Bound States in the Continuum Based on the Total Internal Reflection of Bloch Waves

TL;DR

This paper introduces a new approach to creating bound states in the continuum (BICs) in photonic-crystal slabs using total internal reflection of Bloch waves, supported by a fast, efficient BIC solver and topological analysis.

Contribution

It presents a generalized TIR condition for Bloch waves, a low-complexity BIC solver applicable at high frequencies, and demonstrates multi-channel BICs with topological charge analysis.

Findings

BICs can be formed via phase conditions of Bloch waves.

The developed solver works efficiently beyond the diffraction limit.

Multi-channel BICs exhibit topological charge coincidence.

Abstract

A photonic-crystal slab can support bound states in the continuum (BICs) which have infinite lifetimes but embedded into the continuous spectrum of optical modes in free space. The formation of BICs requires a total internal reflection (TIR) condition at both interfaces between the slab and free space. Here, we show that the TIR of Bloch waves can be directly obtained based on the generalized Fresnel equations proposed. If each of these Bloch waves picks up a phase with integer multiples of 2pi for traveling a round trip, light can be perfectly guided in the slab, namely, forming a BIC. A BIC solver with low computational complexity and fast convergence speed is developed, which can also work efficiently at high frequencies beyond the diffraction limit where multiple radiation channels exist. Two examples of multi-channel BICs are shown, and their topological nature in momentum space is also revealed. Both can be attributed to the coincidence of the topological charges of far-field radiations from different radiation channels. The concept of the generalized TIR and the TIR-based BIC solver developed offer highly effective approaches for explorations of BICs which could have many potential applications in guided-wave optics and enhanced light-matter interactions.