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Register a new userAcoustic Willis metamaterials beyond the passivity bound
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Acoustic bianisotropy, also known as the Willis parameter, expands the field of acoustics by providing nonconventional couplings between momentum and strain in constitutive relations. Sharing the common ground with electromagnetics, the realization of acoustic bianisotropy enables the exotic manipulation of acoustic waves in cooperation with a properly designed inverse bulk modulus and mass density. While the control of entire constitutive parameters substantiates intriguing theoretical and practical applications, a Willis metamaterial that enables independently and precisely designed polarizabilities has yet to be developed to overcome the present restrictions of the maximum Willis bound and the nonreciprocity inherent to the passivity of metamaterials. Here, by extending the recently developed concept of virtualized metamaterials, we propose acoustic Willis metamaterials that break the passivity and reciprocity limit while also achieving decoupled control of all constitutive parameters with designed frequency responses. By instituting basis convolution kernels based on parity symmetry for each polarization response, we experimentally demonstrate bianisotropy beyond the limit of passive media. Furthermore, based on the notion of inverse design of the frequency dispersion by means of digital convolution, purely nonreciprocal media and media with a broadband, flat-response Willis coupling are also demonstrated. Our approach offers all possible independently programmable extreme constitutive parameters and frequency dispersion tunability accessible within the causality condition and provides a flexible platform for realizing the full capabilities of acoustic metamaterials.
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Willis coupling in acoustic materials defines the cross-coupling between strain and velocity, analogous to bianisotropic phenomena in electromagnetics. While these effects have been garnering significant attention in recent years, to date their effects have been considered mostly perturbative. Here, we derive general bounds on the Willis response of acoustic scatterers, show that they can become dominant in suitably designed scatterers, and outline a systematic venue for the realistic implementation of maximally bianisotropic inclusions. We then employ these inclusions to realize acoustic metasurfaces for sound bending with unitary efficiency.
Acoustophoresis deals with the manipulation of sub-wavelength scatterers in an incident acoustic field. The geometric details of manipulated particles are often neglected by replacing them with equivalent symmetric geometries such as spheres, spheroids, cylinders or disks. It has been demonstrated that geometric asymmetry, represented by Willis coupling terms, can strongly affect the scattering of a small object, hence neglecting these terms may miss important force contributions. In this work, we present a generalized formalism of acoustic radiation force and radiation torque based on the polarizability tensor, where Willis coupling terms are included to account for geometric asymmetry. Following Gorkovs approach, the effects of geometric asymmetry are explicitly formulated as additional terms in the radiation force and torque expressions. By breaking the symmetry of a sphere along one axis using intrusion and protrusion, we characterize the changes in the force and torque in terms of partial components, associated with the direct and Willis Coupling coefficients of the polarizability tensor. We investigate in detail the cases of standing and travelling plane waves, showing how the equilibrium positions and angles are shifted by these additional terms. We show that while the contributions of asymmetry to the force are often negligible for small particles, these terms greatly affect the radiation torque. Our presented theory, providing a way of calculating radiation force and torque directly from polarizability coefficients, shows that in general it is essential to account for shape of objects undergoing acoustophoretic manipulation, and this may have important implications for applications such as the manipulation of biological cells.
Using both multiple scattering theory and effective medium theory, we find that an acoustic metamaterial consisting of an array of spinning cylinders can possess a host of unusual properties including folded bulk and interface-state bands in the subwavelength regime. The folding of the bands has its origin in the rotation-induced antiresonance of the effective compressibility with its frequency at the angular velocity of the spinning cylinders, as well as in the rotational Doppler effect which breaks the chiral symmetry of the effective mass densities. Both bulk and interface-state bands exhibit remarkable variations as the filling fraction of the spinning cylinders is increased. In particular, a zero-frequency gap appears when exceeds a critical value. The uni-directional interface states bear interesting unconventional characteristics and their robust one-way transport properties are demonstrated numerically.
By designing tailor-made resonance modes with structured atoms, metamaterials allow us to obtain constitutive parameters outside their limited range from natural or composite materials. Nonetheless, tuning the constitutive parameters relies much on our capability in modifying the physical structures or media in constructing the metamaterial atoms, posing a fundamental challenge to the range of tunability in many real-time applications. Here, we propose a completely new notion of virtualized metamaterials to lift the traditional boundary inherent to the physical structure of a metamaterial atom. By replacing the resonating physical structure with a designer mathematical convolution kernel with a fast digital signal processing circuit, we show that a decoupled control of the effective bulk modulus and density of the metamaterial is possible on-demand through a software-defined frequency dispersion. Purely noninterfering to the incident wave in the off-mode operation while providing freely reconfigurable amplitude, center frequency, bandwidth, and phase delay of frequency dispersion in on-mode, our approach adds an additional dimension to wave molding and can work as an essential building block for time-varying metamaterials.
The recently proposed concept of metamaterials has opened exciting venues to control wave-matter interaction in unprecedented ways. Here we demonstrate the relevance of metamaterials for inducing acoustic birefringence, a phenomenon which has already found its versatile applications in optics in designing light modulators or filters, and nonlinear optic components. This is achieved in a suitably designed acoustic metamaterial which is non-Eulerian, in the sense that at low frequencies, it cannot be homogenized to a uniform acoustic medium whose behavior is characterized by Euler equation. Thanks to the feasibility of engineering its subwavelength structure, such non-Eulerian metamaterial allows one to desirably manipulate the birefringence process. Our findings may give rise to generation of innovative devices such as tunable acoustic splitters and filters.
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