Locally resonant sonic materials

Tailoring of phononic band structures in colloidal crystals

We report an experimental study of the elastic properties of a two-dimensional (2D) colloidal crystal subjected to light-induced substrate potentials. In agreement with recent theoretical predictions [H. H. von Grünberg and J. Baumgartl, Phys. Rev. E 75, 051406 (2007).10.1103/PhysRevE.75.051406] the phonon band structure of such systems can be tuned depending on the symmetry and depth of the substrate potential. Calculations with binary crystals suggest that phononic band engineering can be also performed by variations of the pair potential and thus opens novel perspectives for the fabrication of phononic crystals with band gaps tunable by external fields.

Negative birefraction of acoustic waves in a sonic crystal

Optical birefringence and dichroism are classical and important effects originating from two independent polarizations of optical waves in anisotropic crystals. Furthermore, the distinct dispersion relations of transverse electric and transverse magnetic polarized electromagnetic waves in photonic crystals can lead to birefringence more easily. However, it is impossible for acoustic waves in the fluid to show such a birefringence because only the longitudinal mode exists. The emergence of an artificial sonic crystal (SC) has significantly broadened the range of acoustic materials in nature that can give rise to acoustic bandgaps and be used to control the propagation of acoustic waves. Recently, negative refraction has attracted a lot of attention and has been demonstrated in both left-handed materials and photonic crystals. Similar to left-handed materials and photonic crystals, negative refractions have also been found in SCs. Here we report, for the first time, the acoustic negative-birefraction phenomenon in a two-dimensional SC, even with the same frequency and the same 'polarization' state. By means of this feature, double focusing images of a point source have been realized. This birefraction concept may be extended to other periodic systems corresponding to other forms of waves, showing great impacts on both fundamental physics and device applications.

Metamaterial with simultaneously negative bulk modulus and mass density

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.

Multicoaxial cylindrical inclusions in locally resonant phononic crystals

It is known that the transmission spectrum of the so-called locally resonant phononic crystal can exhibit absolute sharp dips in the sonic frequency range due to the resonance scattering of elastic waves. In this paper, we study theoretically, using a finite difference time domain method, the propagation of acoustic waves through a two-dimensional locally resonant crystal in which the matrix is a fluid (such as water) instead of being a solid as in most of the previous papers. The transmission is shown to be dependent upon the fluid or solid nature of the matrix as well as upon the nature of the coating material in contact with the matrix. The other main purpose of this paper is to consider inclusions constituted by coaxial cylindrical multilayers consisting of several alternate shells of a soft material (such as a soft rubber) and a hard material (such as steel). With respect to the usual case of a hard core coated with a soft rubber, the transmission spectrum can exhibit in the same frequency range several peaks instead of one. If two or more phononic crystals are associated together, we find that the structure displays all the zeros of transmission resulting from each individual crystal. Moreover, we show that it is possible to overlap the dips by an appropriate combination of phononic crystals and create a larger acoustic stop band.

Complete transmission through a periodically perforated rigid slab

The propagation of a normally incident plane acoustic wave through a three-dimensional rigid slab with periodically placed holes is modeled and analyzed. The spacing of the holes A and B, the wavelength lambda, and the thickness of the slab L are order one parameters compared to the characteristic size D of the holes, which is a small quantity. Scattering matrix techniques are used to derive expressions for the transmission and reflection coefficients of the lowest mode. These expressions depend only on the transmission coefficient, tau(0), of an infinitely long slab with the same configuration. The determination of tau(0) requires the solution of an infinite set of algebraic equations. These equations are approximately solved by exploiting the small parameter D/square root(AB). Remarkably, this structure is transparent at certain frequencies and opaque for all others. Such a structure may be useful in constructing narrow-band filters and resonators.

Hypersonic acoustic excitations in binary colloidal crystals: big versus small hard sphere control

The phononic band structure of two binary colloidal crystals, at hypersonic frequencies, is studied by means of Brillouin light scattering and analyzed in conjunction with corresponding dispersion diagrams of the single colloidal crystals of the constituent particles. Besides the acoustic band of the average medium, the authors' results show the existence of narrow bands originating from resonant multipole modes of the individual particles as well as Bragg-type modes due to the (short-range) periodicity. Strong interaction, leading to the occurrence of hybridization gaps, is observed between the acoustic band and the band of quadrupole modes of the particles that occupy the largest fractional volume of the mixed crystal; the effective radius is either that of the large (in the symmetric NaCl-type crystalline phase) or the small (in the asymmetric NaZn(13)-type crystalline phase) particles. The possibility to reveal a universal behavior of the phononic band structure for different single and binary colloidal crystalline suspensions, by representing in the dispersion diagrams reduced quantities using an appropriate length scale, is discussed.

Observation and tuning of hypersonic bandgaps in colloidal crystals

Composite materials with periodic variations of density and/or sound velocities, so-called phononic crystals, can exhibit bandgaps where propagation of acoustic waves is forbidden. Phononic crystals are the elastic analogue of the well-established photonic crystals and show potential for manipulating the flow of elastic energy. So far, the experimental realization of phononic crystals has been restricted to macroscopic systems with sonic or ultrasonic bandgaps in the sub-MHz frequency range. In this work, using high-resolution Brillouin spectroscopy we report the first observation of a hypersonic bandgap in face-centred-cubic colloidal crystals formed by self-assembly of polystyrene nanoparticles with subsequent fluid infiltration. Depending on the particle size and the sound velocity in the infiltrated fluid, the frequency and the width of the gap can be tuned. Promising technological applications of hypersonic crystals, ranging from tunable filters and heat management to acousto-optical devices, are anticipated.

Reduction of guided acoustic wave Brillouin scattering in photonic crystal fibers

Guided acoustic wave Brillouin scattering (GAWBS) generates phase and polarization noise of light propagating in glass fibers. This excess noise affects the performance of various experiments operating at the quantum noise limit. We experimentally demonstrate the reduction of GAWBS noise in a photonic crystal fiber in a broad frequency range by tailoring the acoustic modes using the photonic also as a phononic crystal. We compare the noise spectrum to the one of a standard fiber and observe a tenfold noise reduction in the frequency range up to 200 MHz. Based on our measurement results as well as on numerical simulations, we establish a model for the reduction of GAWBS noise in photonic crystal fibers.

Ultrasonic metamaterials with negative modulus

The emergence of artificially designed subwavelength electromagnetic materials, denoted metamaterials, has significantly broadened the range of material responses found in nature. However, the acoustic analogue to electromagnetic metamaterials has, so far, not been investigated. We report a new class of ultrasonic metamaterials consisting of an array of subwavelength Helmholtz resonators with designed acoustic inductance and capacitance. These materials have an effective dynamic modulus with negative values near the resonance frequency. As a result, these ultrasonic metamaterials can convey acoustic waves with a group velocity antiparallel to phase velocity, as observed experimentally. On the basis of homogenized-media theory, we calculated the dispersion and transmission, which agrees well with experiments near 30 kHz. As the negative dynamic modulus leads to a richness of surface states with very large wavevectors, this new class of acoustic metamaterials may offer interesting applications, such as acoustic negative refraction and superlensing below the diffraction limit.

Acoustic quasimodes in two-dimensional dispersed random media

Using the generalized coherent-potential-approximation approach, we present the dispersion relation of the two-dimensional dispersed random media. In the intermediate-frequency regime, two acoustic modes are found in colloidal suspensions including cylindrical plastic rod in water background. The scattering cross section offers a good explanation for the two modes and the observed frequency gaps in the excitation spectra.

Time reversal of ultrasound through a phononic crystal

In this Letter, we experimentally investigate time reversal focusing through a phononic crystal consisting of a periodic square arrangement of steel rods in water. An acoustic pulse is transmitted through the medium, received at a transducer array, time reversed and backpropagated. Both spatial focusing and time compression are studied and compared with those obtained through an equivalent disordered medium. With the phononic crystal, we do not observe the "hyperfocusing effect" that is typical of time reversal through disordered samples.

Anomalous Doppler effects in phononic band gaps

Doppler effects in periodic acoustic media were studied theoretically and experimentally. Analytical formulas are derived using the Green's function formalism. We found that a far field observer cannot hear the sound inside a band gap from a stationary source, but a moving source can be heard even if the frequency is inside the gap, and the Doppler shifts can be inverted or anomalously large.

The spectrum of vibration modes in soft opals

Numerous vibrational modes of spherical submicrometer particles in fabricated soft opals are experimentally detected by Brillouin light scattering and theoretically identified by their spherical harmonics by means of single-phonon scattering-cross-section calculations. The particle size polydispersity is reflected in the line shape of the low-frequency modes, whereas lattice vibrations are probably responsible for the observed overdamped transverse mode.

Two-dimensional sonic crystals with Helmholtz resonators

We present a type of sonic crystal composed with an array of two-dimensional Helmholtz resonators, which in the long-wave regime have both a high relative acoustic refractive index n and at the same time, a small acoustic impedance Z mismatch with air for airborne sound. We analyze the n and Z of such sonic crystals by finite-difference time-domain simulations, and by mapping our results to a corresponding electromagnetic (EM) model, and we find that our Helmholtz resonant sonic crystal has a bigger effective magnetic permeability mu than the conventional rigid-cylinder sonic crystal in its EM counterpart. As a result, a thin convergent lens with very good focusing effect is demonstrated based on our crystal.

Hypersonic phononic crystals

In this Letter we propose the use of hypersonic phononic crystals to control the emission and propagation of high frequency phonons. We report the fabrication of high quality, single crystalline hypersonic crystals using interference lithography and show that direct measurement of their phononic band structure is possible with Brillouin light scattering. Numerical calculations are employed to explain the nature of the observed propagation modes. This work lays the foundation for experimental studies of hypersonic crystals and, more generally, phonon-dependent processes in nanostructures.

Piezoelectric-induced polariton coupling in a superlattice

Propagation of electromagnetic waves in a piezoelectric superlattice is studied. Because of the piezoelectric effect, a coupling between two orthogonally polarized electromagnetic waves is induced by the superlattice vibration. As a consequence of the strong coupling, two types of polariton modes are found: one is supported in the band gap while the other prohibited. This unusual coupling effect is not present in classical lattices.

Double-negative acoustic metamaterial

We show here the existence of acoustic metamaterial, in which both the effective density and bulk modulus are simultaneously negative, in the true and strict sense of an effective medium. Our double-negative acoustic system is an acoustic analogue of Veselago's medium in electromagnetism, and shares many unique consequences, such as negative refractive index. The double negativity in acoustics is derived from low-frequency resonances, as in the case of electromagnetism, but the negative density and modulus are derived from a single resonance structure as distinct from electromagnetism in which the negative permeability and negative permittivity originates from different resonance mechanisms.

Two-dimensional locally resonant phononic crystals with binary structures

The lumped-mass method is applied to study the propagation of elastic waves in two-dimensional binary periodic systems, i.e., periodic soft rubber/epoxy and vacuum/epoxy composites, for which the conventional methods fail or converge very slowly. A comprehensive study is performed for the two-dimensional binary locally resonant phononic crystals, which are composed of periodic soft rubber cylinders immersed in epoxy host. Numerical simulations predict that subfrequency gaps also appear because of the high contrast of mass density and elastic constant of the soft rubber. The locally resonant mechanism in forming the subfrequency gaps is thoroughly analyzed by studying the two-dimensional model and its quasi-one-dimensional mechanical analog. The rule used to judge whether a resonant mode in the phononic crystals can result in a corresponding subfrequency gap or not is found.

Focusing of sound in a 3D phononic crystal

We present a combined experimental and theoretical study of phonon focusing phenomena in a pass band above the complete band gap in a 3D phononic crystal. Wave propagation was found to depend dramatically on both frequency and incident direction. This propagation anisotropy leads to very large negative refraction, which can be used to focus a diverging ultrasonic beam into a narrow focal spot with a large focal depth. The experimental field patterns are well explained using a Fourier imaging technique, based on the 3D equifrequency surfaces calculated from multiple scattering theory.

Splitting and tuning characteristics of the point defect modes in two-dimensional phononic crystals

Point defect modes of acoustic wave in two-dimensional square arrays of square water rods in a mercury host were studied. The defects are created by three kinds of geometry, namely, square defect, circular defect, and rectangular defect, respectively. The results show that for both square defect and circular defect, the defect modes are only related to the defect filling fraction F(d), but not with the geometry of defects (square or circular), as well as the orientations of the square defect. For the rectangular defect, the defect modes could be tuned by changing the ratio of edge width of the defect, moreover, the double degenerate one will split into two nondegenerate modes when the ratio of edge widths Lx / L(y) >9.0. Meanwhile the corresponding pressure distributions also will be changed.

Modelling and simulation of acoustic wave propagation in locally resonant sonic materials

Sonic crystals are artificial structures consisting of a periodic array of acoustic scatterers embedded in a homogeneous matrix material, with a usually large impedance mismatch between the two materials. They exhibit strong sound attenuation at selective frequency bands due to the interference of multiply reflected waves. However, sound attenuation bands in the audible range are only achieved by unfunctionally large sonic crystals. If local resonators are used instead of simple scatterers, the frequencies of the attenuation bands can be reduced by about two orders of magnitude. In the present paper we perform numerical simulations of acoustic wave propagation through sonic crystals consisting of local resonators using the local interaction simulation approach (LISA). Three strong attenuation bands are found at frequencies between 0.3 and 6.0 kHz, which do not depend on the periodicity of the crystal. The results are in good qualitative agreement with experimental data. We analyze the dependence of the resonance frequencies on the structural parameters of the local resonators in order to create a tool for design and optimization of any kind of sonic crystal.

Scattering of antiplane shear waves by layered circular elastic cylinder

An exact analytical solution for the scattering of antiplane elastic waves by a layered elastic circular cylinder is obtained. The solution and its degenerate cases are compared with other simpler models of circular cylindrical scatterers. The effects of the geometrical and physical properties of the interphase are studied. Numerical results confirm the existence of a resonance mode in which the scatterer's core undergoes a rigid-body motion when the outer layer of the scatterer is very compliant. This resonance mode has been attributed [Liu et al., Science 289, 1734 (2000)] to a new mechanism for the band gap formed in the extremely low frequency range for phononic crystals made of layered spherical scatterers. Numerical results also show the existence of a similar resonance mode when the outer layer of the scatterer has very high mass density.

Phonons in suspensions of hard sphere colloids: Volume fraction dependence

The propagation of sound waves in suspensions of hard sphere colloids is studied as a function of their volume fraction up to random close packing using Brillouin light scattering. The rich experimental phonon spectra of up to five phonon modes are successfully described by theoretical calculations based on the multiple scattering method. Two main types of phonon modes are revealed: Type A modes are acoustic excitations which set up deformations in both the solid (particles) and the liquid (solvent) phases; for type B modes the stress and strain are predominantly localized near the interface between the solid particles and the surrounding liquid (interface waves). While the former become harder (increase their effective sound velocity) as the particle volume fraction increases the latter become softer (the corresponding sound velocity decreases).

Systematic design of phononic band-gap materials and structures by topology optimization

Phononic band-gap materials prevent elastic waves in certain frequency ranges from propagating, and they may therefore be used to generate frequency filters, as beam splitters, as sound or vibration protection devices, or as waveguides. In this work we show how topology optimization can be used to design and optimize periodic materials and structures exhibiting phononic band gaps. Firstly, we optimize infinitely periodic band-gap materials by maximizing the relative size of the band gaps. Then, finite structures subjected to periodic loading are optimized in order to either minimize the structural response along boundaries (wave damping) or maximize the response at certain boundary locations (waveguiding).

Acoustic excitations in a self-assembled block copolymer photonic crystal

High resolution Brillouin light scattering can sensitively detect acoustic phonons in concentrated solutions of a high molecular weight poly(styrene-b-isoprene) symmetric copolymer in toluene. This block copolymer lamellar forming system also possesses a photonic stop band in the visible spectrum. Based on the low but finite contrast in mechanical properties between the styrene and isoprene components and taking into account the geometrical characteristics of the layered microstructure, we calculate the acoustic band structure and represent the observed acousticlike and opticlike phonons.

Epitaxial growth of granular single crystals

Compaction from a random-loose-packed to a random-close-packed phase is observed when monodisperse granular beds are shaken, but beyond this packing, the system freezes up in a jammed structure. Here we report a technique to grow large hard-sphere granular crystals, with perfect stacking and no defects by means of a "gas phase" epitaxial procedure. We study the growth mechanism and provide evidence that the observed granular crystallization is driven by gravity and energy dissipation.

Acoustic band gaps created by rotating square rods in a two-dimensional lattice

Acoustic band gaps can be opened and tuned by rotating square rods in two-dimensional liquid sonic crystals. For the systems of mercury rods with square cross section in a water host, the width of lowest gaps increases as the rotation angle of the square rods increases. But opposite results are found for the inverse systems of water rods in mercury, where the lowest gaps narrow with an increase in the rotation angle. This gap-tuning effect becomes more evident with the filling fraction increase. Such an effect should open up a new way for designing acoustic band gaps in two-dimensional phononic crystals.

Evidence of fano-like interference phenomena in locally resonant materials

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.

Ultrasound tunneling through 3D phononic crystals

We report the study of ultrasound tunneling in 3D phononic crystals, consisting of fcc arrays of close-packed tungsten carbide beads in water. The transmission coefficient, phase velocity, and group velocity were measured along the [111] direction, allowing us to systematically investigate the tunneling of ultrasound at frequencies in the lowest band gap. Our experimental data are interpreted using multiple scattering theory, which provides a good explanation of our results. The effect of absorption and the difference between the tunneling of classical waves and quantum waves are discussed.

Stopping of acoustic waves by sonic polymer-fluid composites

A two-dimensional periodic array of air cylinders in water is known to have giant acoustic stop bands [M.S. Kushwaha and B. Djafari-Rouhani, J. Appl. Phys. 84 (1998) 4677]. It is shown in the present paper that hollow cylinders made of an elastically-soft polymer containing air inside and arranged on a square lattice in water can still give rise to large acoustic band gaps. Similar properties can also be obtained with a close-packed array of tubes containing water when arranged on a honeycomb lattice in air. The transmission coefficient of films made of such polymer-fluid composites has been calculated by finite difference time domain method. With film thickness not exceeding 75 mm, a deep sonic attenuation band was found with, in the best cases, a lower limit below 1 kHz and an upper limit above 10 kHz.