Sagittal acoustic waves in phononic crystals:k-dependent polarization

Abstract

We have studied the polarization states of the sagittal acoustic waves in one- and two-dimensional phononic crystals. Our theoretical results show the continuous variation of the field displacement components when the Bloch wave vector sweeps the Brillouin zone; thus, the vibrational modes of the same dispersion curve $\ensuremath{\omega}(\mathbf{k})$ can have different polarizations. We first present the polarization map of sagittal waves in an epoxy/Sn superlattice. The band polarization---the transverse and longitudinal contributions---is discussed and related to the characteristics of the transmission spectra of a multilayer sample. In addition, we discuss the polarization of the sagittal bands in two-dimensional phononic crystals. We calculated the band polarization for two arrays of cylindrical holes in epoxy which recently were constructed for experimental tests in the hypersonic regime [T. Gorishnyy, C. K. Ullal, M. Maldovan, G. Fytas, and E. L. Thomas, Phys. Rev. Lett. 94, 115501 (2005)]. As we shall see, the mixed modes can be either predominantly transverse or predominantly longitudinal. For calculations, we have used an energy balance criterion.