Tunneling and dispersion in 3D phononic crystals

Abstract

Abstract Tunneling and dispersion of ultrasonic pulses is investigated in 3D phononic crystals consisting of 0.8 mm-diameter tungsten carbide beads that are close packed in a fcc crystal array embedded in either water or epoxy. Pulsed ultrasonic techniques allow us to measure the phase velocity and group velocity, i.e. the dynamics of wave propagation, as well as the transmission coefficient. Our experimental data are well interpreted using multiple scattering theory (MST). In the tungsten carbide/water crystals, dispersion phenomena were studied at frequencies in and around the gap in the ΓL direction. A strong suppression of the group velocity, and large variations of the group velocity dispersion (GVD) were found at frequencies around the band edges. By contrast, fast group velocities and nearly constant GVD with values around zero were observed at gap frequencies, indicating that tunneling in phononic crystals is essentially dispersionless. In the tungsten carbide/epoxy crystals a wide gap (to our knowledge, largest measured 3D band gap) was measured covering a frequency range from 1.2 MHz to 4.3 MHz along the ΓL crystal direction. The agreement between the theory and experiments gives strong evidence of the existence of a large complete gap (1.5 MHz to 3.9 MHz), which is theoretically predicted from the band structure calculations.