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

Nan Zhang; Ya Yan Lu

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arXiv · 2408.08162

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

Nan Zhang·Ya Yan Lu

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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.

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Nan Zhang, Ya Yan Lu. 2024-08-15. Perturbation theory for resonant states near a bound state in the continuum. https://arxiv.org/abs/2408.08162

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