Showing papers by "Zhengyou Liu published in 2007"

Metamaterial with simultaneously negative bulk modulus and mass density.

Abstract: We report a metamaterial which simultaneously possesses a negative bulk modulus and mass density. This metamaterial is a zinc blende structure consisting of one fcc array of bubble-contained-water spheres (BWSs) and another relatively shifted fcc array of rubber-coated-gold spheres (RGSs) in epoxy matrix. The negative bulk modulus and mass density are simultaneously derived from the coexistent monopolar resonances from the embedded BWSs and dipolar resonances from the embedded RGSs. The Poisson ratio of the metamaterial also turns negative near the resonance frequency.

Tuning Fabry-Perot resonances via diffraction evanescent waves

Abstract: By studying acoustic and electromagnetic wave transmission through a periodic array of subwavelength holes or slits with various channel lengths, we demonstrate both experimentally and theoretically that diffraction evanescent waves can play an important role in tuning the Fabry-Perot (FP) resonances. In particular, there can be total transmission peaks at wavelengths much below that of the Rayleigh-Wood limit, and FP resonances can occur for channel length $\ensuremath{\sim}16%$ thinner than the half wavelength. In addition, the FP resonance condition can be tuned via both the periodicity and area fraction of holes. As a function of the ratio between the periodicity and plate thickness, the FP resonance is smoothly linked to the surface-wave-like mode induced by the periodic structure factor.

Effective Mass Density of Fluid-Solid Composites

Abstract: We show through rigorous derivation and experimental support that the dynamic effective mass density of an inhomogeneous mixture, used in the prediction of wave velocities in the long wavelength limit, can differ from the static version—the volume average of the component mass densities. The physical reason for this difference is explained. The dynamic mass density expression, first derived by Berryman more than two decades ago, is shown to give a closer correspondence between the acoustic and electromagnetic metamaterials by allowing for negative mass densities at frequencies around resonances. The effective mass density of a composite is one of the most basic quantities in the study of materials. It is common sense that the effective mass density of a mixture of

Dynamic Mass Density and Acoustic Metamaterials

Abstract: Elastic and electromagnetic waves are two types of classical waves that, though very different, nevertheless display many analogous features. In particular, for the acoustic waves, there can be a correspondence between the two material parameters of the acoustic wave equation, the mass density and bulk modulus, with the dielectric constant and magnetic permeability of the Maxwell equations. We show that the classical mass density, a quantity that is often regarded as positive definite in value, can display complex finite-frequency characteristics for a composite that comprises local resonators, thereby leading to acoustic metamaterials in exact analogy with the electromagnetic metamaterials. In particular, we demonstrate that through the anti-resonance mechanism, a locally resonant sonic material is capable of totally reflecting low-frequency sound at a frequency where the effective dynamic mass density can approach positive and negative infinities. The condition that leads to the anti-resonance thereby offers a physical explanation of the metamaterial characteristics for both the membrane resonator and the 3D locally resonant sonic materials. Besides the metamaterials arising from the dynamic mass density behavior at finite frequencies, we also present a review of other relevant types of acoustic metamaterials. At the zero-frequency limit, i.e., in the absence of resonances, the dynamic mass density for the fluid–solid composites is shown to still differ significantly from the usual volume-averaged expression. We offer both a physical explanation and a rigorous mathematical derivation of the dynamic mass density in this case.

Effective Dynamic Mass Density of Composites

Abstract: The static mass density of a composite is simply the volume average of its constituents' densities. The dynamic density of a composite is defined to be the quantity that enters in evaluating the elastic wave velocity at the low-frequency limit. We show through a rigorous derivation that the effective dynamic mass density of an inhomogeneous mixture can differ from its static counterpart when the composite matrix is a fluid or, more generally, when there are relative motions between the matrix and inclusions. Derivation of the dynamic mass density expressions, involving taking the long wavelength limit of the rigorous multiple scattering theory, is detailed for the two-dimensional case. We also extend the effective dynamic mass density expression to finite frequencies where there can be low-frequency resonances. By combining both analytical and numerical approaches, negative or complex dynamic mass density is obtained for composites that contain a sufficient fraction of locally resonant inclusions. Thus, the dynamic mass density of a composite can differ from the static (volume-averaged) value even in the zero frequency limit, although both must be positive in that limit. Negative or complex dynamic mass density can occur at finite frequencies. These two results are shown to be consistent with each other, as well as related by the same underlying physics. As by-products of our rigorous derivation, we also verify some prior known results on the effective elastic moduli of composites.

High refractive-index sonic material based on periodic subwavelength structure

Abstract: We show that a steel plate with periodic array of subwavelength slits or holes can serve as a material of tunable refractive index for acoustic waves. The effective refractive index is inversely proportional to the filling factor of the slits or holes, which enables the realization of high refractive-index material for acoustic waves. An acoustic wave focusing lens based on this material is exemplified.

Experimental demonstration of directional acoustic radiation based on two-dimensional phononic crystal band edge states

Abstract: The authors have experimentally studied the radiation of a point acoustic source placed inside a two-dimensional phononic crystal of square lattice. They show that a highly directional radiation with a half-power angular width of 6° can be achieved when operating at the band edge frequency for the phononic crystal. Such combination of a point source and a phononic crystal may serve as highly directional acoustic source in applications.

Surface acoustic waves in two-dimensional phononic crystals: Dispersion relation and the eigenfield distribution of surface modes

Abstract: In this paper, we have demonstrated the existence of surface acoustic waves in two-dimensional phononic crystals with fluid matrix, which is composed of a square array of steel cylinders put in air background. By using the supercell method, we investigate the dispersion relation and the eigenfield distribution of surface modes. Surface waves can be easily excited at the surface of a finite size phononic crystal by line source or Gaussian beam placed in or launched from the background medium, and they propagate along the surface with the form of 'beat.' Taking advantage of these surface modes, we can obtain a highly directional emission wave beam by introducing an appropriate corrugation layer on the surface of a waveguide exit.

Acoustic Bloch oscillations in a two-dimensional phononic crystal.

Abstract: We report the observation of acoustic Bloch oscillations at megahertz frequency in a two-dimensional phononic crystal. By creating periodically arrayed cavities with a decreasing gradient in width along one direction in the phononic crystal, acoustic Wannier-Stark ladders are created in the frequency domain. The oscillatory motion of an incident Gaussian pulse inside the sample is demonstrated by both simulation and experiment.

Surface resonant-states-enhanced acoustic wave tunneling in two-dimensional phononic crystals.

Abstract: We show that by placing a metal plate next to a two-dimensional phononic crystal, acoustic waves can tunnel through the combined structure at a specific frequency that lies inside the band gap of the phononic crystal. The enhanced transmission is attributed to the coupling of the input waves with the acoustically resonant states created between the metal plate and the phononic crystal. Experiments are in excellent agreement with the theoretical predictions.

Peculiar transmission property of acoustic waves in a one-dimensional layered phononic crystal

Abstract: In this article, we report both theoretical calculation and experimental observation of acoustic waves abnormally through a one-dimensional layered transmitted phononic crystal at frequencies within the band gap into a material of large acoustic impedance mismatch, with an efficiency as high as unity. The transmission peaks can be interpreted as a result of the interference of acoustic waves reflected from all periodically aligned interfaces. The condition for the appearance of peaks is analyzed in detail and the optimized layer number is given for different configurations.

Generalizing the Concept of Negative Medium to Acoustic Waves

Abstract: Electromagnetic metamaterials are artificial materials exhibiting simultaneously negative permeability and permittivity, and the “double negativity” gives rise to many interesting phenomena such as negative refraction, backward waves and superlensing effects. We will see that the concept can be extended to acoustic waves. We will show the existence of acoustic metamaterial, in which both the effective density and bulk modulus are simultaneously negative at some particular frequency range, in the sense of an effective medium. Such a double negative acoustic system is an acoustic analog of Veselogo’s medium in electromagnetism, and shares many novel consequences such as negative refractive index, flat slab focusing and super-resolution. The double negativity in acoustics is derived from low frequency resonances, as in the case of electromagnetism, but the negative density and modulus can come from a single resonance structure, as distinct from electromagnetism in which the negative permeability and negative permittivity originates from different resonance mechanisms.