Resonant field enhancement near bound states in the continuum on periodic structures

TL;DR

This paper investigates how bound states in the continuum (BICs) on periodic structures lead to high-Q resonances that significantly enhance local electromagnetic fields, providing analytical and numerical insights for practical applications.

Contribution

It introduces a perturbation method to relate field enhancement to the Q-factor and explores the dependence on resonant modes and coupling efficiency, advancing understanding of BIC-related resonances.

Findings

Field enhancement scales with the square-root of Q-factor.

Different BICs exhibit distinct asymptotic behaviors.

Numerical results validate the analytical relations.

Abstract

On periodic structures sandwiched between two homogeneous media, a bound state in the continuum (BIC) is a guided Bloch mode with a frequency within the radiation continuum. BICs are useful, since they give rise to high quality-factor ($Q$-factor) resonances that enhance local fields for diffraction problems with given incident waves. For any BIC on a periodic structure, there is always a surrounding family of resonant modes with $Q$-factors approaching infinity. We analyze field enhancement around BICs using analytic and numerical methods. Based on a perturbation method, we show that field enhancement is proportional to the square-root of the $Q$-factor, and it depends on the adjoint resonant mode and its coupling efficiency with incident waves. Numerical results are presented to show different asymptotic relations between the field enhancement and the Bloch wavevector for different BICs. Our study provides a useful guideline for applications relying on resonant enhancement of local fields.