerical solutions.

Contribution

It introduces a new analytical framework with explicit formulas for CMT parameters based on eigenmodes, enhancing understanding of BIC-related resonances in dielectric arrays.

Findings

CMT parameters can be calculated from eigenfrequencies and eigenvectors.

The theory accurately reproduces Fano resonances near BICs.

Different asymptotic behaviors of line width depend on BIC symmetry.

Abstract

We consider optical response induced by bound states in the continuum (BICs) in arrays of dielectric spheres. By combining quasi-mode expansion technique with coupled mode theory (CMT) we put forward a theory of the optical response by high-Q resonance surrounding BICs in momentum space. The central result are analytical expressions for the CMT parameters, which can be easily calculated from the eigenfrequencies and eigenvectors of the interaction matrix of the scattering systems. The results obtained are verified in comparison against exact numerical solutions to demonstrate that the CMT approximation is capable of reproducing Fano features in the spectral vicinity of the BIC. Based on the quasi-mode expansion technique we derived the asymptotic scaling law for the CMT parameters in the vicinity of the $\Gamma$-point. It is rigorously demonstrated that the line width in the CMT approximation exhibits different asymptotic behaviour depending on the symmetry of the BIC.