Rayleigh–Bloch waves above the cutoff

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