Observation of acoustic Dirac-like cone and double zero refractive index

ARTICLE Received 9 Jan 2017 | Accepted 6 Feb 2017 | Published 20 Mar 2017 DOI: 10.1038/ncomms14871 OPEN Observation of acoustic Dirac-like cone and double zero refractive index Marc Dubois1,*, Chengzhi Shi1,*, Xuefeng Zhu1, Yuan Wang1 & Xiang Zhang1,2 Zero index materials where sound propagates without phase variation, holds a great potential for wavefront and dispersion engineering. Recently explored electromagnetic double zero index metamaterials consist of periodic scatterers whose refractive index is significantly larger than that of the surrounding medium. This requirement is fundamentally challenging for airborne acoustics because the sound speed (inversely proportional to the refractive index) in air is among the slowest. Here, we report the first experimental realization of an impedance matched acoustic double zero refractive index metamaterial induced by a Dirac-like cone at the Brillouin zone centre. This is achieved in a two-dimensional waveguide with periodically varying air channel that modulates the effective phase velocity of a high-order waveguide mode. Using such a zero-index medium, we demonstrated acoustic wave collimation emitted from a point source. For the first time, we experimentally confirm the existence of the Dirac-like cone at the Brillouin zone centre. 1 NSF Nano-scale Science and Engineering Centre (NSEC), University of California, Berkeley, 3112 Etcheverry Hall, Berkeley, California 94720, USA. 2 Materials Science Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to X.Z. (email: ). NATURE COMMUNICATIONS | 8:14871 | DOI: 10.1038/ncomms14871 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms14871 A coustic wave behaviour is affected by material parameters such as mass density and bulk modulus of the media where the wave propagates. Metamaterials provide a new strategy to design unprecedented material properties that do not exist in nature1–17. Metamaterials with negative effective mass density and bulk modulus were experimentally developed using locally resonant sonic crystal1 and Helmholtz resonators2, respectively. These materials are called single negative materials as only one of their parameters is negative. The refractive index of such materials is dominantly imaginary, due to a band gap. With proper design of the multiple scattering in bi-periodic crystals, single negative materials can be used to realize a superlens that breaks the diffraction limit3. Double negative materials with negative refractive index whose mass density and bulk modulus are simultaneously negative were demonstrated using a one-dimensional waveguide with membranes and side holes5,18 and coiled space structures19–21. Anisotropic materials were realized for the design of an acoustic hyperlens6, super-resolution imaging7 and cloaking8,9. While single zero materials have been explored both in electromagnetic (epsilon near zero)22–25 and acoustic metamaterials (density near zero)26–29, these media suffer from low-transmission due to an impedance mismatch. pffiffiffiffiffiffi In acoustics, the impedance of a material is given by Z¼ rk, where r is the mass density and k is the bulk modulus. An acoustic double zero refractive index metamaterial with simultaneously zero density and infinite bulk modulus achieving finite impedance overcomes such an obstacle (Supplementary Notes 1 and 2; Supplementary Figs 1 and 2). Recently developed electromagnetic metamaterials with a Dirac-like cone at the Brillouin zone centre exhibit double zero-index properties30–33. These electromagnetic metamaterials consist of periodic scatterers with phase velocity lower than the surrounding materials30,31. But this requirement is extremely challenging for airborne sound applications because the sound speed in air is slow compared with other materials. Here, we apply cylindrical scatterers with height larger than the background air channel in a two-dimensional waveguide, where the acoustic phase velocity is smaller than air sound speed for a high-order waveguide mode to realize an acoustic double zero refractive index metamaterial. The acoustic double zero refractive index metamaterial is used to collimate cylindrical waves emitted from a point source at the centre of the medium. Our analysis of the collimated acoustic beam exhibits a high-directivity performance. The holey structure of the double zero index metamaterial allows us to measure the acoustic field inside the medium and map the reciprocal space to confirm the existence of a Dirac-like cone at the Brillouin zone centre experimentally. Acoustic zero refractive index metamaterials open new possibilities for effective acoustic wave engineering in applications such as ultrasound medical imaging and underwater communication. Results Design of an acoustic double zero index metamaterial. In this letter, we experimentally realize an acoustic metamaterial with simultaneous zero mass density and infinite bulk modulus induced by a Dirac-like cone at the Brillouin zone centre by periodically varying the thickness of an air channel in a two-dimensional waveguide (Fig. 1), resulting in the change of the effective sound speed of the first order waveguide mode (Supplementary Note 3; Supplementary Fig. 3) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!  1 1 p2  2 2 ; ð1Þ cðo; hÞ¼ 2 c0 o h where c0 ¼ 343 ms  1 is the sound speed in air, o is the angular frequency and h is the thickness of the air channel. The periodic cylindrical air columns with larger air thickness in Fig. 1, have slower phase velocity than in the surrounding waveguide. With proper scatterer dimensions and lattice constant, this material exhibits a Dirac-like cone at the Brillouin zone centre for the first a 0.1 m b c D h1 h0 a Figure 1 | Acoustic metamaterial with simultaneous zero effective mass density and infinite effective bulk modulus. (a) Photograph of the fabricated sample with square lattice of 10  10 symmetric blind holes constituting an array of cylindrical scatterers. A through hole provides access to the centre of zero index metamaterial for a point source to excite the first order waveguide mode. Four spacers located at the corners of the sample ensure the height of the air channel in the waveguide and the alignments of the top and bottom plates. (b,c) Top and side views of a unit cell of the zero refractive index metamaterial, respectively. Grey areas mark the solid structures of the waveguide. The light grey circle in the top view denotes the blind holes on the top and bottom plates inside the waveguide. The top and bottom plates are symmetric about the central plane. D ¼ 16 mm, h0 ¼ 10 mm, h1 ¼ 14.5 mm and a ¼ 30 mm. 2 NATURE COMMUNICATIONS | 8:14871 | DOI: 10.1038/ncomms14871 | www.nature.com/naturecommunications ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms14871 b 0.3 8 c (...truncated)