Caleb F. Sieck

Sound isolation and giant linear nonreciprocity in a compact acoustic circulator

Acoustically Isolated The control of sound transmission is desirable in a number of circumstances from noise suppression to imaging technologies. Fleury et al. (p. 516; see the cover; see the Perspective by Cummer) studied a subwavelength acoustic meta-atom consisting of a resonant ring cavity biased by an internally circulating fluid. The direction of rotational flow of the fluid (air) changed the resonant properties of the ring cavity, allowing the propagation of sound waves within the cavity to be controlled. With several ports connected to the cavity, sound could be directed to a certain port while isolating transmission in another. Directional fluid flow is used to control and isolate the propagation of sound. [Also see Perspective by Cummer] 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.

Experimental evidence of Willis coupling in a one-dimensional effective material element

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.

Reciprocity, passivity and causality in Willis materials

Materials that require coupling between the stress–strain 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.

Noise propagation through open windows of finite depth into an enclosure.

Predicting the insertion loss of an opening backed with an enclosed space is important for building noise control. Recent research in sound transmission through apertures of finite depth in infinite rigid baffles has included the effects of propagating and evanescent modes within the aperture in order to extend models to higher frequencies. The present study extends the model to the case of the aperture backed by a cavity as opposed to sound radiating into half-space. The role of coupling between the aperture modes, radiation modes, and cavity modes in the transmission was investigated. The results were compared to those of previous models which neglected the depth of the aperture and finite element modeling using COMSOL Multiphysics. Comparisons show that the current model is effective at predicting the sound transmission loss through the aperture and the acoustic field within the cavity for an obliquely incident plane wave. By changing impedance conditions on the half-space side of the aperture and with...

Acoustic supercoupling and enhancement of nonlinearities in density-near-zero (DNZ) metamaterial channels

Recent theoretical and experimental work has demonstrated that acoustic wave tunneling and energy squeezing can be achieved using density-near-zero (DNZ) metamaterial channels [Fleury et al, J. Acoust. Soc. Am. 132(3), 1956 (2012)]. These channels are directly analogous to supercoupling of electromagnetic waves in near-zero permittivity channels. In optics, the field enhancement and uniformity of response within a near-zero permittivity channel can be employed to produce switching behavior, harmonic generation, and wave mixing even with low amplitude input intensities. These optical channels have been already shown to significantly outperform enhancement of nonlinearity in conventional Fabry-Perot resonant gratings [Argyropoulos et al., Phys. Rev. B 85, 045129 (2012)]. The analogous properties of velocity field within a DNZ metamaterial channel can result in significant and uniform amplification that may be employed to enhance material or structural nonlinearities in the channel for applications like tran...

Acoustic supercoupling through a density-near-zero metamaterial channel

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.

A discussion of macroscopic properties for acoustic metamaterials: Models and measurements

Macroscopic material properties are useful to describe long wavelength dynamics of inhomogeneous media. Analytically, these properties are often determined by weighted field averages, which define the effective fields of a representative unit cell. The relations between these effective fields provide macroscopic properties. In addition to traditional properties (wavenumber, impedance, density, and compressibility), recent research has shown that inhomogeneous media require coupling parameters between effective volume-strain and momentum fields, known as Willis coupling or bianisotropy. However in the absence of embedded sources, metamaterial properties are non-unique allowing for macroscopic descriptions which only include traditional properties or traditional properties and coupling parameters. Many acoustic metamaterial measurements extract macroscopic properties using reflection and transmission coefficients of finite samples. Unfortunately, this widely used technique returns properties which relate bo...

Experimental measurement of the Willis coupling coefficient in a one-dimensional system

The primary objective of acoustic metamaterial research is to design subwavelength systems that behave as effective materials with novel acoustical properties. Willis coupling is one such property. Initially described by J. R. Willis [Wave Motion 3, pp. 1-11 (1981)], subwavelength structural asymmetry and/or nonlocal effects couple the stress-strain relation to the momentum-velocity relation. This coupling is absent in typical materials. While various theoretical models have predicted the existence of Willis coupling, experimental observation of Willis coupling has not, to our knowledge, been reported in the literature. We present here the first experimental evidence of Willis coupling in a one-dimensional unit cell consisting of a 0.12-mm-thick polyimide membrane under tension, a 5.9-mm-thick layer of air, and a perforated sheet of 0.45-mm-thick paper (perforation surface fraction 0.48, circular holes 3.1 mm in diameter). The properties of the unit cell were extracted using reflection and transmission da...

Reciprocity, passivity, and causality in media with coupled strain-momentum constitutive relations

Metamaterials are heterogeneous materials and structures which, under certain circumstances, may be interpreted as a homogeneous material displaying extreme physical properties such as negative effective density or modulus. Acoustic metamaterials (AMM) therefore expand the parameter space for acoustic device design and are thus of interest for a wide range of applications. Most AMM are composed of linear and passive constituent materials. Any physically meaningful approximation of their overall response must therefore obey reciprocity, passivity, and causality. This requirement constrains the effective parameters and delineates the range of possible material properties for an AMM. While restrictions for standard constitutive equations in acoustics and elastodynamics are well known, they have not been explored in detail for media with coupled strain-momentum behavior which is required to fully describe AMM [Norris et al., Proc. R. Soc. A, 467, 1749–1769 (2011)]. This work derives the restrictions on couple...

Source driven homogenization and spatial dispersion effects in acoustic metamaterials

Acoustic metamaterials (AMM) composed of dynamic subwavelength heterogeneities in a host fluid may generate an overall response that can be represented with dynamic effective parameters such as negative dynamic density or compressibility. Dynamic parameters imply that highly variable effective wavelengths exist even in the long wavelength limit where k0a << 1, with k0 representing the wavenumber in the host and a the descriptive size of the heterogeneity. The variability in effective wavelength is the result of strong frequency dispersion, often accompanied by nonlocal and spatial dispersion effects that complicate efforts to correctly homogenize the medium. This work presents a three-dimensional, source-driven, non-local homogenization scheme for a periodic AMM composed of a host fluid containing dynamic heterogeneities. The resulting constitutive relations couple macroscopic volume-strain and momentum fields and are analogous to the Willis relations of elastodynamics and bianisotropy in electromagnetism...