Polarization States in 2D Phononic Crystals and Phononic Crystal Waveguides

We investigate, using the Plane Wave Expansion method and an energy balance criterion, the polarization states of elastic waves in a two dimensional phononic crystal made of vacuum holes in a silicon host matrix. Pure modes can be identified for the out of plane polarization while a continuous variation of the in-plane polarization with the Bloch wave vector can be observed. The study is then extended to two-dimensional phononic crystal waveguides by using the super-cell technique. The dependence of the elastic wave polarization state on the wave guide width is investigated and shows as well a continuous variation with the Bloch wave vector. Moreover, the variation of the width of the waveguide can be used to tune both the dispersion and the polarization of guided waves.