Layer Multiple-Scattering Theory And Application Designing For Two-Dimensional Phononic Crystals

In this paper, we extend the layer Multi-Scattering theory (LMST) to elastic system for calculating the transmission/reflection coefficient of two-dimensional (2D) Phononic Crystals (PCs). Further more, we design some acoustic devices by using the characters of 2D PCs. More detailedly:First, we extend the LMST method to elastic waves propagating in 2D periodical composites. The formalism to calculate the reflection and transmission coefficients for elastic waves through finite slabs is presented. In this spirit, the crystal is viewed as a sequence of identical monolayer which has one-dimensional (1D) periodicity along a given direction. The reflection and transmission coefficients for a multilayer slab can be obtained by a double-layer scheme through the calculation of the scattering matrix of a monolayer. To demonstrate the application of this formalism, we calculate transmission coefficients for systems consisting of pure solid components or mixing (solid and fluid) components. The validity of this method is checked by both band structure calculations and transmission measurement of ultrasonic experiment.Then we investigate the negative refraction behavior and imaging effect for acoustic waves in 2D PCs consisting of hexagonal arrays of steel cylinders in air. The negative refraction and left-handed behaviors are demonstrated by the simulation of a Gaussian beam through a PC slab with finite thickness. Imaging effects by the PC slab with effective refraction index n ≠ -1 and n= -1 are investigated, respectively. Far-field images by 2D PC-based superlens for both cases are obtained through exact numerical simulations, which is agreement with the physical analysis based on the wave-beam refraction law.Next, we detailedly discussed the resonant tunneling (RT) states in 2D double phononic potential barriers (DPPB) system consisting of pure solid components. We find that the RT states of longitudinal mode can be distinguished easily from those of transverse mode. Therefore, a new kind of Mode-Selecting acoustic filter, which can pick out the single longitudinal wave component or transverse wave component at a certain frequency, isdesigned by using this kind of states.Finally, we design the directive acoustic source (DAS) by utilizing two different kinds of method. A) By using the band-edge state, our simulation results show that it is possible to obtain a highly DAS with a large radiation enhancement, operating at the band-edge frequency of the 2D PCs. The angular distributions of power and radiation enhancement factor strongly depend on the position of acoustic source relative to the unit-cell where the source is placed. Finally, by using the full-gap PC substrate, the directional acoustic radiation with a single branch whose half-power angular width is about 5.2 degree, is obtained. B) We report a design of DAS formed by placing a line source inside a planar cavity of 2D PCs. Radiation field with half-power angular width of less than 6 degrees is obtained. The operating frequency of the DAS can be extended to any desired value within the full-gap by adjusting the separation of the cavity.