We report on a phononic crystal ͑PC͒ consisting of a square array of cylindrical polyvinylchloride inclusions in air that exhibits positive, negative, or zero refraction depending on the angle of the incident sound beam. For all three cases of refraction, the transmitted beam undergoes splitting upon exiting the crystal. These properties are analyzed theoretically using finite difference time domain method and are demonstrated experimentally. Band structures and equifrequency surfaces ͑EFSs͒ calculated with the plane-wave expansion method show that the observed properties result from the unique geometry of the PC's EFS as compared to that of the incident media.

We report on the subwavelength imaging capabilities of a Phononic Crystal (PC) flat lens consisting of a triangular array of steel cylinders in methanol, all surrounded by water. The image resolution of the PC flat lens beats the Rayleigh diffraction limit because bound modes in the lens can be excited by evanescent waves emitted by the source. These are modes that only propagate in the direction parallel to the water/lens interface. These modes resonantly amplify evanescent waves that contribute to the reconstruction of an image. By employing the Finite Difference Time Domain (FDTD) method and ultrasonic experiments, we also explore the effect on the image resolution and focal point on various structural and operational parameters such as source frequency, geometry of the lens, source position and time. The mechanisms by which these factors affect resolution are discussed in terms of the competition between the contribution of propagative modes to focusing and the ability of the source to excite bound modes of the PC lens.

We report on a phononic crystal ͑PC͒ consisting of a square array of cylindrical polyvinylchloride inclusions in air that can be used to control the relative phase of two incident acoustic waves with different incident angles. The phase shift between waves propagating through the crystal depends on the angle of incidence of the incoming waves and the PC length. The behavior of the PC is analyzed using the finite-difference-time-domain method. The band structure and equifrequency contours calculated via the plane wave expansion method show that the distinctive phase controlling properties are attributed to noncollinear wave and group velocity vectors in the PC as well as the degree of refraction.Phononic crystals ͑PCs͒ are composite materials which derive their spectral ͑-space͒ and wave vector ͑k-space͒ properties from the scattering of elastic waves by periodic arrays of elastic inclusions embedded in an elastic matrix. Bulk or defected PCs have been shown to exhibit numerous useful spectral capabilities including transmission band gaps, local modes for guiding, filtering, and multiplexing. 1-15 k-space properties result from features in the band structure that impact refraction. 16-28 These properties parallel many of those found in photonic crystals. 29,30 The -space and k-space properties are directly related to the size, geometry, scale, and composition of the constitutive materials of the PC.In the present letter, we demonstrate that the band structure of a two-dimensional PC constituted of a square array of cylindrical polyvinylchloride ͑PVC͒ inclusions in an air matrix can be used to control the relative phase of elastic waves. Phase control is due to the propagation of elastic waves in the PC with wave vectors that are not collinear with their group velocity vectors. This condition implies that excited Bloch waves travel at different phase velocities in the direction of their group velocity. Additionally, this crystal shows near zero-angle refraction permitting wave collimation as well as enabling the superposition of beams with different wave vectors in the same volume of crystal. Phase manipulation of these superposed waves can result in constructive or destructive interferences between noncollinear incident beams. Finally, there are operating frequencies for which the circular equifrequency contour ͑EFC͒ in air is larger than the first Brillouin zone of the PC, allowing several Bloch modes to exit the crystal, leading to the phenomenon of beam splitting. The work presented in this letter constitutes a significant move toward broadening the range of properties and applications of PCs beyond their more common spectral and wave number properties.The PVC-air system parameters are: PVC = 1364 kg/ m 3 , c t,PVC = 1000 m / s, c l,PVC = 2230 m / s, AIR = 1.3 kg/ m 3 , c t,AIR =0 m/ s, and c l,AIR = 340 m / s, where is density, c t is transverse speed of sound, and c l is longitudinal speed of sound. The inclusion radius is 12.9 mm and the lattice parameter is 27 mm. The plane wave expansion ͑PWE͒ method was e...

In this paper, we present a theoretical analysis of the propagation of acoustic waves through elastic and viscoelastic two-dimensional phononic crystal structures. Numerical calculations of transmission spectra are conducted by extending the finite-difference-time-domain method to account for linear viscoelastic materials with time-dependent moduli. We study a phononic crystal constituted of a square array of cylindrical air inclusions in a solid viscoelastic matrix. The elastic properties of the solid are those of a silicone rubber. This system exhibits very wide band gaps in its transmission spectrum that extend to frequencies in the audible range of the spectrum. These gaps are characteristic of fluid matrix/air inclusion systems and result from the very large contrast between the longitudinal and transverse speeds of sound in rubber. By treating the matrix as a viscoelastic medium within the standard linear solid (SLS) model, we demonstrate that viscoelasticity impacts the transmission properties of the rubber/air phononic crystal not only by attenuating the transmitted acoustic waves but also by shifting the passing bands frequencies toward lower values. The ranges of frequencies exhibiting attenuation or frequency shift are determined by the value of the relaxation time in the SLS model. We show that viscoelasticity can be used to decrease the frequency of pass bands (and consequently stop bands) in viscoelastic/air phononic crystals.