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We report a procedure to design 2-dimensional acoustic structures with prescribed scattering properties. The structures are designed from targeted properties in the reciprocal space so that their structure factors, i.e., their scattering patterns under the Born approximation, exactly follow the desired scattering properties for a set of wavelengths. The structures are made of a distribution of rigid circular cross-sectional cylinders embedded in air. We demonstrate the efficiency of the procedure by designing 2-dimensional stealth acoustic materials with broadband backscattering suppression independent of the angle of incidence and equiluminous acoustic materials exhibiting broadband scattering of equal intensity also independent of the angle of incidence. The scattering intensities are described in terms of both single and multiple scattering formalisms, showing excellent agreement with each other, thus validating the scattering properties of each material.

Mirror-symmetric acoustic metascreens producing perfect absorption independently of the incidence side are theoretically and experimentally reported in this work. The mirror-symmetric resonant building blocks of the metascreen support symmetric and antisymmetric resonances that can be tuned to be at the same frequency (degenerate resonances). The geometry of the building blocks is optimized to critically couple both the symmetric and the antisymmetric resonances at the same frequency allowing perfect absorption of sound from both sides of the metascreen. A hybrid analytical model based on the transfer matrix method and the modal decomposition of the exterior acoustic field is developed to analyze the scattering properties of the metascreen. The resulting geometry is 3D printed and experimentally tested in an impedance tube. Experimental results agree well with the theoretical predictions proving the efficiency of these metascreens for the perfect absorption of sound in the ventilation problems.

We report the experimental design of a 1D stealth acoustic material, namely a material that suppresses the acoustic scattering for a given set of incident wave vectors. The material consists of multiple scatterers, rigid diaphragms, located in an air-filled acoustic waveguide. The position of the scatterers has been chosen such that in the Born approximation a suppression of the scattering for a broad range of frequencies is achieved and thus a broadband transparency. Experimental results are found in excellent agreement with the theory despite the presence of losses and the finite size of the material, features that are not captured in the theory. This robustness as well as the generality of the results motivates realistic potential applications for the design of transparent materials in acoustics and other fields of wave physics.

The limits of flexural wave absorption by open lossy resonators are analytically and numerically reported in this work for both the reflection and transmission problems. An experimental validation for the reflection problem is presented. The reflection and transmission of flexural waves in 1D resonant thin beams are analyzed by means of the transfer matrix method. The hypotheses, on which the analytical model relies, are validated by experimental results. The open lossy resonator, consisting of a finite length beam thinner than the main beam, presents both energy leakage due to the aperture of the resonators to the main beam and inherent losses due to the viscoelastic damping. Wave absorption is found to be limited by the balance between the energy leakage and the inherent losses of the open lossy resonator. The perfect compensation of these two elements is known as the critical coupling condition and can be easily tuned by the geometry of the resonator. On the one hand, the scattering in the reflection problem is represented by the reflection coefficient. A single symmetry of the resonance is used to obtain the critical coupling condition. Therefore the perfect absorption can be obtained in this case. On the other hand, the transmission problem is represented by two eigenvalues of the scattering matrix, representing the symmetric and anti-symmetric parts of the full scattering problem. In the geometry analyzed in this work, only one kind of symmetry can be critically coupled, and therefore, the maximal absorption in the transmission problem is limited to 0.5. The results shown in this work pave the way to the design of resonators for efficient flexural wave absorption.

We experimentally report perfect acoustic absorption through the interplay of the inherent losses and transparent modes with high $Q$ factor. These modes are generated in a two-port, one-dimensional waveguide which is side-loaded by isolated resonators of moderate $Q$ factor. In symmetric structures, we show that in the presence of small inherent losses, these modes lead to coherent perfect absorption associated with one-sided absorption slightly larger than 0.5. In asymmetric structures, near perfect one-sided absorption is possible (96 \%) with a deep sub-wavelength sample ($\lambda/28$). The control of strong absorption by the proper tuning of few resonators with weak losses will open new possibilities in various wave-control devices.

We experimentally and analytically report broadband and narrowband perfect absorption in two different acoustic waveguide-resonator geometries by the mechanism of critical coupling. In the first geometry the resonator (a Helmholtz resonator) is side-loaded to the waveguide and it has a moderate quality factor. In the second geometry the resonator (a viscoelastic porous plate) is in-line loaded and it contains two resonant modes with low quality factor. The interplay between the energy leakage of the resonant modes into the waveguide and the inherent losses of the system reveals a perfect and a broadband nearly perfect absorption. The results shown in this work can motivate relevant research for the design of broadband perfect absorbers in other domains of wave physics.

We report Bessel-like beam formation of acoustic waves by means of an axisymmetric grating of rigid tori. The results show that the generated beam pattern is similar to that of Bessel beams, characterized by elongated non-diffracting focal spots. A multiple foci structure is observed, due to the finite size of the lens. The dependence of the focal distance on the frequency is also discussed, on the basis of an extended grating theory. Experimental validation of acoustic Bessel-like beam formation is also reported for sound waves. The results can be generalized to wave beams of different nature, as optical or matter waves.

We investigate the sound propagation in an air-filled tube periodically loaded with Helmholtz resonators. By tuning the Helmholtz with the Bragg resonance, we study the efficiency of slow sound propagation in the presence of the intrinsic viscothermal losses of the system. While in the lossless case the overlapping of the resonances results in slow sound induced transparency of a narrow frequency band surrounded by a strong and broadband gap, the inclusion of the unavoidable losses imposes limits to the slowdown factor and the maximum transmission. Experiments, theory and finite element simulations have been used for the characterization of acoustic wave propagation. Experiments, in good agreement with the lossy theory, reveal the possibility of slowing sound at low frequencies by 20 times. A trade-off among the relevant parameters (delay time, maximum transmission, bandwidth) as a function of the tuning between Bragg and Helmholtz resonance frequency is also presented.

We present the design of a structured material supporting complete absorption of sound with a broadband response and functional for any direction of incident radiation. The structure which is fabricated out of porous lamellas is arranged into a low-density crystal and backed by a reflecting support. Experimental measurements show that strong all-angle sound absorption with almost zero reflectance takes place for a frequency range exceeding two octaves. We demonstrate that lowering the crystal filling fraction increases the wave interaction time and is responsible for the enhancement of intrinsic material dissipation, making the system more absorptive with less material.

The symmetry matching between the source and the lens results of fundamental interest for lensing applications. In this work we have modeled an axisymmetric gradient index (GRIN) lens made of rigid toroidal scatterers embedded in air considering this symmetry matching with radially symmetric sources. The sound amplification obtained in the focal spot of the reported lens (8.24 dB experimentally) shows the efficiency of the axisymmetric lenses with respect to the previous Cartesian acoustic GRIN lenses. The axisymmetric design opens new possibilities in lensing applications in different branches of science and technology.

We propose and experimentally demonstrate a novel mechanism of sound wave concentration based on soft reflections in chirped sonic crystals. The reported controlled field enhancement occurs at around particular (bright) planes in the crystal, and is related to a progressive slowing down of the sound wave as it propagates along the material. At these bright planes, a substantial concentration of the energy (with a local increase up to 20 times) was obtained for a linear chirp and for frequencies around the first band gap. A simple couple mode theory is proposed, that interprets and estimates the observed effects. The results are obtained for the case of sound waves and sonic crystals, however they are extendable to other type of waves in modulated host matter.

A theoretical and experimental study of the propagation of sound beams in- and behind three-dimensional sonic crystals at frequencies close to the band edges is presented. An efficient collimation of the beam behind the crystal is predicted and experimentally demonstrated. This effect could allow the design of sources of high spatial quality sound beams.

The effect of the presence of a finite impedance surface on the wave propagation properties of a two-dimensional periodic array of rigid cylinders with their axes perpendicular to the surface is both numerically and experimentally analyzed in this work. In this realistic situation both the incident and the scattered waves interact with these two elements, the surface and the array. The interaction between the excess attenuation effect, due to the destructive interference produced by the superposition of the incident wave and the reflected one by the surface, and the bandgap, due to the periodicity of the array, is fundamental for the design of devices to control the transmission of waves based on periodic arrays. The most obvious application is perhaps the design of Sonic Crystals Noise Barriers. Two different finite impedance surfaces have been analyzed in the work in order to observe the dependence of the wave propagation properties on the impedance of the surface.

Complex Band Structures and Multiple Scattering Theory have been used in this paper to analyze the overlapping of the evanescent waves localized in point defects in Sonic Crystals. The Extended Plane Wave Expansion (EPWE) with supercell approximation gives the imaginary part of the Bloch vectors that produces the decay of the localized modes inside the periodic system. Double-cavities can present a coupling between the evanescent modes localized in the defect, showing a symmetric or antisymmetric modes. When point defects are close, the complex band structures reveal a splitting of the frequencies of the localized modes. Both the real part and the imaginary values of wave vector of the localized modes in the cavities present different values for each localized mode, which gives different properties for each mode. Novel measurements, in very good agreement with analytical data, show the experimental evidences of the symmetric and antisymmetric localized modes for a double-point defect in Sonic Crystals (SC). The investigation on the localization phenomena and the coupling between defects in periodic systems has a fundamental importance both in pure and in applied physics.

The complex band structures calculated using the Extended Plane Wave Expansion (EPWE) reveal the presence of evanescent modes in periodic systems, never predicted by the classical \omega(\vec{k}) methods, providing novel interpretations of several phenomena as well as a complete picture of the system. In this work we theoretically and experimentally observe that in the ranges of frequencies where a deaf band is traditionally predicted, an evanescent mode with the excitable symmetry appears changing drastically the interpretation of the transmission properties. On the other hand, the simplicity of the sonic crystals in which only the longitudinal polarization can be excited, is used to interpret, without loss of generality, the level repulsion between symmetric and antisymmetric bands in sonic crystals as the presence of an evanescent mode connecting both repelled bands. These evanescent modes, obtained using EPWE, explain both the attenuation produced in this range of frequencies and the transfer of symmetry from one band to the other in good agreement with both experimental results and multiple scattering predictions. Thus, the evanescent properties of the periodic system have been revealed necessary for the design of new acoustic and electromagnetic applications based on periodicity.

This work theoretically and experimentally reports the evanescent connections between propagating bands in periodic acoustic materials. The complex band structures obtained by solving for the $k(\omega)$ problem reveal a complete interpretation of the propagation properties of these systems. The prediction of evanescent modes, non predicted by classical $\omega(\vec{k})$ methods, is of interest for the understanding of these propagation properties. Complex band structures provide an interpretation of the evanescent coupling and the level repulsion states showing the possibility to control of evanescent waves in periodic materials.

An acoustic metamaterial made of a two-dimensional (2D) periodic array of multi-resonant acoustic scatterers is analysed in this paper. The building blocks consist of a combination of elastic beams of Low-Density Polyethylene Foam (LDPF) with cavities of known volume. Sound inside the structure can excite elastic resonances of the material as well as acoustic resonances in the cavities producing several attenuation peaks in the low-frequency range. Due to this behaviour at the subwavelength regime we can define this periodic array as a Locally Multi-Resonant Acoustic Metamaterial (LMRAM) presenting strong dispersive characteristics of the effective properties with subwavelength multi-resonant structural units. The results shown in this paper could be use to design effective Sonic Crystal Acoustic Barriers with wide tunable attenuation bands in the low-frequency range.

The physical properties of a periodic distribution of absorbent resonators is used in this work to design a tunable wideband bandstop acoustic filter. Analytical and numerical simulations as well as experimental validations show that the control of the resonances and the absorption of the scatterers along with their periodic arrangement in air introduces high technological possibilities to control noise. Sound manipulation is perhaps the most obvious application of the structures presented in this work. We apply this methodology to develop a device as an alternative to the conventional acoustic barriers with several properties from the acoustical point of view but also with additional aesthetic and constructive characteristics.

The use of Sonic Crystals as environmental noise barriers has certain advantages from the acoustical and the constructive point of view with regard to conventional ones. One aspect do not studied yet is the acoustic interaction between the Sonic Crystals and the ground due to, up to now, this latter is not included in the analytical models used to characterize these Sonic Crystals. We present here an analytical model, based on multiple scattering theory, to study this interaction considering the ground as a finite impedance surface. Using this model we have obtained interesting conclusions that allow to design more effectively noise screens based on Sonic Crystals. The obtained results have been compared with experimental and numerical, finding a good agreement between them.

Research into properties of heterogeneous artificial materials, consisting of arrangements of rigid scatterers embedded in a medium with different elastic properties, has been intense throughout last two decades. The capability to prevent the transmission of waves in predetermined bands of frequencies -called bandgaps- becomes one of the most interesting properties of these systems, and leads to the possibility of designing devices to control wave propagation. The underlying physical mechanism is destructive Bragg interference. Here we show a technique that enables the creation of a wide bandgap in these materials, based on fractal geometries. We have focused our work in the acoustic case where these materials are called Phononic/Sonic Crystals (SC) but, the technique could be applied any types of crystals and wave types in ranges of frequencies where the physics of the process is linear.

Evanescent modes in complete sonic crystals (SC) and SC with point defects are reported both theoretically and experimentally in this paper. Plane wave expansion (PWE) and, in general, $\omega(k)$ methods have been used to calculate band structures showing gaps that have been interpreted as ranges of frequencies where no real $k$ exists. In this work, we extend PWE to solve the complex $k(\omega)$ problem applied to SC, introducing the supercell approximation for studying one vacancy. Explicit matrix formulation of the equations is given. This $k(\omega)$ method enables the calculation of complex band structures, as well as enabling an analysis of the propagating modes related with real values of the function $k(\omega)$, and the evanescent modes related with imaginary values of $k(\omega)$. This paper shows theoretical results and experimental evidences of the evanescent behavior of modes inside the SC band gap. Experimental data and numerical results using the finite elements method are in very good agreement with the predictions obtained using the $k(\omega)$ method., Comment: 15 pages, 3 figures

We show both experimentally and theoretically the evanescent behaviour of modes in the Band Gap (BG) of finite Phononic Crystal (PC). Based on experimental and numerical data we obtain the imaginary part of the wave vector in good agreement with the complex band structures obtained by the Extended Plane Wave Expansion (EPWE). The calculated and measured acoustic field of a localized mode out of the point defect inside the PC presents also evanescent behaviour. The correct understanding of evanescent modes is fundamental for designing narrow filters and wave guides based on Phononic Crystals with defects., Comment: 8 pages, 3 figures