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This work reports topological extraordinary properties of sound transmission through topological states in sonic crystals denominated Suzuki phase, consisting of a rectangular lattice of vacancies created in a triangular lattice. These low-symmetry crystals exhibit unique properties due to the embedded lattice of vacancies. A generalized folding method explains the band structure and the quasi-type-II Dirac point in the Suzuki phase, which is related to the underlying triangular lattice. In analogy to the acoustic valley Hall effect, the Suzuki phase contains three types of topological edge states on the four possible interfaces separating two Suzuki phase crystals with distinct topological phases. The edge states have defined symmetries with inherent directionality, which affect the topological sound transmission and are different from chirality, valley vorticity or helicity. Particularly, the existence of topological deaf bands is here reported. The propagation of topological eigenmodes on the same interface is also different, which is quantified using the acoustic Shannon entropy, making the topological transport dependent on the frequency of the edge states. Based on the abundant topological edge states of Suzuki phase crystals, a multifunctional device with acoustic diodes, multi-channel transmission, and selective acoustic transmission can be designed. Numerical simulations and measurements demonstrate the topological transmission. Our work extends the research platform of acoustic topological states to lattices with low symmetry, which opens new avenues for enriching topological states with broad engineering applications., Comment: 29 pages, 9 figures, and 17 pages of supplementary materials

The study of topological states in electronic structures, which allows robust transport properties against impurities and defects, has been recently extended to the realm of elasticity. This work shows that nontrivial topological flexural edge states located on the free boundary of the elastic graphene-like metamaterial can be realized without breaking the time reversal, mirror, or inversion symmetry of the system. Numerical calculations and experimental studies demonstrate the robust transport of flexural waves along the boundaries of the designed structure. The topological edge states on the free boundary are not limited by the size of the finite structure, which can reduce the scale of the topological state system. In addition, unlike the edge states localized on the free boundary in graphene where the group velocity is zero, the edge states on the elastic metamaterial plate have propagation states with non-zero group velocity. There is a frequency range for the edge states, and we introduce the concept of Shannon entropy for elastic waves and use it to assess the frequency range of the edge states in graphene-like elastic metamaterials. This work represents a relevant advance in the study of elastic wave topological states, providing a theoretical basis for engineering applications such as vibration reduction and vibration isolation of mechanical structures., Comment: 22 pages, 8 figures, and 12 pages of supplementary information

Topological phases have recently been realised 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, Kekul\'e-distorted triangular acoustic lattice. Such lattice realises an acoustic analogue 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 \edit{\emph{analogue}} of Majorana bound state, \edit{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.

The unusual viscoelastic properties of silica aerogel plates are efficiently used to design subwavelength perfect sound absorbers. We theoretically, numerically and experimentally report a perfect absorbing metamaterial panel made of periodically arranged resonant building blocks consisting of a slit loaded by a clamped aerogel plate backed by a closed cavity. The impedance matching condition is analyzed using the Argand diagram of the reflection coefficient, i.e., the trajectory of the reflection coefficient as a function of frequency in the complex plane. The lack or excess of losses in the system can be identified via this Argand diagram in order to achieve the impedance matching condition. The universality of this tool can be further exploited to design more complex metasurfaces for perfect sound absorption, thus allowing the rapid design of novel and efficient absorbing metamaterials.

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 with this type of resonators. Numerical experiments performed within the framework of the finite element method support the accuracy of the model here developed., Comment: 16 pages, 8 figures

Soft acoustic metamaterials utilizing mesoporous structures have recently been proposed as a novel means for tuning the overall effective properties of the metamaterial and providing better coupling to the surrounding air. In this work, the use of silica aerogel is examined theoretically and experimentally as part of a compact soft acoustic metamaterial structure, which enables a wide range of exotic effective macroscopic properties to be demonstrated, including negative density, density-near-zero and non-resonant broadband slow sound propagation. Experimental data is obtained on the effective density and sound speed using an air-filled acoustic impedance tube for flexural metamaterial elements, which have previously only been investigated indirectly due to the large contrast in acoustic impedance compared to that of air. Experimental results are presented for silica aerogel arranged in parallel with either 1 or 2 acoustic ports, and are in very good agreement with the theoretical model.

Spatial gradients in refractive index have been used extensively in acoustic metamaterial applications to control wave propagation through phase delay. This study reports the design and experimental realization of an acoustic gradient index lens using a sonic crystal lattice that is impedance matched to water over a broad bandwidth. In contrast to previous designs, the underlying lattice features refractive indices that are lower than the water background, which facilitates propagation control based on a phase advance as opposed to a delay. The index gradient is achieved by varying the filling fraction of hollow, air-filled aluminum tubes that individually exhibit a higher sound speed than water and matched impedance. Acoustic focusing is observed over a broad bandwidth of frequencies in the homogenization limit of the lattice, with intensity magnifications in excess of 7 dB. An anisotropic lattice design facilitates a flat-faceted geometry with low backscattering at 18 dB below the incident sound pressure level. Three dimensional Rayleigh-Sommerfeld integration that accounts for the anisotropic refraction is used to accurately predict the experimentally measured focal patterns., Comment: Under Review, 9 pages, 5 figures, note that Figs. 5(b,c) would not compile correctly on arxiv.org, likely because arxiv does not support revtex4.1. Please see final published article for the correct version of Fig. 5

This work presents the experimental demonstration of total absorption by a metal-dielectric metasurface. Following the theoretical proposal [A. D\'iaz-Rubio et al. Phys. Rev. B 89, 245123 (2014)], we fabricated a metasurface consisting of a low absorbing dielectric layer (made of FR4) deposited on top of a metallic surface patterned with a square distribution of coaxial cavities. For P-polarized waves, it is observed a low frequency peak with perfect absorption. The behavior of this peak has been experimentally characterized for different dielectric layer thicknesses, coaxial cavity lengths and incidence angles. The experimental results are in excellent agreement with numerical simulation and support the previous theoretical findings., Comment: 5 figures

This work presents an experimental study of giant and pure optical activity in a periodic structure consisting of twisted crosses and complementary crosses patterned on the sides of a copper coated dielectric board. Additionally, a multilayer system is proposed and numerically studied to broaden the transmission bandwidth. Our results show that a dual band behavior can be obtained due to coupling effects between the layers whilst maintaining the dispersionless giant optical activity and negligible circular dichroism. We theoretically study the effect of the separation between layers and its influence on the transmission spectra., Comment: 9 pages, 4 figures

In this work, a recent theoretically predicted phenomenon of enhanced permittivity with electromagnetic waves using lossy materials is investigated for t he analogous case of mass density and acoustic waves, which represents inertial enhancement. Starting from fundamental relationships for the homogenized quasi-static effective density of a fluid host with fluid inclusions, theoretical expressions are developed for the conditions on the real and imaginary parts of the constitutive fluids to have inertial enhancement, which are verified with numerical simulations. Realizable structures are designed to demonstrate this phenomenon using multi-scale sonic crystals, which are fabricated using a 3D printer and tested in an acoustic impedance tube, yielding good agreement with the theoretical predictions and demonstrating enhanced inertia., Comment: 18 pages with 5 figures

Theoretical, numerical and experimental results examining thermoviscous losses in sonic crystals are presented in this work, enabling the fabrication and characterization of an acoustic metamaterial absorber with complex-valued anisotropic inertia. The formulations developed can be written with no unknown or empirical coefficients, due to the structured lattice of the sonic crystals and organized layering scheme, and it is shown that higher filling fraction arrangements can be used to provide a large enhancement in the loss factor. To accurately describe these structures in a realizable experimental configuration, confining structures are needed which modify the effective properties, due to the thermal and viscous boundary layer effects within the sonic crystal lattice. Theoretical formulations are presented which describe the effects of these confined sonic crystals, both individually and as part of an acoustic metamaterial structure, and is demonstrated experimentally in an acoustic impedance tube. It is observed that confined sonic crystals demonstrate an increase in the viscous losses and a reduction in the effective bulk modulus, enabling better acoustic absorber performance through improved impedance matching and enhanced absorption., Comment: The following article has been submitted to the Journal of the Acoustical Society of America (JASA). After it is published, it will be found at http://scitation.aip.org/JASA

The study of metallic corrugated surfaces has recently received strong attention due to their ability to mimic the behaviour of surface plasmons. In this work, this plasmon-like behaviour is employed to design an open cylindrical waveguide. The structure consists on a longitudinally corrugated metallic cylinder with corrugations filled with a dielectric material. The dispersion relation of this waveguide is analyzed in the \`Ocontinuous limit\'O, defined as the limit in which the number of corrugations is infinite, but keeping their periodicity constant. It is found that, in this limit, the waveguide supports only TE guided modes and their dispersion relation becomes highly degenerated. Finally, it is shown that the waveguide behaves as an anisotropic cylindrical rod with extreme electromagnetic parameters, what makes it possible to apply these structures not only as waveguides but also as building blocks for metamaterials.

The behavior of strongly coupled Radial Photonic Crystals shells is investigated as a potential alternative to transfer electromagnetic energy wirelessly. These sub-wavelength resonant microstructures, which are based on anisotropic metamaterials, can produce efficient coupling phenomena due to their high quality factor. A configuration of selected constitutive parameters (permittivity and permeability) is analyzed in terms of its resonant characteristics. The coupling to loss ratio between two coupled resonators is calculated as a function of distance, the maximum (in excess of 300) is obtained when the shells are separated by three times their radius. Under practical conditions an 83% of maximum power transfer has been also estimated., Comment: submitted to Annals of Physics

This work presents a gradient index device for insulating from vibrations a circular area of a thin plate. The gradient of the refractive index is achieved by locally changing the thickness of the plate, exploiting in this way the thickness-dependence of the dispersion relation of flexural waves in thin plates. A well-like thickness profile in an annular region of the plate is used to mimic the combination of an attractive and repulsive potentials, focusing waves at its bottom and dissipating them by means of a properly designed absorptive layer placed on top of the plate. The central area is therefore isolated from vibrations while they are dissipated at the bottom of the well. Simulations have been done using the multilayer multiple scattering method and the results prove their broadband efficiency and omnidirectional properties.

Anisotropic and inhomogeneous metamaterial shells are studied in order to exploit all their resonant mode richness. These multilayer structures are based on a cylindrical distribution of radially dependent constitutive parameters including an inner void cavity. Shell, cavity and whispering gallery modes are characterized, and special attention is paid to the latter ones. The whispering gallery modes are created at the boundary layers of the shell with the background and energy localization is produced with highly radiative characteristics. These low-Q resonant states have frequencies that are independent of the shell thickness. However, their quality factors can be controlled by the number of layers forming the shell, which allows confining electromagnetic waves at the interface layers (internal or external), and make them suitable for the harvesting of electromagnetic energy.

It is demonstrated that sonic crystals (periodic structures of sound scatterers) can be used to design acoustic barriers that attenuate efficiently broadband noise. Traffic noise is chosen here as an example in which our design procedure is applied. The structures consist of cylindrical units containing rubber crumb, a sound absorbing material. An optimization algorithm is developed to obtain the material distribution and the dimensions of the sonic crystal giving the best attenuation properties for this noise. The good agreement found between predictions and measurements for a barrier (3m height) characterized in a transmission room gives strong support to our proposal.

This work presents a multiple scattering formulation of two dimensional acoustic metamaterials. It is shown that in the low frequency limit multiple scattering allows us to define frequency-dependent effective acoustic parameters for arrays of both ordered and disordered cylinders. This formulation can lead to both positive and negative acoustic parameters, where the acoustic parameters are the scalar bulk modulus and the tensorial mass density and, therefore, anisotropic wave propagation is allowed with both positive or negative refraction index. It is also shown that the surface fields on the scatterer are the main responsible of the anomalous behavior of the effective medium, therefore complex scatterers can be used to engineer the frequency response of the effective medium, and some examples of application to different scatterers are given. Finally, the theory is extended to electromagnetic wave propagation, where Mie resonances are found to be the responsible of the metamaterial behavior. As an application, it is shown that it is possible to obtain metamaterials with negative permeability and permittivity tensors by arrays of all-dielectric cylinders and that anisotropic cylinders can tune the frequency response of these resonances.

We study the acoustic scattering properties of a phononic crystal designed to behave as a gradient index lens in water, both experimentally and theoretically. The gradient index lens is designed using a square lattice of stainless-steel cylinders based on a multiple scattering approach in the homogenization limit. We experimentally demonstrate that the lens follows the graded index equations derived for optics by mapping the pressure intensity generated from a spherical source at 20 kHz. We find good agreement between the experimental result and theoretical modeling based on multiple scattering theory., Comment: 10 pages, 4 figures

Gradient index sonic lenses based on two-dimensional sonic crystals are here designed, fabricated and characterized. The index-gradient is achieved in these type of flat lenses by a gradual modification of the sonic crystal filling fraction along the direction perpendicular to the lens axis. The focusing performance is well described by an analytical model based on ray theory as well as by numerical simulations based on the multiple-scattering theory., Comment: 4 pages, 4 figures

A systematic study of noise barriers based on sonic crystals made of cylinders that use recycled materials like absorbing component is here reported. 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 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.

Radial sonic crystals (RSC) are fluidlike structures infinitely periodic along the radial direction. They have been recently introduced and are only possible thanks to the anisotropy of specially designed acoustic metamaterials [see Phys. Rev. Lett. {\bf 103} 064301 (2009)]. We present here a comprehensive analysis of two-dimensional RSC shells, which consist of a cavity defect centered at the origin of the crystal and a finite thickness crystal shell surrounded by a fluidlike background. We develop analytic expressions demonstrating that, like for other type of crystals (photonic or phononic) with defects, these shells contain Fabry-Perot like resonances and strongly localized modes. The results are completely general and can be extended to three dimensional acoustic structures and to their photonic counterparts, the radial photonic crystals.

We introduce Shannon's information entropy to characterize the avoided crossing appearing in the resonant Zener-like phenomenon in ultrasonic superlattices made of two different fluidlike meta- materials. We show that Shannon's entropy gives a correct physical insight of the localization effects taking place and manifest the informational exchange of the involved acoustic states in the narrow region of parameters where the avoided crossing occurs. Results for ultrasonic structures consisting of alternating layers of methyl-metacrylate and water cavities, in which the acoustic Zener effect were recently demonstrated, are also reported., Comment: 4 pages, 5 figures. Submitted to Phys. Rev. Lett

We present theoretical and experimental studies of the size and thickness dependencies of the optical emission spectra from microcavities with hexagonal shape in films of two-dimensional photonic crystal. A semiclassical plane-wave model, which takes into account the electrodynamic properties of quasi-2D planar photonic microcavity, is developed to predict the eigenfrequencies of the confined photon modes as a function of both the hexagon-cavity size and the film thickness. Modes with two different symmetries, triangular and hexagonal, are critically analyzed. It is shown that the model of confined photon modes with triangular symmetry gives a better agreement between the predicted eigenmodes and the observed resonances., Comment: 14 pages, 6 figures

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 have employed 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., Comment: 5 pages, 4 figures. Submitted to Phys. Rev. Lett

Recently, Smajic et al. published an article on numerical structural opti- mizations of two-dimensional photonic crystals using two different classes of optimization algorithms i.e, deterministic for local searches and stochastic for global. In this comment we reexamine some of their conclusions regarding the global stochastic search strategies. It is concluded that the steps taken to increase the efficiency of the optimization of the test problem chosen by Smajic et al., which was selected to keep the search space tractable, can be mislead- ing when applied to intractable problems., Comment: 5 pages

This work deals with the inverse design in the field of photonic crystal based devices. Here an inverse method containing a fast and accurate simulation method integrated with a competent optimization method is presented. Two designs yielded from this conjunction of multiple scattering theory with a genetic algorithm is analyzed. The potential of this approach is illustrated by designing a lens that has a very low F-number (F=0.47) and a conversion ratio of 11:1. We have also designed a coupler device that introduces the light from an optical fiber into a PC based wave-guide with a predicted coupling efficiency that exceeds 87%., Comment: 8 pages with figures