Three-Dimensional Acoustic Double-Zero-Index Medium with a Fourfold Degenerate Dirac-like Point

Changqing Xu, Guancong Ma, Ze-Guo Chen, Jie Luo, Jinjie Shi, Yun Lai, and Ying Wu

Phys. Rev. Lett. 124, 074501 – Published 19 February 2020

Abstract

We report the first realization of a three-dimensional (3D) acoustic double-zero-index medium (DZIM) made of a cubic lattice of metal rods. While the past decade has seen several realizations of 2D DZIM, achieving such a medium in 3D has remained an elusive challenge. Here, we show how a fourfold degenerate point with conical dispersion can be induced at the Brillouin zone center, such that the material becomes a 3D DZIM with the effective mass density and compressibility simultaneously acquiring near-zero values. To demonstrate the functionalities of this new medium, we have fabricated an acoustic waveguide of 3D DZIM in form of a “periscope” with two 90° turns and observed tunneling of a normally incident planar wave through the waveguide yielding undistorted planar wave front at the waveguide exit. Our findings establish a practical route to realize 3D DZIM as an effective acoustic “void space” that offers unprecedented control over acoustic wave propagation.

Received 14 April 2019
Accepted 15 January 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.074501

Physics Subject Headings (PhySH)

Photonic crystals

Acoustic metamaterials

Atomic, Molecular & Optical

Authors & Affiliations

Changqing Xu¹, Guancong Ma^2,*, Ze-Guo Chen^1,2, Jie Luo^3,4, Jinjie Shi⁴, Yun Lai^4,†, and Ying Wu^1,‡

¹Division of Computer, Electrical and Mathematical Science and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
²Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
³School of Physical Science and Technology, Soochow University, Suzhou 215006, China
⁴MOE Key Laboratory of Modern Acoustics, National Laboratory of Solid State Microstructures, School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

^*phgcma@hkbu.edu.hk
^†laiyun@nju.edu.cn
^‡Ying.Wu@kaust.edu.sa

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 124, Iss. 7 — 21 February 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Band structure and eigenstates of the 3D PC. (a) 3D view and (b) (001) top view of unit cell. The host medium (gray) is air. Colored square blocks with side length $L \times L \times a$ are aluminum blocks. The black dashed line and red dashed box in (b) represents the direction of mirror plane $M_{- x y}$ and the unit cell shown in (a). (c) Band structure of the PC with $L = 0.3 a$ . Black and blue dots represent the monopolar state and the threefold degenerate dipolar states at the Brillouin Zone center, respectively. (d)–(g) Acoustic pressure field distributions of the monopolar state and dipolar states.
Reuse & Permissions
Figure 2
Realization of 3D acoustic DZIM by accidental degeneracy. (a) Band structure of the PC with $L = 0.35 a$ . A fourfold degenerate point (the Dirac-like point) at the $Γ$ point is observed. (b) An enlargedplot of the dispersion surfaces near the Dirac-like point in the $k_{x} − k_{y}$ plane. (c) The normalized effective mass density $ρ_{eff}$ (black curves) and compressibility $β_{eff}$ (blue curves) for the cases of $L = 0.35 a$ (solid curves) and $L = 0.3 a$ (dashed curves).
Reuse & Permissions
Figure 3
Transmission of sound through an acoustic “periscope.” (a) Illustration of the designed acoustic periscope consisting of a bending waveguide with two 90° bends (gold color). The red and blue regions represent the 3D DZIM and air, respectively. Wave incident from the top. (b) Simulated pressure field distribution when the waveguide is filled with PC at $f_{Dirac} = 9742 Hz$ . (c) The same as (b) but the PC is replaced by its effective medium. (d) The same as (b) and (c), but without any filling.
Reuse & Permissions
Figure 4
Experimental setup. (a) A loudspeaker emits a plane wave along the negative $z$ direction. The waveguide bends twice and the output is along the positive $x$ direction. A microphone is mounted on a translational stage to scan the sound at the outlet in $y − z$ , $x − y$ , and $x − z$ planes. (b) Some boundaries of the waveguide are removed to show the PC inside.
Reuse & Permissions
Figure 5
Plane wave tunneling. (a) The 2D Fourier transforms of the scanned field patterns at frequencies near $f_{Dirac} = 9680 Hz$ . In the $k_{y} − k_{z}$ plane, the Fourier transform has a distribution that peaks at $k_{y} = k_{z} = 0$ at $f_{Dirac}$ , the distribution gradually expands as the frequency moves away from $f_{Dirac}$ . All maps in (a) share the same coordinates. (b),(c) The same as (a) but for $k_{x} − k_{y}$ and $k_{x} − k_{z}$ planes. At $f_{Dirac}$ (middle panels), the Fourier transforms imply a plane wave in the positive $x$ direction. The red arrows mark the position of $k_{x} = 2 π f_{Dirac} / c = 177 m^{- 1}$ , $k_{y} (k_{z}) = 0$ . Away from $f_{Dirac}$ , nonzero $k_{y} (k_{z})$ components appear. (d) and (e) Scanned real-space field patterns of $x − y$ plane and $x − z$ plane at $f_{Dirac}$ , respectively, showing a planar wave front.
Reuse & Permissions

Physical Review Letters