Frequency perturbation theory of bound states in the continuum in a periodic waveguide

TL;DR

This paper develops a frequency perturbation theory for bound states in the continuum (BICs) in periodic waveguides, analyzing eigenmodes near BIC frequencies and their complex Bloch wavenumbers, with implications for optical device design.

Contribution

It introduces a novel approach to study eigenmodes near BICs in periodic waveguides for given real frequencies, expanding understanding of high-Q resonances.

Findings

Eigenmodes near BICs have complex Bloch wavenumbers.

Such eigenmodes can be leaky or exponentially decaying.

The theory aids in analyzing photonic devices near BIC frequencies.

Abstract

In a lossless periodic structure, a bound state in the continuum (BIC) is characterized by a real frequency and a real Bloch wavevector for which there exist waves propagating to or from infinity in the surrounding media. For applications, it is important to analyze the high-$Q$ resonances that either exist naturally for wavevectors near that of the BIC or appear when the structure is perturbed. Existing theories provide quantitative results for the complex frequency (and the $Q$-factor) of resonant modes that appear/exist due to structural perturbations or wavevector variations. When a periodic structure is regarded as a periodic waveguide, eigenmodes are often analyzed for a given real frequency. In this paper, we consider periodic waveguides with a BIC, and study the eigenmodes for given real frequencies near the frequency of the BIC. It turns out that such eigenmodes near the BIC always have a complex Bloch wavenumber, but they may or may not be leaky modes that radiate out power laterally to infinity. These eigenmodes can also be complex modes that decay exponentially in the lateral direction. Our study is relevant for applications of BICs in optical waveguides, and it is also helpful for analyzing photonic devices operating near the frequency of a BIC.