Light trapping above the light cone in one-dimensional array of dielectric spheres

TL;DR

This paper demonstrates the existence of bound states in the continuum (BSC) in a linear array of dielectric spheres, classifies them by symmetry and polarization, and discusses their detection via Fano resonance collapse.

Contribution

It provides a comprehensive classification of BSCs in dielectric sphere arrays, including symmetry-protected and robust Bloch BSCs, and explores their detection methods.

Findings

BSCs exist in TE and TM continua above the light cone.

Symmetry-protected BSCs occur for specific parameters.

BSCs can be detected through Fano resonance collapse.

Abstract

We demonstrate bound states in the first TE and TM diffraction continua (BSC) in a linear periodic array of dielectric spheres in air above the light cone. We classify the BSCs according to the symmetry specified by the azimuthal number $m$, the Bloch wave vector $\beta$ directed along the array, and polarization. The most simple symmetry protected TE and TM polarized BSCs have $m=0$ and $\beta=0$ and occur in a wide range of the radius of the spheres and dielectric constant. More complicated BSCs with $m\neq 0$ and $\beta=0$ exist only for a selected radius of spheres at a fixed dielectric constant. We also find robust Bloch BSCs with $\beta\neq 0, m=0$. We present also the BSCs embedded into two and three diffraction continua. We show that the BSCs can be easily detected by the collapse of Fano resonance for scattering of electromagnetic plane waves by the array.