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首页> 外文期刊>Physical review >Locally resonant surface acoustic wave band gaps in a two-dimensional phononic crystal of pillars on a surface
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Locally resonant surface acoustic wave band gaps in a two-dimensional phononic crystal of pillars on a surface

机译：表面柱的二维声子晶体中的局部共振表面声波带隙

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摘要

We investigate theoretically the propagation of acoustic waves in a two-dimensional array of cylindrical pillars on the surface of a semi-infinite substrate. Through the computation of the band structure of the periodic array and of the transmission of waves through a finite length array, we show that the phononic crystal can support a number of surface propagating modes in the nonradiative region of the substrate, or sound cone, as limited by the slowest bulk acoustic wave. The modal shape and the polarization of these guided modes are more complex than those of classical surface waves propagating on a homogeneous surface. Significantly, an in-plane polarized wave and a transverse wave with sagittal polarization appear that are not supported by the free surface. In the band structure, guided modes define band gaps that appear at frequencies markedly lower than those expected from the Bragg interference condition. We identify them as originating from local resonances of the individual cylindrical pillars and show their dependence on the geometrical parameters, in particular with the height of the pillars. The transmission of surface acoustic waves across a finite array of pillars shows the signature of the locally resonant band gaps for surface modes and their dependence on the symmetry of the source and its polarization. Numerical simulations are performed by using the finite element method and considering silicon pillars on a silicon substrate.
机译：我们从理论上研究声波在半无限基底表面上的圆柱状圆柱的二维阵列中的传播。通过计算周期阵列的能带结构以及通过有限长度阵列的波传输，我们表明，声子晶体可以在基板或音锥的非辐射区域中支持多种表面传播模式，如下受最慢的体声波限制。这些引导模式的模态形状和极化比在均质表面上传播的经典表面波要复杂得多。明显地，出现了自由表面不支持的面内极化波和矢状极化的横向波。在带结构中，导模定义的带隙出现在明显低于布拉格干扰条件的频率范围内。我们将它们确定为源自各个圆柱体柱的局部共振，并显示出它们对几何参数的依赖性，尤其是柱体高度的依赖性。表面声波在柱子的有限阵列上的传输显示了表面模式的局部共振带隙的特征及其对声源对称性及其极化的依赖性。通过使用有限元方法并考虑硅衬底上的硅柱来进行数值模拟。

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