Topological nature of bound states in the radiation continuum

TL;DR

This paper reveals that bound states in the continuum (BICs) are topological vortices in polarization space, with their robustness rooted in conserved topological charges, impacting laser emission properties.

Contribution

It demonstrates that BICs are vortex centers with topological charges, unifying symmetry-protected and accidental BICs through topological polarization analysis.

Findings

BICs correspond to polarization vortices in far-field radiation.

Topological charges explain BIC robustness and creation/annihilation rules.

Implications for vector beam laser emission.

Abstract

Bound states in the continuum (BICs) are unusual solutions of wave equations describing light or matter: they are discrete and spatially bounded, but exist at the same energy as a continuum of states which propagate to infinity. Until recently, BICs were constructed through fine-tuning parameters in the wave equation or exploiting the separability of the wave equation due to symmetry. More recently, BICs that that are both robust and not symmetry-protected (accidental) have been predicted and experimentally realized in periodic structures; the simplest such system is a periodic dielectric slab, which also has symmetry-protected BICs. Here we show that both types of BICs in such systems are vortex centers in the polarization direction of far-field radiation. The robustness of these BICs is due to the existence of conserved and quantized topological charges, defined by the number of times the polarization vectors wind around the vortex centers. Such charges can only be generated or annihilated by making large changes in the system parameters, and then only according to strict rules, which we derive and test numerically. Our results imply that laser emission based on such states will generate vector beams.