Tracking Rayleigh-Bloch waves swapping between Riemann sheets

Abstract

Rayleigh-Bloch waves are modes localized to periodic arrays of scatterers with unbounded unit cells. Here, Rayleigh-Bloch waves are studied for line arrays of sound-hard circular scatterers embedded in a two-dimensional acoustic medium, for which it has recently been shown that Rayleigh-Bloch waves exist for higher frequencies than previously thought. Moreover, it was shown that Rayleigh-Bloch waves can cut off (disappear) and cut on (reappear), and additional Rayleigh-Bloch waves can cut on and interact with the existing ones. These complicated behaviours are reconsidered using a family of quasi-periodic Green's functions that allow particular plane-wave components to become unbounded away ..