Merging bound states in the continuum at third-order $\Gamma$ point enabled by controlling Fourier harmonic components in lattice parameters

TL;DR

This paper presents a method to merge bound states in the continuum at the third-order $$ point in photonic lattices by controlling Fourier harmonic components, leading to ultrahigh-Q resonances with potential applications in light-matter interactions.

Contribution

The study introduces a novel approach to merge BICs at the third-order $$ point in 1D photonic lattices through precise lattice parameter adjustments, enabling topologically stable and controllable BIC merging.

Findings

Accidental BICs are topologically stable.

BIC positions can be precisely controlled by lattice parameters.

BICs can be merged at the third-order $$ point with or without symmetry protection.

Abstract

Recent studies have demonstrated that ultrahigh-$Q$ resonances, which are robust to fabrication imperfections, can be realized by merging multiple bound states in the continuum (BICs) in momentum space. The merging of multiple BICs holds significant promise for practical applications, providing a robust means to attain ultrahigh-$Q$ resonances that greatly enhance light-matter interactions. In this study, we introduce a novel approach to achieve the merging of BICs at the edges of the fourth stop band, which opens at the third-order $\Gamma$ point, in one-dimensional leaky-mode photonic lattices. Photonic band gaps and BICs arise from periodic modulations in lattice parameters. However, near the third-order $\Gamma$ point, out-of-plane radiation arises by the first and second Fourier harmonic components in the lattice parameters. Accidental BICs can emerge at specific $k$ points where an optimal balance exists between these two Fourier harmonic components. We demonstrate that these accidental BICs are topologically stable, and their positions in momentum space can be precisely controlled by adjusting a specific lattice parameter that influences the strength of the first and second Fourier harmonic components. Furthermore, we show that accidental BICs can be merged at the third-order $\Gamma$ point, with or without a symmetry-protected BIC, by finely adjusting this specific lattice parameter while keeping other parameters constant.