Perturbation theory for resonant states near a bound state in the continuum

TL;DR

This paper develops a perturbation theory to analyze resonant states near bound states in the continuum in photonic crystal slabs, providing insights into Q-factor behavior, polarization, and super-BIC identification.

Contribution

The work introduces a rigorous perturbation framework for BICs, enabling precise analysis of resonant states, polarization, and super-BIC conditions without merging processes.

Findings

Resonant states near BIC can be nearly circularly polarized under certain conditions.

The theory provides a clear criterion for identifying super-BICs in various structures.

A practical super-BIC was demonstrated in a square lattice of rods on a dielectric substrate.

Abstract

In this work, we develop a perturbation theory to analyze resonant states near a bound state in the continuum (BIC) in photonic crystal slabs. The theory allows us to rigorously determine the asymptotic behavior of $Q$-factor and the far-field polarization. We show that the resonant states close to a BIC can be nearly circularly polarized if the scattering matrix satisfies a certain condition. Moreover, our theory offers a novel perspective on super-BICs and provides a clear and precise condition to efficiently identify them in both symmetric and asymmetric structures without requiring a merging process. For practical applications, we find a super-BIC in a square lattice of rods on a dielectric substrate. Our theory addresses the non-Hermitian nature of the system, can be generalized to treat other structures that support BICs, and has potential applications in resonance and chiral optics.