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.
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