二维声子晶体能带带隙与对称群的关系

用平面波展开法计算了由水柱体放入水银中所组成的二维声子晶体的能带结构．通过考虑4种对称程度不同的散射体和两种排列晶格，从不同的角度分析了对称性与声子带隙的关系．先采用调节散射体方位角度的方式来改变系统所构成的空间群．发现声予带隙的极大值和极小值都出现在空间群对称性最高时．然后找出不同填充率下的带隙极大值．结果表明．散射体形状和排列点阵所属点群对称性的升高均有利于大带隙的产生．

Dependence of Acoustic Band-gaps in Two-dimensional Phononic Crystals on Symmetric Groups

By using the plane wave expansion method we calculate the band structures of two--dimensional phononic crystals composed of water rods arranged in mercury. The relationship between symmetry and acoustic band--gaps is discussed from several angles by considering four kinds of rods and two lattices with different symmetry. We first change the system＇s space group through adjusting the rods＇ orientation, and find that both the maximal and minimal band--gaps appear under the condition of highest symmetry. Then the maximum of band--gaps can be obtained under any filling fraction. Our results show that the width of band--gap increases with the point groups＇ symmetry of rods and lattices.