Acoustic isolation and nonreciprocal sound transmission are highly desirable in many practical scenarios. They may be realized with nonlinear or magneto-acoustic effects, but only at the price of high power levels and impractically large volumes. In contrast, nonreciprocal electromagnetic propagation is commonly achieved based on the Zeeman effect, or modal splitting in ferromagnetic atoms induced by a magnetic bias. Here, we introduce the acoustic analog of this phenomenon in a subwavelength meta-atom consisting of a resonant ring cavity biased by a circulating fluid. The resulting angular momentum bias splits the ring's azimuthal resonant modes, producing giant acoustic nonreciprocity in a compact device. We applied this concept to build a linear, magnetic-free circulator for airborne sound waves, observing up to 40-decibel nonreciprocal isolation at audible frequencies.

The primary objective of acoustic metamaterial research is to design subwavelength systems that behave as effective materials with novel acoustical properties. One such property couples the stress–strain and the momentum–velocity relations. This response is analogous to bianisotropy in electromagnetism, is absent from common materials, and is often referred to as Willis coupling after J.R., Willis, who first described it in the context of the dynamic response of heterogeneous elastic media. This work presents two principal results: first, experimental and theoretical demonstrations, illustrating that Willis properties are required to obtain physically meaningful effective material properties resulting solely from local behaviour of an asymmetric one-dimensional isolated element and, second, an experimental procedure to extract the effective material properties from a one-dimensional isolated element. The measured material properties are in very good agreement with theoretical predictions and thus provide improved understanding of the physical mechanisms leading to Willis coupling in acoustic metamaterials.

Willis fluids, or more generally Willis materials, are homogenized composites that exhibit coupling between momentum and strain. This coupling is intrinsic to inhomogeneous media and can play a significant role in the overall response in acoustic metamaterials. In this paper, we draw connections between bianisotropy in electromagnetism and Willis coupling in elastodynamics to provide a qualitative understanding. Building upon these analogies, we introduce a new homogenization for acoustic metamaterials based on a source-driven, multiple scattering approach that highlights the physical origins of Willis coupling. Moreover through numerical examples, we compare several macroscopic material descriptions of acoustic metamaterials with non-negligible Willis coupling. The descriptions neglecting Willis coupling may not satisfy restrictions stemming from reciprocity, passivity, and causality, which suggests that including Willis coupling in macroscopic descriptions is necessary to realize physically meaningful macroscopic parameters.

Materials that require coupling between the stressstrain and momentum-velocity constitutive relations were first proposed by Willis (Willis 1981 Wave Motion 3, 1-11. (doi:10.1016/0165-2125(81)90008-1)) and are now known as elastic materials of the Willis type, or simply Willis materials. As coupling between these two constitutive equations is a generalization of standard elastodynamic theory, restrictions on the physically admissible material properties for Willis materials should be similarly generalized. This paper derives restrictions imposed on the material properties of Willis materials when they are assumed to be reciprocal, passive and causal. Considerations of causality and low-order dispersion suggest an alternative formulation of the standard Willis equations. The alternative formulation provides improved insight into the subwavelength physical behaviour leading to Willis material properties and is amenable to time-domain analyses. Finally, the results initially obtained for a generally elastic material are specialized to the acoustic limit.

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In this work, a thin functionally-graded sound absorber that achieves an absorption coefficient near unity is demonstrated. The sound absorber consists of a multilayer arrangement of an interwoven sonic crystal lattice with varying filling fractions, backed by a thin elastic coating that acts as a flexural acoustic element. The overall thickness of the sound absorber is about one tenth of the wavelength in air, and it was 3D printed with a thermoplastic polyurethane. Samples were fabricated and acoustically tested in an air-filled acoustic impedance tube, from which absorption and effective acoustic properties were obtained. A theoretical formulation for the effective acoustic properties of the sonic crystal lattice was used to guide the design process, and excellent agreement was found between measured and theoretically predicted results. A range of sonic crystal filling fractions and thicknesses were tested to verify the fabrication process and robustness of the theoretical formulation, and both were found to be in excellent agreement. Based on this testing and analysis, an optimal arrangement was found that achieved simultaneous near zero reflectance and transmittance over a given frequency band, thereby resulting in an absorption coefficient near unity. [Work supported by the Office of Naval Research.]

Originally demonstrated with electromagnetic waves, supercoupling describes the extraordinary matched transmission, energy squeezing, and anomalous quasistatic tunneling through narrow channels. This behavior is the result of impedance matching achieved when the effective properties within the channel approach zero. For electromagnetic waves, supercoupling is observed when the electric permittivity in the channel approaches zero. These channels are accordingly known as epsilon-near-zero (ENZ) channels. This work shows that analogous behavior exists in the acoustic domain when the effective density is nearly zero, which can be achieved by tailoring the structure of the channel. Such channels are therefore known as density-near-zero (DNZ) metamaterial channels. Unlike tunneling based on Fabry-Perot resonances, DNZ transmission is independent of channel length and geometry and yields a uniform field along the entire length of the channel. Transmission-line theory is used to describe this peculiar phenomenon and finite element simulations are presented to confirm the unusual transmission properties of the metamaterial channel. It is further shown that acoustic waves may provide a unique possibility of squeezing acoustic energy through arbitrarily small channels in three dimensions, overcoming limitations that arise in the electromagnetic case.