Merging and band transition of bound states in the continuum in leaky-mode photonic lattices

TL;DR

This paper investigates how bound states in the continuum (BICs) in photonic lattices merge and transition between bands, providing analytical and numerical insights into achieving ultrahigh-Q resonances despite fabrication imperfections.

Contribution

It introduces an analytical framework for understanding BIC merging and band transition in photonic lattices, aiding the design of robust high-Q resonances.

Findings

BICs can merge at the second stop band edges with or without symmetry protection.

The merged BIC state transitions from upper to lower band edge as lattice thickness increases.

Coupled-mode analysis predicts the specific thickness for BIC merging at the $ ext{Γ}$ point.

Abstract

Bound states in the continuum (BICs) theoretically have the ability to confine electromagnetic waves in limited regions with infinite radiative quality ($Q$) factors. However, in practical experiments, resonances can only exhibit finite $Q$ factors due to unwanted scattering losses caused by fabrication imperfections. Recently, it has been shown that ultrahigh-$Q$ guided-mode resonances (GMRs), which are robust to fabrication imperfections, can be realized by merging multiple BICs in momentum space. In this study, we analytically and numerically investigate the merging and band transition of accidental BICs in planar photonic lattices. Accidental BICs can merge at the edges of the second stop band, either with or without a symmetry-protected BIC. We show that as the thickness of the photonic lattice gradually increases, the merged state of BICs transitions from the upper to the lower band edge. Using coupled-mode analysis, we present the analytical merging thickness at which multiple accidental BICs merge at the second-order $\Gamma$ point. Our coupled-mode analysis could be beneficial for achieving ultrahigh-$Q$ GMRs in various photonic lattices composed of materials with different dielectric constants.