Wave phenomena in phononic crystals

Novel wave phenomena in two- and three-dimensional (2D and 3D) phononic crystals were investigated experimentally using ultrasonic techniques. These ultrasonic techniques allow the full wave field to be imaged directly, which is a considerable advantage in fundamental studies of wave propagation in periodic media.; Resonant tunnelling of ultrasonic waves was successfully observed for the first time by measuring the transmission of ultrasound pulses through a double barrier consisting of two 3D phononic crystals separated by a cavity. This effect is the classical analogue of resonant tunnelling of a quantum mechanical particle through a double potential barrier, in which transmission reaches unity at resonant frequencies. For phononic crystals, the tunnelling peak was found to be less than unity, an effect that was explained by absorption. Absorption introduces a small propagating component inside the crystals in addition to the dominant evanescent mode at band gap frequencies, and causes leakage of the pulse from the cavity. The dynamics of resonant tunnelling was explored by measuring the group velocities of the ultrasonic pulses. Very slow and very fast velocities were found at frequencies close to and at the resonance, respectively. These extreme values are less than the speed of sound in air and greater than the speed of sound in any of the crystal's constituent materials.; Negative refraction and focusing effects in 2D phononic crystals were also observed. Negative refraction of ultrasound was demonstrated unambiguously in a prism-shaped 2D crystal at frequencies in the 2nd pass band, where the equifrequency contours are circular so that the wave vector and group velocity are antiparallel. The Multiple Scattering Theory and Snell's law allowed theoretical predictions of the refraction angles. Excellent agreement was found between theory and experiment. The negative refraction experiments revealed a mechanism that can be used to focus ultrasound using a flat phononic crystal, and experiments to demonstrate the focusing of ultrasound emitted by several point sources were successfully carried out. The importance of using phononic crystals with circular equi frequency contours, as well as matching the size of the contours inside and outside the crystal, was established. Both conditions were satisfied by a flat phononic crystal of steel rods, in which the liquid inside the crystal (methanol) was different from the outside medium (water). The possibility of achieving subwavelength resolution using this phononic crystal was investigated with a subwavelength line source (a miniature strip-shaped transducer, approximately lambda/5 wide). A resolution of 0.55lambda was found, which is just above the diffraction limit lambda/2.