Dimensional Phononic Crystal Negative Refraction Imaging Mechanism And Characteristics Of Study

The negative refraction imaging of photonic crystals or phononic crystals can be used for constructing a perfect lens, which can overcome the diffraction limit of traditional lens imaging. In this paper, the imaging conditions, laws and mechanism in 2-D phononic crystal (PC) slabs have been investigated.First, we extend the multiple scattering theory(MST) from light waves to elastic waves in 2D phononic crystal, which include periodic and quasi-periodic structure, infinite slabs and finite slabs. Transmission coefficient and pressure intensity of sound waves were deduced theoretically.Secondly, for the model of a 2D steel-water PC constructed in a triangular lattice, the focusing characteristics and imaging rules of scattering wave in a 9-layer PC slab with periodic structure were discussed. The results show:The PC slab exhibit a characteristic of directional scattering channel which is different from the general positional waveguide, it is the result of periodic scattering of the rods in PC slab; These scattering channels are closely related to the slab structure, materials, sound source location and the angle of incident wave; Only in some appropriate structure, material composition, filling rate, incident direction and slab incident surface, the slab can focus imaging with negative refractive-like characteristic for some certain frequencies. Under a certain distance and incidence angle, the imaging behavior of PC slabs can be described with an equivalent negative refractive index and refraction law as the imaging in traditional geometrical optics. The definite rule among the source-slab distance, imaging position and slab thickness was reported.For the case of n=-l, an ideal imaging situation, the location of imaging has nothing to do with the angle of incidence, and point source correspond to a point image; For the case of n≠-1, a non-ideal imaging situation, the location of imaging will change with the wave incidence angle varying, and naturally, a imaging aberration occur; The Small-angle incident waves can be coupled into channels better than the large-angle incident wave, and contributed to the imaging intensity bigger than the large-angle incident wave. So, a sound diaphragm can improve the quality of image by restricting the large-angle wave incidenceFinally, a 9-layer PC slab with quasi-periodic structure was studied. It was found that the obstacle rods in the direction of the conduction band have a close influence on the intensity of the imaging. With the increasing of location disorder of the scatter rods, the scattering channels is gradually damaged, image become more blurry, and finally disappear; Correspondingly, radius disorder of the rods affect the image a little.This research is a scientific exploration about the mechanism of negative refraction imaging in PC slab, the conclusion is significant for the application of the PC slab imaging.