We demonstrate experimentally the guiding and the bending of acoustic waves in highly confined waveguides formed by removing rods from a periodic two-dimensional lattice of steel cylinders immersed in water. Full transmission is observed for a one-period-wide straight waveguide within the full band gap of the perfect phononic crystal. However, when the waveguide width is doubled, destructive interference causes the transmission to vanish in the center of the passband. Waveguiding over a wide frequency range is obtained for a one-period-wide waveguide with two sharp 90° bends. Finite-difference time-domain computations are found to be in good agreement with the measurements.

The propagation of acoustic waves in a phononic crystal slab consisting of piezoelectric inclusions placed periodically in an isotropic host material is analyzed. Numerical examples are obtained for a square lattice of quartz cylinders embedded in an epoxy matrix. It is found that several complete band gaps with a variable bandwidth exist for elastic waves of any polarization and incidence. In addition to the filling fraction, it is found that a key parameter for the existence and the width of these complete band gaps is the ratio of the slab thickness, $d$, to the lattice period, $a$. Especially, we have explored how these absolute band gaps close up as the parameter $d∕a$ increases. Significantly, it is observed that the band gaps of a phononic crystal slab are distinct from those of bulk acoustic waves propagating in the plane of an infinite two-dimensional phononic crystal with the same composition. The band gaps of the slab are strongly affected by the presence of cutoff frequency modes that cannot be excited in infinite media.

Sonic crystals consisting of three-dimensional arrays of units which exhibit localized resonances have been discovered recently. Here, it is shown that their two-dimensional counterparts behave in a similar manner. Particularly, it is observed that the transmittance spectra show very asymmetric peaks which are explained as a Fano-like interference phenomenon. A finite difference time domain method is employed to perform a comprehensive study of the resonance line shape as a function of the mass density of the structural units. Also, a simple analytical model is introduced to give an intuitive account of the origin of the interference phenomenon.

Acoustic band gap (ABG) materials constituted of steel hollow cylinders immersed in water can exhibit a tunable narrow pass band (NPB) located inside their gap. We theoretically investigate, using the finite difference time domain (FDTD) method, the properties of waveguides composed of a row of hollow cylinders in a two-dimensional (2D) phononic crystal made of filled steel cylinders. These waveguides exhibit NPB’s at frequencies slightly higher than their infinite periodic ABG counterpart. The frequency of the waveguide’s NPB can be selected by adjusting the inner radius of the hollow cylinders or by changing the nature of the fluid that fills them. We show that a waveguide constituted of a row of hollow cylinders with different inner radii can transport waves at two different frequencies. By selectively filling the cylinders with water or mercury we have created an active device that permits the transmission of waves at one, both, or neither of these frequencies. Finally, we examine the multiplexing and demultiplexing capabilities of Y shaped waveguides constituted of hollow cylinders.

We report on the experimental observation of the existence and the interaction of localized defect modes in a full acoustic band gap in a two-dimensional lattice of steel cylinders immersed in water. The confinement of defect modes and the splitting of their resonance frequencies are observed and are explained by their evanescent coupling. A different type of waveguiding in a phononic crystal based on the evanescent coupling of defect modes is proposed and demonstrated experimentally. The finite-difference time-domain method is used to interpret the experimental data and it is found that theoretical predictions properly account for the observed spectra.

A complete surface acoustic wave band gap is found experimentally in a two-dimensional square-lattice piezoelectric phononic crystal etched in lithium niobate. Propagation in the phononic crystal is studied by direct generation and detection of surface waves using interdigital transducers. The complete band gap extends from $203\text{to}226\mathrm{MHz}$, in good agreement with theoretical predictions. Near the upper edge of the complete band gap, it is observed that radiation to the bulk of the substrate dominates. This observation is explained by introducing the concept of the sound line.