中文摘要：

声表面波声子晶体对于实现声表面波的精确操控有着非常重要的应用价值。针对两大类最为主要的声表面波声子晶体的结构类型，即：“凹陷”孔洞阵列型和“凸起”柱体阵列型，采用三维有限元方法，数值计算并获得了基于压电铌酸锂基底的声表面波声子晶体的能带结构，同时验证了声子晶体中所具有的声表面波带隙，并进一步分析了这两大类声表面波声子晶体中的各种本征模式所呈现的特征。结果表明，在这两大类声表面波声子晶体中，均可以存在由于带边布拉格散射导致的声表面波的部分（方向）带隙甚至全（方向）带隙；在“凸起”型声表面波声子晶体中，更是存在由于“凸起”结构中的局域共振而导致的局域共振带隙。局域共振带隙的频率可以远小于布拉格带隙所具有的频率，同时，其频率范围仅由局域共振体本身的几何形貌及声学参数决定，而与声子晶体整体的晶格常数或对称性无关。

英文摘要：

Surface acoustic waves（SAW）,with advantages of its integratable micro-scale,high signal noise ratio,low energy loss and the biocompatible nature,are the excellent participants in nowadays communications industry and ex-tensive detecting fields,etc.In this research,we focused on the phononic crystals（PnCs）based on surface acoustic waves.By using three dimensional finite element method,we calculated and analyzed the surface acoustic band-structures and eigen modes of two major types phononic crystals on elastic surface,especially on the industrial common used lithium niobate substrate：one is the periodical hollow structures in the substrate surface and the other is the periodical pillar structures attached on the substrate.The result shows that both the two types of surfacenbsp;phononic crystals provide the surface acoustic dispersions and the Bragg band-gaps.However,in the latter type surface phononic crystal,i.e.,the periodical pillar structure,there is also existed the local-resonant（LR）band-gap caused by the LR modes of the pillars.We also shows that these LR modes and the frequency ranges of the LR band-gaps are only determined by the acoustic/geometry parameters of the attached pillars but have no relationship with the lattice constant or the symmetry of the surface PnCs.