Multiple Scattering Formulation of Two Dimensional Acoustic and Electromagnetic Metamaterials

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

Sound focusing by gradient index sonic lenses

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 figure

Viscothermal effects in a two-dimensional acoustic black hole: A boundary element approach

[EN] The acoustic analog of the quantum black hole for airborne sound in two dimensions was denominated as an omnidirectional acoustic absorber by Climente et al. [see Appl. Phys. Lett., 100, 144103 (2012)], who characterized its absorbing properties without providing any theoretical support. The viscothermal losses of the underlying structure, which consists of an absorbing core and a surrounding gradient-index (GRIN) lens both made of periodic distributions of cylindrical rods, are here comprehensively studied by using the boundary element method (BEM) in two dimensions. It is shown that the numerical simulations in two dimensions reproduce fairly well the increase in absorption of the core when the GRIN lens is added and reveal that the discrepancy between measured and calculated values of absorbance is an artifact of the experimental setup. The possibility of independent calculation of viscous and thermal losses contributions in the two-dimensional (2D) BEM algorithm is employed for the comparison with a homogenization theory in which the cluster of cylinders is represented by a single fluidlike viscous cylinder with effective parameters. We conclude that viscous losses represent about 90% of the total energy dissipated in the core. The homogenization approach results are only 2% below the results calculated with 2D BEM, indicating that the effective parameters obtained by the homogenization are very accurate.Cutanda-Henríquez, V.; Sánchez-Dehesa Moreno-Cid, J. (2021). Viscothermal effects in a two-dimensional acoustic black hole: A boundary element approach. Physical Review Applied. 15(6):1-14. https://doi.org/10.1103/PhysRevApplied.15.064057S11415

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.This work was partially supported by the Office of Naval Research (USA) under Grant No. N000140910554, and by the Ministerio de Economia y Competitividad (Spain) under Contract No. TEC2010-19751. J. C. gratefully acknowledges financial support from the Danish Council for Independent Research and a Sapere Aude Grant (12-134776).García Chocano, VM.; Christensen, J.; Sánchez-Dehesa Moreno-Cid, J. (2014). Negative refraction and energy funneling by hyperbolic materials : an experimental demonstration in acoustics. Physical Review Letters. 112(14). https://doi.org/10.1103/PhysRevLett.112.144301S1121

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

[EN] The Poisson-like effect, describing the redirection of waves by 90 degrees, 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. (C) 2018 Acoustical Society of America.Work supported by the Ministerio de Economia y Competitividad of Spain and the EU Fondo Europeo de Desarrollo Regional under Project No. TEC2014-53088-C3-1-R, and the National Natural Science Foundation of China under Grants Nos. 11432004 and 11421091. P.G. acknowledges a scholarship with No. 201606120070 provided by China Scholarship Council.Gao, P.; Sánchez-Dehesa Moreno-Cid, J.; Wu, L. (2018). Poisson-like effect for flexural waves in periodically perforated thin plates. The Journal of the Acoustical Society of America. 144(2):1053-1058. https://doi.org/10.1121/1.5051648S10531058144