Complex modes in an open lossless periodic waveguide

TL;DR

This paper investigates complex guided modes in open lossless periodic waveguides, revealing their band structure and classification, which enhances understanding and guides practical applications of such waveguides.

Contribution

It provides a detailed analysis of complex modes in lossless periodic waveguides, classifying their endpoints and elucidating their physical significance, which was not comprehensively understood before.

Findings

Complex modes form bands in the waveguide

Endpoints include extrema, bound states in continuum, and diffraction solutions

Provides a classification framework for complex mode endpoints

Abstract

Guided modes of an open periodic waveguide, with a periodicity in the main propagation direction, are Bloch modes confined around the waveguide core with no radiation loss in the transverse directions. Some guided modes can have a complex propagation constant, i.e. a complex Bloch wavenumber, even when the periodic waveguide is lossless (no absorption loss). These so-called complex modes are physical solutions that can be excited by incident waves whenever the waveguide has discontinuities and defects. We show that the complex modes in an open dielectric periodic waveguide form bands, and the endpoints of the bands can be classified to a small number of cases, including extrema on dispersion curves of the regular guided modes, bound states in the continuum, degenerate complex modes, and special diffraction solutions with blazing properties. Our study provides an improved theoretical understanding on periodic waveguides and a useful guidance to their practical applications.