Complex dispersion relation of Rayleigh-Bloch waves trapped by slow inclusions

TL;DR

This paper investigates the complex dispersion relations of Rayleigh-Bloch waves guided by slow, permeable inclusions in a fast medium, revealing multiple leaky bands and bound states in the continuum due to symmetry and periodicity.

Contribution

It introduces the concept of guided quasi-normal modes and derives the complex dispersion relation considering radiation, showing new leaky wave phenomena in periodic structures.

Findings

Multiple bands of leaky Rayleigh-Bloch waves identified

Guided bound states in the continuum demonstrated

Complex dispersion relations derived with radiation effects

Abstract

Rayleigh-Bloch waves are guided acoustic waves propagating along a periodic line of inclusions placed inside an open, infinite medium. Below the sound cone, they are transversely evanescent on both sides of the line of inclusions. Guidance is then achieved without any cladding surrounding the segmented core. Inclusions usually impose definite boundary conditions, resulting in a single guided band. We consider instead the case of permeable, slow inclusions inside a fast medium. Introducing the concept of guided quasi-normal modes, we obtain the complex dispersion relation taking into account radiation at infinity. We thus show that multiple bands of leaky Rayleigh-Bloch waves appear and that guided bound states in the continuum arise as a result of the combination of symmetry and periodicity.