Rayleigh-Bloch waves above the cutoff

Abstract

Extensions of Rayleigh-Bloch waves above the cutoff frequency are studied via the discrete spectrum of a transfer operator for a channel containing a single cylinder with quasi-periodic side-wall conditions. Above the cutoff, the Rayleigh-Bloch wavenumber becomes complex valued and an additional wavenumber appears. For small-to intermediate-radius values, the extended Rayleigh-Bloch waves are shown to connect the Neumann and Dirichlet trapped modes before embedding in the continuous spectrum. A homotopy method involving an artificial damping term is proposed to identify the discrete spectrum close to the embedding. Moreover, Rayleigh-Bloch waves vanish beyond some frequency but reappear at h..