RayleighBloch waves above the cut-off

TL;DR

This paper investigates the behavior of Rayleigh-Bloch waves above the cut-off frequency, revealing their complex wavenumbers, connection to trapped modes, and relation to finite-array resonances.

Contribution

It extends the understanding of Rayleigh-Bloch waves above the cut-off, showing their complex spectrum and connection to trapped modes and resonances.

Findings

Wavenumbers become complex-valued above the cut-off.

Extended Rayleigh-Bloch waves connect trapped modes and embed in the continuous spectrum.

Rayleigh-Bloch waves reappear at high frequencies for small and large cylinders.

Abstract

Extensions of Rayleigh-Bloch waves above the cut-off frequency are studied via the discrete spectrum of a transfer operator for a generalised channel containing a single cylinder. Their wavenumbers are shown to become complex-valued and an additional pair of wavenumbers to appear. For small to intermediate radius values, the extended Rayleigh-Bloch waves are shown connect the Neumann and Dirichlet trapped modes, then embed in the continuous spectrum. Rayleigh-Bloch waves vanish as frequency increases but reappear at high frequencies for small and large cylinders. The existence and properties of the Rayleigh-Bloch waves are connected with finite-array resonances.