Phononic Crystal Flat Lens Imaging Characteristics Of Study

In recent years, there is a growing interest in the studies of the material which has a negative refractive index. The negative refraction behavior, as one of the most important feature of this kind of material, is the base of the imaging in the flat lens system. In this paper, By the methods of theoretical analysis and numerical simulation, the imaging phenomenon and factors in flat lens made by the two- dimensional (2D) phononic crystals (PC) slab have been investigated.1,With the model of a 2D steel-air PC with a triangular lattice, and the multiple scattering theory (MST), the imaging conditions and laws of the negative refraction were analyzed. The results show:The negative refraction in a 2D PC slab was decided by its band structure and the equal frequency curve (EFC). It is also closely related with the frequency of the sound source and the incident angle. For the PC with a certain lattice structure (as the 2D steel-air PC with a triangular lattice discussed in this paper), the negative refraction occurred under the conditions of a certain frequency and incident angle range only. Under a certain frequency range, the imaging behavior of PC slabs can be described with an equivalent negative refractive index.2,Based on the negative refractive imaging of PC slab, the imaging laws of flat lens system made by PC were analyzed. The conclusion was following: the PC slabs can be used as a flat lens system with a certain index of refraction, and the imaging laws follow the object-imaging relation of the traditional multi-surface refraction lens system.3,Under the excitation of the sound source with a specific frequency, the imaging situation of the sound wave with different incident angles in PC slabs were analyzed. Found that:The incident angle of the sound source has a great impact on the imaging. There was a critical angle corresponding to the incident frequency in the negative refraction imaging forming. Only just the acoustic signal with a incident angle less than the critical angle has effects on the imaging, The acoustic signal with a incident angle more than the critical angle has no contribution to the imaging.4,By simulating the negative refraction behavior of the signal with different frequency in a 2D PC slab, the effects of frequency on the imaging were investigated. The results show:Within the frequency range in which the imaging could be found, the change of frequency also affects the imaging. The strength, as well as the definition of the imaging will be decreasing with the increasing of frequency.