Avoided crossings and bound states in the continuum in low-contrast dielectric gratings

TL;DR

This paper investigates bound states in the continuum (BICs) in low-contrast dielectric gratings, revealing their origin from guided modes and analyzing resonance behaviors including avoided crossings.

Contribution

It demonstrates the origin of BICs from guided modes in low-contrast dielectric gratings and analyzes resonance phenomena near avoided crossings using a generic formalism.

Findings

BICs originate from reduced guided modes on an effective dielectric slab.

Positions of BICs can be determined from two-wave dispersion relationships.

Near avoided crossings, transmittance and BIC emergence are described by a universal formalism.

Abstract

We consider bound states in the continuum (BICs) in low-contrast dielectric gratings (DGs). It is demonstrated that the BICs originate from the reduced guided modes on the effective dielectric slab with the permittivity equal to the average permittivity of the DG. In case of isolated resonances the positions of BICs can be found from two-wave dispersion relationships for guided leaky modes. In the case of the degeneracy between the two families of leaky modes the system exhibits an avoided crossing of resonances. In the spectral vicinity of the avoided crossing the transmittance as well as the emergence of BICs is described in the framework of the generic formalism by Volya and Zelevinsky [Physical Review C 67, 054322 (2003)] with a single fitting parameter.