The Brillouin zones and band gaps of a two-dimensional phononic crystal with parallelogram lattice structure

作     者：HU JiaGuang XU Wen 

作者机构：School of Physical Science and TechnologyYunnan University Department of Math and PhysicsWenshan University Institute of Solid State PhysicsChinese Academy of Sciences 

出 版 物：《Science China(Physics,Mechanics & Astronomy)》 (中国科学：物理学、力学、天文学（英文版）)

年 卷 期：2014年第57卷第6期

页      面：1013-1019页

核心收录：

学科分类：07[理学] 070205[理学-凝聚态物理] 08[工学] 080501[工学-材料物理与化学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0703[理学-化学] 0702[理学-物理学] 

基　　金：supported by the National Natural Science Foundation of China(Grant No.10974206) 

主　　题：phononic crystal band gap lattice basis vectors plane wave expansion method 

摘      要：We present a detailed theoretical study on the acoustic band structure of two-dimensional （2D） phononic crystal. The 2D pho- nonic crystal with parallelogram lattice structure is considered to be formed by rigid solid rods embedded in air. For the circu- lar rods, some of the extrema of the acoustic bands appear in the usual high-symmetry points and, in contrast, we find that some of them are located in other specific lines. For the case of elliptic rods, our results indicate that it is necessary to study the whole first Brillouin zone to obtain rightly the band structure and corresponding band gaps. Furthermore, we evaluate the first and second band gaps using the plane wave expansion method and find that these gaps can be tuned by adjusting the side lengths ratio R, inclined angle 0 and filling fraction F of the parallelogram lattice with circular rods. The results show that the largest value of the first band gap appears at θ=90° and F--0.7854. In contrast, the largest value of the second band gap is at θ=60° and F=0.9068. Our results indicate that the improvement of matching degree between scatterers and lattice pattern, ra- ther than the reduction of structural symmetry, is mainly responsible for the enhancement of the band gaps in the 2D phononic crystal.