Origin of degenerate bound states in the continuum in a grating waveguide: Parity symmetry breaking due to mode crossing

TL;DR

This paper elucidates the formation of degenerate bound states in the continuum (BICs) in a planar grating waveguide, highlighting a parity symmetry breaking mechanism caused by mode crossing, which leads to high-Q resonances.

Contribution

It introduces an analytical theory explaining how degenerate BICs form via mode crossing and parity symmetry breaking in a grating waveguide, expanding understanding of BIC mechanisms.

Findings

Degenerate BICs result from crossing of two modes with mixed parity.

Destructive interference of crossing modes creates high-Q resonances.

Parity symmetry breaking is key to the formation of degenerate BICs.

Abstract

We explain the origin of bound states in the continuum (BICs) in a planar grating waveguide, in particular, a mechanism for formation of degenerate BICs, via the analytical theory of the infinite-grating eigenmodes. Conventional symmetry-protected BICs are formed at normal incidence mainly by a single infinite-grating eigenmode that has an odd spatial parity on both sides of the BIC resonance. The odd parity is the reason for a cutoff from the radiation-loss channel and appearance of such BICs. The mechanism of emergence of a degenerate BIC in a vicinity of a degenerate frequency of two infinite-grating eigenmodes is different. The degenerate BIC is formed by an anti-phased coherent superposition of two crossing infinite-grating eigenmodes both of which possess a mixed parity and experience parity symmetry breaking as the frequency scans through the degeneracy point. In this case a cutoff from the radiation-loss channel and extremely high-Q narrow resonance is achieved due to the destructive interference of the two crossing eigenmodes. Implementation of such a mechanism can be instructive for designing BICs in other photonic crystals and structures.