Study Of Scattering Matrix Of Surface Acoustic Wave In Two-dimensional Piezoelectric Phononic Crystal

Phononic crystal(PCs) is a kind of composite material consisting of two elastic mediums with different density and elastic constants periodically. In recent years, the study of this acoustic wave composite material has become a focus recently. Like the photonic crystal, acoustic wave has a special dispersion relation that band structure under the influence of periodic structure. The space between two bands is the band gap, in which the propagation of acoustic wave within the PCs has been forbidden. The property of band gap make PCs has a broad application prospect in the decreasing vibration, noise reduction and acoustic devices. It has been more than 20 years since the study of PCs. The influence factors of PCs band gap, the optimization of band gap, the transmission and reflection coefficient, as well as the acoustic device based on PCs have been studied successively.In this paper, the fourth oeder scattering matrix is used to describe the propagation characteristic of surface acoustic wave in the two-dimensional piezoelectric PCs. The fourth oeder scattering matrix not only includes the transmission and reflection coefficient, but also includes the scattering. The research content includes three parts as follows:(1)This paper has proposed a method to describe the four ports model of two-dimensional(2D) piezoelectric phononic crystal(PCs) in a fourth order scattering matrix. Firstly, considering the two-dimensional charateristic of PCs on the plane, the fourth order scattering matrix has built. In order to obtain the parameters in this scattering matrix, a model of PCs with interdigital transducer used to excite and receive acoustic wave has been built. The electrical parameters of this model can be worked out through finite element software. Then, the parameters of this scattering matrix can be obtained through combining the P matrix of interdigital transducer and fourth order scattering matrix of PCs.(2) The band gap distribution of two-dimensional piezoelectric PCs with rectangular lattice has obtained through the transmission coefficient of the fourth order scattering matrix. The two lattice constants(‘a' and ‘b') of the rectangular lattice structures in the x direction and y direction is different, and different lattice structure can be obtained through adjusting the two the two lattice constants. This paper has studied the variation tendency of band gaps in two direction following the increase of b/a. The results show that with the increase of b/a, the band gaps in two directions has gradually decoupled. The miscomplete parts of two band gaps make the acoustic waves forbidden to propagate in one direction. The acoustic energy is constrainted in the other direction, so as to realize the fuction of acoustic waveguide.(3) In order to prove the validity of the theory, the actual device of air/128°YX Lithium Niobate PCs composed of 128°YX Lithium Niobate matrix with circular hole has been producted. Through the electrical tests on the device, the result show that it has a good consistency between the experiment and theory.