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Experimental measurements of acoustic transmission through a solid-solid two-dimensional binary-composite medium constituted of a triangular array of parallel circular steel cylinders in an epoxy matrix are reported. Attention is restricted to propagation of elastic waves perpendicular to the cylinders. Measured transmitted spectra demonstrate the existence of absolute stop bands, i.e., band gaps independent of the direction of propagation in the plane perpendicular to the cylinders. Theoretical calculations of the band structure and transmission spectra using the plane wave expansion and the finite difference time domain methods support unambiguously the absolute nature of the observed band gaps.

We show experimentally and theoretically that super resolution can be achieved while imaging with a flat lens consisting of a phononic crystal exhibiting negative refraction. This phenomenon is related to the coupling between the incident evanescent waves and a bound slab mode of the phononic crystal lens, leading to amplification of evanescent waves by the slab mode. Super resolution is only observed when the source is located very near to the lens, and is very sensitive to the location of the source parallel to the lens surface as well as to site disorder in the phononic crystal lattice.

We introduce a supercell plane wave expansion ͑SC-PWE͒ method for the calculation of elastic band structures of two-dimensional phononic crystal plates. We compute the band structure of solid-solid and air-solid two-dimensional phononic crystal plates. The air is modeled as a low impedance medium ͑LIM͒ with very low density and very high velocities of sound. We investigate the influence of the constituent materials, of the plate thickness, and of the geometry of the array on the band structure. We establish the range of validity of the SC-PWE method in terms of the rate of convergence with respect to the number of plane waves and contrast in physical properties of the matrix and inclusion materials. We show that for high contrast solid-solid phononic crystal plates, our SC-PWE method, as other PWE-based methods introduced to date, suffers from convergence difficulties. In the case of air ͑modeled as the LIM͒ holes-solid plates, we demonstrate that the SC-PWE method leads to fast convergence for a wide range of values of solid physical properties. With these constituent materials, we find that the largest absolute forbidden bands occur in the band structure of the phononic crystal plate provided the thickness of the plate is of the order of magnitude of the periodicity of the array of inclusions. We demonstrate the existence of guided modes in an air-silicon phononic crystal plate containing a linear defect.

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.

The objective of this chapter is to introduce the broad subject of phononic crystals and acoustic metamaterials. From a historical point of view, we have tried to refer to some of the seminal contributions that have made the field. This introduction is not an exhaustive review of the literature. However, we are painting in broad strokes a picture that reflects the biased perception of this field by the authors and coauthors of the various chapters of this book. Properties of Phononic Crystals and Acoustic MetamaterialsThe field of phononic crystals (PCs) and acoustic metamaterials emerged over the past two decades. These materials are composite structures designed to tailor elastic wave dispersion (i.e., band structure) through Bragg's scattering or local resonances to achieve a range of spectral (o-space), wave vector (k-space), and phase (f-space) properties.

By using a combination of finite difference time domain ͑FDTD͒ and plane wave expansion ͑PWE͒ methods, we study the propagation of acoustic waves through waveguide structures in phononic band gap crystals composed of solid constituents. We investigate transmission through perfect linear waveguides, waveguides containing a resonant cavity, or waveguides coupled with a side branch resonator such as a cavity or a stub. A linear guide can support one or several modes falling in the absolute band gap of the phononic crystal. It can be made monomode over a large frequency range of the band gap by varying the width of the guide. The transmission through a guide containing a cavity can be made very selective and reduced to narrow peaks associated with some of the eigenmodes of the cavity. The effect of a side branch resonator is to induce zeros of transmission in the spectrum of the perfect guide that appear as narrow dips with frequencies depending upon the shape of the resonator and its coupling with the guide. We find perfect correspondences between the peaks in the transmission spectrum of a waveguide containing a cavity and the dips in the transmission of a cavity side coupled waveguide. Finally, when a gap exists in the spectrum of the perfect guide, a stub can also permit selective transmission of frequency in this gap. The results are discussed in relation with the symmetry of the modes associated with a linear guide or with a cavity.

Transmission of acoustic waves in two-dimensional binary solid/solid composite media composed of arrays of Duralumin cylindrical inclusions embedded in an epoxy resin matrix is studied. The experimental transmission spectrum and theoretical band structure of two periodic arrays of cylinders organized on a square lattice and on a centred rectangular network are reported. Absolute gaps extending throughout the first two-dimensional Brillouin zone are predicted. The measured transmission is observed to drop to noise level throughout frequency intervals in reasonable agreement with the calculated forbidden frequency bands.