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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.
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The effective medium representation is fundamental in providing a performance-to-design approach for many devices based on metamaterials. While there are recent works in extending the effective medium concept into the temporal domain, a direct implementation is still missing. Here, we construct an acoustic metamaterial dynamically switching between two different configurations with a time-varying convolution kernel, which can now incorporate both frequency dispersion of metamaterials and temporal modulation. We establish the effective medium formula in temporally averaging the compressibilities, densities and even Willis coupling parameters of the two configurations. A phase disorder between the modulation of different atoms is found negligible on the effective medium. Our realization enables a high-level description of metamaterials in the spatiotemporal domain, making many recent proposals, such as magnet-free non-reciprocity, broadband slow-light and Fresnel drag using spatiotemporal metamaterials possible for implementations in future.
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.
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.
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.
The recent breakthrough in metamaterial-based optical computing devices [Science 343, 160 (2014)] has inspired a quest for similar systems in acoustics, performing mathematical operations on sound waves. So far, acoustic analog computing has been demonstrated using thin planar metamaterials, carrying out the operator of choice in Fourier domain. These so-called filtering metasurfaces, however, are always accompanied with additional Fourier transform sub-blocks, enlarging the computing system and preventing its applicability in miniaturized architectures. Here, employing a simple high-index acoustic slab waveguide, we demonstrate a highly compact and potentially integrable acoustic computing system. The system directly performs mathematical operation in spatial domain and is therefore free of any Fourier bulk lens. Such compact computing system is highly promising for various applications including high throughput image processing, ultrafast equation solving, and real time signal processing.
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