二维三组元声子晶体中的半狄拉克点及奇异特性  

Semi-Dirac cone and singular features of two-dimensional three-component phononic crystals

作　　者：高汉峰[1] 张欣[1] 吴福根[2] 姚源卫[1] 

机构地区：[1]广东工业大学物理与光电工程学院,广州510006 [2]广东工业大学实验教学部,广州510006

出　　处：《物理学报》2016年第4期155-161,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11374066;11374068);广东省自然科学基金重点项目(批准号:S2012020010885)资助的课题~~

摘　　要：设计了一种二维三组元声子晶体结构,利用偶然简并的方法在布里渊区中心实现了半狄拉克点,探究了随着组元几何参数的改变半狄拉克点的演变过程.利用有限元方法研究发现在半狄拉克点频率附近沿着ΓX方向声子晶体表现出与零折射率材料相似的行为,许多奇异特性如单向透射等均可以观察到.另外还发现在半狄拉克点频率附近声子晶体是各向异性的,沿着不同方向声波的传播现象是不同的,这种特性是狄拉克点及类狄拉克点所不具备的.这种各向异性的声波传播特性有许多重要的应用,如单方向完美透射和单方向波前整形等.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 ΓX direction, but it is quadratic along the ΓY 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 ΓX 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 ΓX direction. However, when the plane wave is incident along the ΓY 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 ΓX 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. Therefo

关 键 词：声子晶体 半狄拉克点 零折射率 各向异性 

分 类 号：O735[理学—晶体学]