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Funneling acoustic waves through largely mismatched channels is of fundamental importance to tailor and transmit sound for a variety of applications. In electromagnetics, zero-permittivity metamaterials have been used to enhance the coupling of energy in and out of ultranarrow channels, based on a phenomenon known as

Over the past decade, significant attention has been paid to zero-index metamaterials, due their extreme capabilities for wave manipulation [

Remarkable properties of zero-index metamaterials have been proposed and experimentally validated. For instance, these metamaterials have been used for cloaking [

These advances have motivated the recent interest in exploring the physics of acoustic metamaterials with near-zero material properties. For example, a space-coiled structure was used to assess a density-near-zero material for acoustic tunneling [

The analogue of zero-permittivity in acoustics, for the realization of acoustic supercoupling, is density-near-zero metamaterials [

A big advantage that has enabled the realization of supercoupling in electromagnetics has been the fact that conducting waveguides naturally support effective zero-index properties at the cut-off of their dominant mode of propagation. This phenomenon has enabled several demonstrations of electromagnetic supercoupling in electromagnetics without having to realize a metamaterial through periodic arrays of small inclusions, but simply operating a hollow waveguide at cut-off [

In order to demonstrate the effect of supercoupling for sound in a simple waveguide geometry, we consider the configuration of Figure _{2}, length_{2} between two narrow input/output channels, each with acoustic impedance_{1} and much narrower cross-sectional area_{1}. As derived in the Methods section, the reflection coefficient at the input port reads

A straightforward way to realize this matching condition in waveguides with large geometrical mismatch, as in Figure

_{tunneling} (i) = 763.0 Hz,_{tunneling} (ii) = 763.3 Hz, and_{tunneling} (iii) = 764.9 Hz. (c) Spatial variation of phase at the CNZ tunneling frequency for waveguides with 90° and 180° bends. We observe uniform phase despite bending of the channel. Here,_{tunneling_90} (i) = 755.10 Hz, and_{tunneling_180} (ii) = 756.52 Hz.

Indeed, for the intermediate channel the effective constitutive parameters can be retrieved as discussed in the Methods, yielding

So far, we have shown that it is possible to achieve the equivalent of zero-compressibility propagation and supercoupling in a waveguide with mixed hard and soft boundary walls, operating near its cut-off frequency. However, this configuration is hardly realizable in a realistic geometry. Interestingly, in the following we show that it is possible to achieve an analogous functionality exciting a waveguide with all hard boundaries, as in the case of a conventional acoustic waveguide filled by air, at the cut-off frequency of one of its higher-order modes. In the Methods we indeed show that the effective constitutive parameters of the (

The difference compared to the soft-hard waveguide in Figure

Figure

_{tunneling} (i)_{tunneling} (ii)_{tunneling} (iii)_{tunneling_90} (i)_{tunneling_180} (ii)

Figure

_{tunneling} (i) = 769.6 Hz,_{tunneling} (ii) = 769.6 Hz, and_{tunneling} (iii) = 769.4 Hz.

In this work, we have presented theoretical and experimental validation of a straightforward way of realizing zero-compressibility acoustic wave propagation in waveguides, by exciting a higher-order mode at the cut-off frequency. We used this unusual propagation regime to realize the supercoupling phenomenon for sound, enabling tunneling of energy through largely mismatched waveguide geometries. Our theoretical results accurately capture the physics behind this anomalous tunneling, and our experiments confirm large phase velocity and anomalous transmission independent of the channel length. The small discrepancies between measurements and numerical predictions can be explained by irregular geometry and uncertainties in the detailed material properties of the off-the-shelf toolbox used for the middle channel in the experiment. We estimate that the supercoupling transmission loss may be practically reduced below 2 dB, if the middle channel was manufactured with a steel wall thickness of approximately 7.5 mm or higher (see Figure

In summary, we can describe the supercoupling phenomenon as a dispersive impedance matching condition, which occurs when the coupling channel (with smaller characteristic impedance than the input waveguide) has input impedance that appears nearly infinitely stiff. At this matching condition, the phase velocity approaches infinity, as long as S_{2}/S_{1} is sufficiently large. Under this condition, we achieve full amplitude transmission and total conservation of the phase, independent of the height and length of the coupling channel. Moreover, our results show that a hard-wall waveguide, when driven near the cut-off frequency of a higher-order mode, exhibits compressibility-near-zero effective material properties and may be thought of as consisting of two effective soft boundaries, along which the pressure field is equal to zero and the uniform phase of the tunneling mode flips by

_{1}, filled with a fluid with characteristic acoustic impedance Z_{1}. These waveguides are connected as an input and output to an intermediate rectangular acoustic channel, as in Figure _{2} and cross-sectional area S_{2}. Using transmission-line theory, the reflection coefficient for a plane wave from one port of this structure is written as

Consider now a waveguide with two parallel soft boundaries at x =

Momentum conservation requires

Then, combining (

This CNZ condition can be exploited to induce supercoupling through a soft-hard channel waveguide. These boundaries however can be difficult to realize in practical acoustic media. For a more realistic case, we assume a waveguide configuration in which all boundaries are composed of a hard material. This is a typical scenario for air-filled waveguides. In this case, the spatial pressure distribution is

^{−1} according to [

The numerical and experimental data are available upon request.

All authors have no conflicts of interest.

H. Esfahlani initiated the research. H. Esfahlani and M. S. Byrne simulated the device and M. S. Byrne and M. McDermott performed the experiments. M. S. Byrne and H. Esfahlani conducted the analysis. A. Alù supervised the research. All authors wrote the manuscript. H. Esfahlani and M. S. Byrne contributed equally to this work.

The authors acknowledge useful discussions with Dr. Michael Haberman, Dr. Dimitrios Sounas, Dr. Mark Hamilton, Dr. Caleb Sieck, and Dr. Anthony Bonomo. Funding was given by ASEE SMART Scholarship, by the National Science Foundation and by the Swiss National Science Foundation’s (SNSF) Doctoral Mobility Fellowship Award under decision Number P1ELP2_165148.