Embedded Rayleigh-Bloch surface waves along periodic rectangular arrays.


R. Porter & D.V. Evans, 2005, Wave Motion. 43, 29--50.

In this paper, surface waves in the presence of an infinite periodic array of obstacles of rectangular cross-section are considered. Rayleigh-Bloch surface waves are described by a localised wave motion which does not propagate energy away from the array. The periodicity of the array implies the existence of a cut-off frequency below which Rayleigh-Bloch surface waves may be sought. Such solutions are well established and Rayleigh-Bloch surface waves have been shown to exist for all rectangular cross-section. In the present paper we generate examples of Rayleigh-Bloch surface waves for the more complicated case of frequencies lying above the first cut-off - such waves correspond mathematically to eigenvalues embedded in the continuous spectrum of the field operator. Numerical results are given for rectangular cross-sections based on an integral equation formulation of the problem. Finally strong numerical evidence is given for embedded Rayleigh-Bloch waves that exist a single family of rectangular cross-section above the second cut-off.

Download PDF