Extreme Acoustic Metamaterial by Coiling Up Space

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Extreme Acoustic Metamaterial by Coiling Up Space

Zixian Liang and Jensen Li

Phys. Rev. Lett. 108, 114301 – Published 16 March 2012

See Focus story: Scenic Route for Sound Allows Extra Control

Abstract

We show that by coiling up space using curled perforations, a two-dimensional acoustic metamaterial can be constructed to give a frequency dispersive spectrum of extreme constitutive parameters, including double negativity, a density near zero, and a large refractive index. Such an approach has band foldings at the effective medium regime without using local resonating subwavelength structures, while the principle can be easily generalized to three dimensions. Negative refraction with a double negative prism and tunneling with a density-near-zero metamaterial are numerically demonstrated.

Received 23 August 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.114301

Focus

Scenic Route for Sound Allows Extra Control

Published 16 March 2012

The propagation of sound waves can be dramatically altered by forcing them to follow meandering channels, according to simulations.

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Authors & Affiliations

Zixian Liang and Jensen Li^*

Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Kowloon, Hong Kong

^*jensen.li@cityu.edu.hk

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Issue

Vol. 108, Iss. 11 — 16 March 2012

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Images

Figure 1
(a) Schematic diagram of metamaterial-repeating units in coiling up space. The hard solid plates (thin solid lines) inserted into the background fluid (white color) have a thickness $w = 0.02 a$ and a length $L = 0.61 a$ . The continuous fluid channels have a width $d = 0.081 a$ , where $a$ is the lattice constant of the primitive unit cell outlined by dashed lines. The connected arrows show the zigzag path of the propagation of acoustic waves, which is equivalent to a high index $n_{0 r}$ (relative to the background fluid) in (b) the simplified view with straightened channels (“X”-shaped region).Reuse & Permissions
Figure 2
(a) The band structure (solid lines) of the metamaterial. The black dashed lines represent the sound lines of the background fluid. The gray dash-dotted lines show the band structure obtained from Eq. (1) with $n_{0 r} = 4.2$ . Inset a1 shows the gap opening at the $Γ$ point, and a2 and a3 show the gap opening on both sides of the $M$ point. (b)–(d) The equifrequency contours (EFCs) of the first, the third and the fifth band. $k_{x / y}$ is the Bloch wave number in the CB/CA direction, $ω$ is the angular frequency, and $c$ is the velocity of the waves in the background fluid.Reuse & Permissions
Figure 3
(a) The relative effective index $n_{r}$ and impedance $Z_{r}$ vary with normalized frequency $ω a / (2 π c)$ . (b) The effective mass density $ρ_{r}$ and bulk modulus $B_{r}$ vary with $ω a / (2 π c)$ . All $n_{r}$ , $Z_{r}$ , $ρ_{r}$ , and $B_{r}$ are parameters normalized to the background fluid.Reuse & Permissions
Figure 4
Pressure field pattern with (a) an acoustic prism with microstructures outlined by black dashed lines and (b) the same acoustic prism with the effective medium outlined by black solid lines. The inset of (a) shows a closer view of the prism’s microstructure at the edge. The black solid lines represent the hard solid plates. A Gaussian beam of width $15.4 a$ impinges on the prism vertically from the bottom at a normalized frequency $ω a / (2 π c) = 0.191$ in the background fluid. The corresponding relative effective index is $n_{r} = - 1$ . All length scales are normalized to the lattice constant $a$ .Reuse & Permissions
Figure 5
Pressure field pattern of (a) an ideal hard solid plate blocking more than half of the width of a waveguide, and (b) tunneling with the density-near-zero metamaterial at a normalized frequency $ω a / (2 π c) \approx 0.214$ . A plane wave impinges from the left side in both (a) and (b). The metamaterial has $10 \times 14$ units excluding the hard solid region of $8 \times 2$ units. All length scales are normalized to the lattice constant $a$ .Reuse & Permissions

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