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Due to accidental degeneracy, a semi-Dirac point is realized at the center of the Brillouin zone in a two-dimensional phononic crystal (PC) consisting of a square array of core-shell-structure elliptical cylinders in water. In the vicinity of the semi-Dirac point, the dispersion is linear along the X direction, but it is quadratic along the Y direction. The semi-Dirac point is formed by the degeneracy of dipole and quadrupole modes, through accurately adjusting the radius of the cores and shells, the two modes will coincide and the dispersion relation will become linear. It is worth to be emphasised that the frequency of the semi-Dirac point is very low in our designed PC, and this is exactly the special advantage of a three-component system. Since the dispersion relation is different in the vicinity of the semi-Dirac point, some new features may be seen. Firstly, the anisotropic transmission phenomenon is demonstrated. A PC slab is placed in a rectangular waveguide where the sound hard boundary conditions are used on the upper and lower walls; a plane wave impinges on the PC slab along the X direction at the semi-Dirac point frequency, and total transmission can be achieved, so that the sound energy transmissivity is also equal to one. In the meantime, the waves experience no spatial phase changes when they are transmitting through the PC slab; this behavior indicates that the PC can be equivalent to zero index medium along the X direction. However, when the plane wave is incident along the Y direction, the transmitted field is very weak, and the sound energy transmission is nearly zero. Secondly, the properties of the semi-Dirac point can be applied to design acoustic diode. The scatterers of the PC are arranged in triangular prism shapes and placed into a straight waveguide; when the wave is incident along the X direction, it can be transmitted through the PC slab and emerge in the right area, but when the waves is incident from the opposite direction, it will be totally reflected back. Therefore, the semi-Dirac point in PC provides a way to realize the acoustic diode. Finally, the unidirectional wave-front shape effect can also be observed in our considered system. We put a square sample with 16-by-16 coating rods into water medium. When a tightly focused Gaussian beam impinges on the PC sample along the X direction at the semi-Dirac point frequency, the outgoing wave will be modulated to a plan wave. Whereas, when the incident wave along the Y direction, the Gaussian beam will be totally reflected. In conclusion, the singular features of semi-Dirac point in PC will provides an advantageous means to manipulate acoustic waves and exploit new functional materials.
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Keywords:
- phononic crystal /
- semi-Dirac point /
- zero index medium /
- anisotropic
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[17] Wei Q, Cheng Y, Liu X J 2013 Appl. Phys. Lett. 102 174104
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[22] Wang X, Chen L C, Liu Y H, Shi Y L, Sun Y 2015 Acta Phys. Sin. 64 174206 (in Chinese) [王晓, 陈立潮, 刘艳红, 石云龙, 孙勇 2015 64 174206]
[23] Wu Y 2014 Opt. Express 22 1906
[24] Liu Z Y, Zhang X X, Mao Y W, Zhu Y Y, Yang Z Y, Chan C T, Sheng P 2000 Science 289 1734
[25] Liu Z Y, Chan C T, Sheng P 2005 Phys. Rev. B 71 014103
[26] Li J, Liu Z Y, Qiu C Y 2006 Phys. Rev. B 73 054302
[27] Li Y, Liang B, Gu Z M, Zou X Y, Cheng J C 2013 Appl. Phys. Lett. 103 053505
[28] Li Y, Mei J 2015 Opt. Express 23 12089
[29] Liang B, Yuan B, Cheng J C 2009 Phys. Rev. Lett. 103 104301
[30] Liang B, Guo X S, Tu J, Zhang D, Cheng J C 2010 Nat. Mater. 10 1038
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[1] Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109
[2] Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201
[3] Katsnelson M I 2006 Eur. Phys. J. B 51 157
[4] Katsnelson M I, Novoselov K S, Geim A K 2006 Nat. Phys. 2 620
[5] Sepkhanov R A, Bazaliy Y B, Beenakker C W J 2007 Phys. Rev. A 75 063813
[6] Zhang X D, Liu Z Y 2008 Phys. Rev. Lett. 101 264303
[7] Yu S Y, Wang Q, Zheng L Y, He C, Liu X P, Lu M H, Chen Y F 2015 Appl. Phys. Lett. 106 151906
[8] Liu F M, Huang X Q, Chan C T 2012 Appl. Phys. Lett. 100 071911
[9] Liu F M, Lai Y, Huang X Q, Chan C T 2011 Phys. Rev. B 84 224113
[10] Peng P, Mei J, Wu Y 2012 Phys. Rev. B 86 134304
[11] Smith M J A, McPhedran R C Meylan M H 2014 Wave Random Complex 24 35
[12] Mei J, Wu Y, Chan C T, Zhang Z Q 2012 Phys. Rev. B 86 035141
[13] Chen Z G, Ni X, Wu Y, He C, Sun X C, Zheng L Y, Lu M H, Chen Y F 2014 Sci. Rep. 4 4613
[14] Lu J Y, Qiu C Y, Xu S J, Ye Y T, Ke M Z, Liu Z Y 2014 Phys. Rev. B 89 134302
[15] Li Y, Wu Y, Mei J 2014 Appl. Phys. Lett. 105 014107
[16] Torrent D, Snchez-Dehesa J 2012 Phys. Rev. Lett. 108 174301
[17] Wei Q, Cheng Y, Liu X J 2013 Appl. Phys. Lett. 102 174104
[18] Fleury R, Al A 2013 Phys. Rev. Lett. 111 055501
[19] Pardo V, Pickett W E 2009 Phys. Rev. Lett. 102 166803
[20] Banerjee S, Singh R R P, Pardo V, Pickett W E 2009 Phys. Rev. Lett. 103 016402
[21] Huang X Q, Chen Z T 2015 Acta Phys. Sin. 64 184208 (in Chinese) [黄学勤, 陈子亭 2015 64 184208]
[22] Wang X, Chen L C, Liu Y H, Shi Y L, Sun Y 2015 Acta Phys. Sin. 64 174206 (in Chinese) [王晓, 陈立潮, 刘艳红, 石云龙, 孙勇 2015 64 174206]
[23] Wu Y 2014 Opt. Express 22 1906
[24] Liu Z Y, Zhang X X, Mao Y W, Zhu Y Y, Yang Z Y, Chan C T, Sheng P 2000 Science 289 1734
[25] Liu Z Y, Chan C T, Sheng P 2005 Phys. Rev. B 71 014103
[26] Li J, Liu Z Y, Qiu C Y 2006 Phys. Rev. B 73 054302
[27] Li Y, Liang B, Gu Z M, Zou X Y, Cheng J C 2013 Appl. Phys. Lett. 103 053505
[28] Li Y, Mei J 2015 Opt. Express 23 12089
[29] Liang B, Yuan B, Cheng J C 2009 Phys. Rev. Lett. 103 104301
[30] Liang B, Guo X S, Tu J, Zhang D, Cheng J C 2010 Nat. Mater. 10 1038
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