The Study On Negative Refraction And Imaging Of Two-dimensional Phononic Crystal With Honeycomb-lattice

Owning the elastic band gap, phononic crystal is a kind of periodic composite materials or structures. The phononic band gap is the most significant physical characteristics of phononic crystal. It means that when the frequency of elastic wave corresponds with that in the range of band gap, the wave will be stop to propagate in this phononic crystal. Because of the properties of phononic crystal, it can be designed into many new acoustic devices and has a great application prospect in the field of noise reduction of vibration isolation. After 20 years of development, the studies on phononic crystal is no longer confined to the band gap characteristics. It gradually turns to the part of pass band with the deeper understanding of phononic crystal. Some peculiar phenomena such as negative refraction, self-collimation, acoustic cloaking, which are in use of the passband performance of phononic crystal, have gain more and more attentions, and the potential applications such as flat lens and invisibility cloak, based on these phenomena, are even exciting. In this paper, negative refraction and imaging features of two-dimensional phononic crystal with honeycomb-lattice are studied by finite element method. The following is the content of the paper.In chapter one, the basic concept of phononic crystals is firstly introduced on the basis of the electronic band theory and the analogy of photonic crystal. Then we discourse its basic features, including the band gap and defect mode characteristics and negative refraction, etc. The research status and the main application of phononic crystal is given in the last.In chapter two, the fundamental theory and knowledges of negative refraction effect of phononic crystal are given. Firstly we introduce the rise of left-handed materials, which is the origin of negative refraction phenomenon, and then we tell the general imaging laws and mechanism of phononic crystal slab lens in detail, using the Snell’s law and equal frequency theory. Meanwhile, we highlight the importance of obtaining the effective refractive index of-1 because it greatly affacts the imaging effect towards flat lens. finally the current research status of negative refraction effect on phononic crystal is given.In chapter three, the study on negative refraction and imaging of two-dimensional phononic crystal with honeycomb-lattice is introduced. Using finite element method, the band structure and the equal frequency contour of the model are calculated, by means of which we thus obtain the range of frequencies of negative refraction imaging. Then, we use the the gaussian beam and point source to simulate the "acoustic wave path" and flat len imaging, the results show that we can get the flat lens with effective refractive index of-1 and realize the ideal imaging by the designed model, while the imaging effect is much poorer when using the same material in square lattice and triangular lattice, failing to realize the perfect imaging.In chapter four, in order to achieve better imaging resolution, the designed model is finally improved by inserting two rows of columns on both sides of the former model. And the introduction of the surface wave can restore the evanescent wave modes so as to enhance the transmission. Through simulation and analysis, the full width at half maximum of the image point is found to change with cylindrical radius. As is known that the full width at half maximum represents the imaging resolution, the smaller the value of full width at half maximum, the higher resolution of the lens. Under the precondition of that the radius of middle columns remains 0.35α, the results show that within a certain range, full width at half maximum will decreases with the increase of radius of cylinder in both sides, and the best resolution is obtained when the radius of cylinder in both sides equals 0.2α, which is about 0.37λ.The research summary is given at the end of this paper.