Mapping the band structure of a surface phononic crystal

We map the band structure of surface acoustic modes of a periodic array of copper lines embedded in a SiO2 film on a silicon substrate by means of the laser-induced transient grating technique. A detailed map of the lowest sheet of the ω(k) surface and partial maps of two higher-order sheets are obtained. We discuss the topology of the ω(k) surface and explain how it arises from the Rayleigh and Sezawa modes of the film/substrate system. In the vicinity of the bandgap formed at the Brillouin zone boundary, the first and second dispersion sheets take the form of a saddle and a bowl, respectively, in agreement with a weak perturbation model. The shape of the third dispersion sheet, however, appears to defy expectations based on the perturbation approach. In particular, it contains minima located off the symmetry directions, which implies the existence of zero group velocity modes with an obliquely directed wavevector.