Parametric dependence of bound states in the continuum in periodic structures: vectorial cases

TL;DR

This paper investigates vectorial bound states in the continuum (BICs) in 2D periodic structures, revealing that such BICs depend on tuning two parameters and are characterized as curves in a three-dimensional parameter space, with implications for less symmetric structures.

Contribution

It extends the understanding of vectorial BICs in less symmetric 2D periodic structures, showing they form curves in parameter space and providing a method to find them systematically.

Findings

Vectorial BICs depend on two parameters in 2D structures.

BICs form continuous curves in a three-parameter space.

Topological charge is conserved during parameter variation.

Abstract

A periodic structure sandwiched between two homogeneous media can support bound states in the continuum (BICs) that are valuable for many applications. It is known that generic BICs in periodic structures with an up-down mirror symmetry and an in-plane inversion symmetry are robust with respect to structural perturbations that preserve these two symmetries. For two-dimensional (2D) structures with one periodic direction and the up-down mirror symmetry (without the in-plane inversion symmetry), it was recently established that some scalar BICs can be found by tuning a single structural parameter. In this paper, we analyze vectorial BICs in such 2D structures, and show that a typical vectorial BIC with nonzero wavenumbers in both the invariant and the periodic directions can only be found by tuning two structural parameters. Using an all-order perturbation method, we prove that such a vectorial BIC exists as a curve in the 3D space of three generic parameters. Our theory is validated by numerical examples involving periodic arrays of dielectric cylinders. The numerical results also illustrate the conservation of topological charge when structural parameters are varied, if both BICs and circularly polarized states (CPSs) are included. Our study reveals a fundamental property of BICs in periodic structure and provides a systematically approach for finding BICs in structures with less symmetry.