We demonstrate that a surface resonance (pseudosurface wave) may transform into a true surface wave, i.e., acquire an infinite lifetime, at a single isolated point within a bulk band (radiative region) in a model of a stressed auxetic material. In contrast with the secluded supersonic elastic surface waves, the one found here does not belong to a dispersion line of true surface waves. Therefore we propose to call it an isolated true surface wave (ITSW). The ITSW manifests itself by a deltalike peak in the local density of states and by anomalies in reflection coefficients. The phenomenon may be useful in redirecting energy and/or information from the bulk to the surface in devices supporting guided acoustic waves.

• Received 9 April 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.075504