Majorana-like Zero Modes in Kekulé Distorted Sonic Lattices.

Topological phases have recently been realized in bosonic systems. The associated boundary modes between regions of distinct topology have been used to demonstrate robust waveguiding, protected from defects by the topology of the surrounding bulk. A related type of topologically protected state that is not propagating but is bound to a defect has not been demonstrated to date in a bosonic setting. Here we demonstrate numerically and experimentally that an acoustic mode can be topologically bound to a vortex fabricated in a two-dimensional, Kekulé-distorted triangular acoustic lattice. Such lattice realizes an acoustic analog of the Jackiw-Rossi mechanism that topologically binds a bound state in a p-wave superconductor vortex. The acoustic bound state is thus a bosonic analog of a Majorana bound state, where the two valleys replace particle and hole components. We numerically show that it is topologically protected against arbitrary symmetry-preserving local perturbations, and remains pinned to the Dirac frequency of the unperturbed lattice regardless of parameter variations. We demonstrate our prediction experimentally by 3D printing the vortex pattern in a plastic matrix and measuring the spectrum of the acoustic response of the device. Despite viscothermal losses, the measured topological resonance remains robust, with its frequency closely matching our simulations.

Poisson-like effect for flexural waves in periodically perforated thin plates.

The Poisson-like effect, describing the redirection of waves by 90°, is shown to be feasible for flexural waves propagating in perforated thin plates. It is demonstrated that the lowest order symmetric leaky guided mode (S0 mode) is responsible for the splitting of wave motion in two orthogonal directions. The S0 mode shows a feature of stationary waves containing standing wave modes in one and two orthogonal directions for smaller and larger holes, respectively. The former case is well understood thanks to the phenomenon of Wood's anomaly, which was first observed in optical gratings supposed to be transparent. On the contrary, the strong scattering caused by the larger holes leads to a mixed mode occurring when the incident wave is totally transmitted. The mixed mode easily couples with the incoming waves and, therefore, the Poisson-like effect activated under this mechanism is much stronger. Using the Poisson-like effect, a device is proposed in which about 82% of the incident mechanical energy is redirected to the perpendicular direction. Results obtained with arrays of free holes also apply to inclusions with parameters properly chosen. The findings may provide applications in beam splitting and waveguiding.

Scattering of flexural waves from an N-beam resonator in a thin plate.

The impedance matrix method is applied to study the scattering of flexural waves propagating in an infinite thin plate containing an N-beam resonator. The resonator consists of a circular hole containing a smaller plate connected to the background plate by a number N of rectangular beams. After representing the boundary conditions in a modal multipole expansion form, a compact expression is obtained for the T-matrix, which relates the incident and the scattered transverse (out-of-plane) waves. The analysis of the scattering cross-section reveals interesting scattering features, like resonances and anisotropy, associated to this type of resonators. Numerical experiments performed within the framework of the finite element method support the accuracy of the model here developed.

Scattering of flexural waves from a hole in a thin plate with an internal beam.

The scattering of flexural waves by a hole in a thin plate traversed by a beam is modeled here by coupling the Kirchhoff-Love and the Euler-Bernoulli theories. A closed form expression is obtained for the transfer matrix (T-matrix) relating the incident wave to the scattered cylindrical waves. For this purpose, a general method has been developed, based on an analogous impedance method for acoustic waves, for calculating the T-matrix for flexural wave scattering problems. The T-matrix for the problem considered displays a simple structure, composed of distinct sub-matrices which decouple the inside and the outside fields. The conservation of energy principle and numerical comparisons with a commercial finite element simulator have been used to prove the theory.

Negative refraction and energy funneling by hyperbolic materials: an experimental demonstration in acoustics.

This Letter reports the design, fabrication, and experimental characterization of hyperbolic materials showing negative refraction and energy funneling of airborne sound. Negative refraction is demonstrated using a stack of five holey Plexiglas plates where their thicknesses, layer separation, hole diameters, and lattice periodicity have been determined to show hyperbolic dispersion around 40 kHz. The resulting hyperbolic material shows a flat band profile in the equifrequency contour allowing the gathering of acoustic energy in a broad range of incident angles and its funneling through the material. Our demonstrations foresee interesting developments based on both phenomena. Acoustic imaging with subwavelength resolution and spot-size converters that harvest and squeeze sound waves irradiating from many directions into a collimated beam are just two possible applications among many.

Acoustic analogue of graphene: observation of Dirac cones in acoustic surface waves.

We demonstrate the presence of Dirac cones in the dispersion relation of acoustic waves propagating on the surface of a plate of methyl methacrylate containing a honeycomb lattice of cylindrical boreholes. This structure represents the acoustic analogue of graphene, the cylindrical cavities playing the role of carbon atoms while acoustic surface waves are the equivalent of electronic waves in graphene. Analytical expressions for the Dirac frequency and Dirac velocity in acoustics are given as a function of the radius and depth of boreholes. These parameters have been experimentally determined for a constructed structure and the data are in fairly good agreement with the predicted values.

Homogenization theory for periodic distributions of elastic cylinders embedded in a viscous fluid.

A multiple-scattering theory is applied to study the homogenization of clusters of elastic cylinders distributed in a isotropic lattice and embedded in a viscous fluid. Asymptotic relations are derived and employed to obtain analytical formulas for the effective parameters of homogenized clusters in which the underlying lattice has a low filling fraction. It is concluded that such clusters behave, in the low frequency limit, as an effective elastic medium. Particularly, it is found that the effective dynamical mass density follows the static estimate; i.e., the homogenization procedure does not recover the non-linear behavior obtained for the inviscid case. Moreover, the longitudinal and transversal sound speeds do not show any dependence on fluid viscosity. Numerical simulations performed for clusters made of brass cylinders embedded in glycerin support the reliability of the effective parameters resulting from the homogenization procedure reported here.

Analysis of equivalent anisotropy arising from dual isotropic layers of acoustic media.

The equivalence between a single mass-anisotropic layer and two isotropic layers is analyzed by studying two systems: one consists of an anisotropic layer sandwiched between two arbitrarily chosen isotropic media; and the other consists of two isotropic layers, of a total thickness equal to that of the anisotropic layer, sandwiched between the same pair of isotropic media. The equivalence is established by matching the transmission and reflection coefficients of the two systems for an arbitrarily chosen incident angle. The first-order equivalence leads to exactly the same set of relations as often quoted in the literature. However, it was concluded that a full second-order equivalence is not possible unless the incident is normal to the surface, or the materials are isotropic. One of the requirements for the second-order equivalence is that the two isotropic layers must have their impedances matched. Together with the first order equivalence requirements, this gives a complete set of conditions for determining all the materials properties of the two isotropic layers. On the other hand, the unattainable full second-order equivalence can be alleviated by a proper placement of layers: by placing the heavier layer adjacent to the medium of greater acoustic impedance. Numerical examples show that this remedy in fact is more important than following the partial requirement for the second order equivalence when the equivalent isotropic layers are used in acoustic cloaking applications.

Resonant coupling of Rayleigh waves through a narrow fluid channel causing extraordinary low acoustic transmission.

Coupling of Rayleigh waves propagating along two metal surfaces separated by a narrow fluid channel is predicted and experimentally observed. Although the coupling through a fluid (water) is weak, a strong synchronization in propagation of Rayleigh waves even for the metals with sufficiently high elastic contrast (brass and aluminum) is observed. Dispersion equation for two polarizations of the coupled Rayleigh waves is derived and experimentally confirmed. Excitation of coupled Rayleigh waves in a channel of finite length leads to anomalously low transmission of acoustic energy at discrete set of resonant frequencies. This effect may find useful applications in the design of acoustic metamaterial screens and reflectors.

Noise control by sonic crystal barriers made of recycled materials.

A systematic study of noise barriers based on sonic crystals made of cylinders that use recycled materials like absorbing component is reported here. The barriers consist of only three rows of perforated metal shells filled with rubber crumb. Measurements of reflectance and transmittance by these barriers are reported. Their attenuation properties result from a combination of sound absorption by the rubber crumb and reflection by the periodic distribution of scatterers. It is concluded that the porous cylinders can be used as building blocks whose physical parameters can be optimized in order to design efficient barriers adapted to different noisy environments.

Anisotropic mass density by radially periodic fluid structures.

This Letter reports physical realization of acoustic metamaterials with anisotropic mass density. These metamaterials consist of a superlattice of two fluidlike components radially periodic. Several structures are spectroscopically characterized at large wavelengths (homogenization limit) by studying the acoustic resonances existing in the circular cavity where they are embedded. This characterization method allows us to extract the diagonal components of the sound speed tensor. Analytical expressions describing the anisotropic behavior as a function of the corrugation parameter are also developed and their predictions are in agreement with measurements.

Sound Insulation and Reflection Properties of Sonic Crystal Barrier Based on Micro-Perforated Cylinders.

A sonic crystal barrier, consisting of empty micro-perforated cylindrical shells, was built on the campus at the Universitat Politècnica de València in 2011 and characterised by using a non-standardised measurement technique. In this paper, the sonic crystal barrier, upgraded with rubber crumb inside the micro-perforated cylindrical shells, was characterised by using standardised measurement techniques according to EN 1793-5 and EN 1793-6. As a result of the characterisation, sound insulation properties of the barrier were shown to be a combination of the absorptive properties of the individual building units and the reflective properties of their periodic distribution. In addition, its performance was compared with a similar barrier consisting of rigid polyvinyl chloride (PVC) cylinders, which was recently characterised using the same standardised techniques. In comparison with the barrier based on PVC cylinders, the barrier investigated here produced a broadband enhancement of the sound insulation and lower reflection indices in the targeted frequency range. It was also shown that the influence of leakage under the barrier and the width of the temporal window on sound insulation was negligible. While EN 1793-5 and 1793-6 allow a direct comparison of the performance of different noise barriers, the applicability to this new type of barriers requires further investigation.

Acoustical scattering by radially stratified scatterers.

A recursive solution procedure is developed to analyze the acoustical scattering by multilayer concentric circular cylindrical scatterers. The procedure is based on multiple scattering in the single-scatterer methodology originally proposed by one of the authors. The solution for a scatterer having an arbitrary number of layers is solved by recursively using the solution for a dual-layer scatterer. The solution procedure and its implementation are extensively validated. Computational characteristics, including potential pitfalls and their avoidance, are explored. The solution procedure can be used to analyze scatterers with continuously varying properties in the radial direction by approximating such a scatterer as a multilayer system. A comprehensive numerical example shows an interesting phenomenon: when a planar wave impinges onto a cooling tube in air, instead of forming a shadow zone, a strongly collimated beam is formed behind the cooling tube. This phenomenon can be explained as due to the gradient-index acoustical lens that is created around the cooling tube, which bends the sound and collimates it in the forward direction.

Acoustic cloak based on Bézier scatterers.

Among the different approaches proposed to design acoustic cloaks, the one consisting on the use of an optimum distribution of discrete scatters surrounding the concealing object has been successfully tested. The feasibility of acoustic cloaks mainly depends on the number and shape of the scatterers surrounding the object to be cloaked. This work presents a method allowing the reduction of the number of discrete scatterers by optimizing their external shape, which is here defined by a combination of cubic Bézier curves. Based on scattering cancellation, a two-dimensional directional cloak consisting of just 20 Bézier scatters has been designed, fabricated and experimentally characterized. The method of fundamental solutions has been implemented to calculate the interaction of an incident plane wave with scatterers of arbitrary shape. The acoustic cloak here proposed shows a performance, in terms of averaged visibility, similar to that consisting of 120 scatterers with equal circular cross sections. The operational frequency of the proposed cloak is 5940 Hz with a bandwidth of about 110 Hz.

Theoretical and experimental study of the Suzuki-phase photonic crystal lattice by angle-resolved photoluminescence spectroscopy.

A complete theoretical and experimental analysis of the photonic band structure for the Suzuki-phase lattice is presented. The band diagrams were calculated by two-dimensional plane wave expansion and three-dimensional guided-mode expansion methods. Angle resolved photoluminescence spectroscopy has been used to measure the emission of the photonic crystal structure realized in active InAsP/InP slabs. Photonic bands with a very low group velocity along an entire direction of the reciprocal lattice have been measured, which may have important applications on future photonic devices. The experimentally determined dispersion is in very good agreement with the calculated photonic bands. The presence of defect modes produced by microcavities in the Suzuki-phase lattice has also been established.

On the origin of pure optical rotation in twisted-cross metamaterials.

We present an experimental and computational study of the response of twisted-cross metamaterials that provide near dispersionless optical rotation across a broad band of frequencies from 19 GHz to 37 GHz. We compare two distinct geometries: firstly, a bilayer structure comprised of arrays of metallic crosses where the crosses in the second layer are twisted about the layer normal; and secondly where the second layer is replaced by the complementary to the original, i.e. an array of cross-shaped holes. Through numerical modelling we determine the origin of rotatory effects in these two structures. In both, pure optical rotation occurs in a frequency band between two transmission minima, where alignment of electric and magnetic dipole moments occurs. In the cross/cross metamaterial, the transmission minima occur at the symmetric and antisymmetric resonances of the coupled crosses. By contrast, in the cross/complementary-cross structure the transmission minima are associated with the dipole and quadrupole modes of the cross, the frequencies of which appear intrinsic to the cross layer alone. Hence the bandwidth of optical rotation is found to be relatively independent of layer separation.

Inverse designed photonic crystal de-multiplex waveguide coupler.

A two-dimensional photonic crystal diplexer integrated with a waveguide coupler is proposed. The design is computer generated through an inverse design process, limited within an area measuring 5 mumx5 mum. The best working device was designed for the optical communication wavelengths, 1.50 mum and 1.55 mum, i.e. a channel spacing of 50 nm. The device exhibits crosstalks suppressed below 40dB and coupling efficiencies close to 80%, for both channels.

Analysis of wave propagation in a two-dimensional photonic crystal with negative index of refraction: plane wave decomposition of the Bloch modes.

This work presents a comprehensive analysis of electromagnetic wave propagation inside a two-dimensional photonic crystal in a spectral region in which the crystal behaves as an effective medium to which a negative effective index of refraction can be associated. It is obtained that the main plane wave component of the Bloch mode that propagates inside the photonic crystal has its wave vector k' out of the first Brillouin zone and it is parallel to the Poynting vector ( S' ? k'> 0 ), so light propagation in these composites is different from that reported for left-handed materials despite the fact that negative refraction can take place at the interface between air and both kinds of composites. However, wave coupling at the interfaces is well explained using the reduced wave vector ( k' ) in the first Brillouin zone, which is opposed to the energy flow, and agrees well with previous works dealing with negative refraction in photonic crystals.

Radial wave crystals: radially periodic structures from anisotropic metamaterials for engineering acoustic or electromagnetic waves.

We demonstrate that metamaterials with anisotropic properties can be used to develop a new class of periodic structures that has been named radial wave crystals. They can be sonic or photonic, and wave propagation along the radial directions is obtained through Bloch states like in usual sonic or photonic crystals. The band structure of the proposed structures can be tailored in a large amount to get exciting novel wave phenomena. For example, it is shown that acoustical cavities based on radial sonic crystals can be employed as passive devices for beam forming or dynamically orientated antennas for sound localization.

Acoustic analogue of electronic BLOCH oscillations and resonant Zener tunneling in ultrasonic superlattices.

We demonstrate the existence of Bloch oscillations of acoustic fields in sound propagation through a superlattice of water cavities and layers of methyl methacrylate. To obtain the acoustic equivalent of a Wannier-Stark ladder, we employ a set of cavities with different thicknesses. Bloch oscillations are observed as time-resolved oscillations of transmission in a direct analogy to electronic Bloch oscillations in biased semiconductor superlattices. Moreover, for a particular gradient of cavity thicknesses, an overlap of two acoustic minibands occurs, which results in resonant Zener-like transmission enhancement.