矩形晶格结构对二维压电声子晶体带隙的影响

Influence of Crystal Structure on the Band Gaps of Two-dimensional Piezoelectric Phononic Crystal

通过计算二维压电声子晶体透射系数,研究了矩形晶格结构对声子晶体带隙的影响。为得到声子晶体的透射系数,构建叉指换能器(IDT)中间放置声子晶体的器件模型,IDT作为激发和接收端,声子晶体作为传输通道。通过有限元软件计算出模型的电学参数,分别结合IDT的混合矩阵(P矩阵)和声子晶体的散射矩阵,推导和计算出声表面波的透射系数,并找出带隙范围。该文在128°-YX铌酸锂基片上制作IDT和矩形晶格以圆孔为散射体的声子晶体。通过调整矩形晶格中y方向上晶格常数,理论和实验上均得到了2个方向上的带隙变化。结果表明,随着y方向上晶格常数的增大,x方向上的带隙逐渐分为两段,y方向上的带隙逐渐缩小,使y方向上的带隙夹在x方向两段带隙间。实验结果与计算结果较吻合。

This paper has studied the influence of crystal structure on the band gaps of two-dimensional piezoelectric phononic crystal（PCs）through calculating the transmission coefficient of PCs.In order to obtain the transmission coefficient of PCs,a model of PCs with interdigital transducer used to excite and receive acoustic wave has been established.The electrical parameters of this model can be worked out through finite element software.Then,the transmission coefficient of PCs can be obtained through combining the P matrix of interdigital transducer and scattering matrix of PCs.As an example,the interdigital transducer and circle hole PCs has produced in the 128°-YX Lithium Niobate matrix.Adjusting the lattice constant of rectangular lattice,the tendency of band gaps of PCs in two directions has been observed both in theory and experiment.The result shows that with the increase of lattice constant in ydirection,the bad gap in xdirection divided into two range and the band gap in xdirection gradually narrowed.Thus the band gap in the ydirection is sandwiched between the two band gaps in xdirection.The experimental result is agreed well with the calculating one.