Bulk acoustic wave delay line in acoustic superlattice Appl. Phys. Lett. 97, 092905 (2010); 10.1063/1.3476350 Robustness of computational time reversal imaging in media with elastic constant uncertaintiesRecent progress in electronic and electromagnetic topological insulators has led to the demonstration of one way propagation of electron and photon edge states and the possibility of immunity to backscattering by edge defects. Unfortunately, such topologically protected propagation of waves in the bulk of a material has not been observed. We show, in the case of sound/elastic waves, that bulk waves with unidirectional backscattering-immune topological states can be observed in a time-dependent elastic superlattice. The superlattice is realized via spatial and temporal modulation of the stiffness of an elastic material. Bulk elastic waves in this superlattice are supported by a manifold in momentum space with the topology of a single twist M€ obius strip. Our results demonstrate the possibility of attaining one way transport and immunity to scattering of bulk elastic waves. V C 2015 AIP Publishing LLC. [http://dx.

A one-dimensional block-spring model that supports rotational waves is analyzed within Dirac formalism. We show that the wave functions possess a spinor and a spatio-temporal part. The spinor part leads to a non-conventional torsional topology of the wave function. In the long-wavelength limit, field theoretical methods are used to demonstrate that rotational phonons can exhibit fermion-like behavior. Subsequently, we illustrate how information can be encoded in the spinor-part of the wave function by controlling the phonon wave phase.

The calculated band structure of a two-dimensional phononic crystal composed of stiff polymer inclusions in a soft elastomer matrix is shown to support rotational modes. Numerical calculations of the displacement vector field demonstrate the existence of modes whereby the inclusions and the matrix regions between inclusions exhibit out of phase rotations but also in phase rotations. The observation of the in-phase rotational mode at low frequency is made possible by the very low transverse speed of sound of the elastomer matrix. A one-dimensional block-spring model is used to provide a physical interpretation of the rotational modes and of the origin of the rotational modes in the band structure. This model is analyzed within Dirac formalism. Solutions of the Dirac-like wave equation possess a spinor part and a spatio-temporal part. The spinor part of the wave function results from a coupling between the senses (positive or negative) of propagation of the wave. The wave-number dependent spinor-part of the wave function for two superposed waves can impose constraints on the integral of the spatio-temporal part that are reflected in a fermion-like lifting of degeneracy in the phonon band structure associated with in-phase rotations.

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...

A phononic crystal (PC) consisting of a square array of cylindrical polyvinylchloride inclusions in air is used to construct a variety of acoustic logic gates. In a certain range of operating frequencies, the PC band structure shows square-like equi-frequency contours centered off the gamma point. This attribute allows for the realization of non-collinear wave and group velocity vectors in the PC wave vector space. This feature can be utilized to control with great precision, the relative phase between propagating acoustic waves in the PC. By altering the incidence angle of the impinging acoustic beams or varying the PC thickness, interferences occur between acoustic wave pairs. It is recognized that information can be encoded with this mechanism (e.g., wave amplitudes/interference patterns) and accordingly to construct a series of logic gates emulating Boolean functions. The NAND, XOR, and NOT gates are demonstrated with finite-difference time-domain simulations of acoustic waves impinging upon the PC.