Research On The Dirac Point And Singular Features Of Two-dimensional Phononic Crystals

Phononic crystal (PC) is a kind of artificial composite material that have periodic spatial structure. PC have attracted much attention since the concept of the PC was raised. PC is expected to play a important role in the field of acoustic and elastic wave control. Over the past twenty years, people’s research mainly focus on the adjustment of the band gap, but the singular features of PC such as negative refraction and self-collimating was attract more attention. Researchers found that some PCs have conical dispersion in the center or boundary of the Brillouin Zone (BZ) and the PC own many special properties in the vicinity of the Dirac point. All kinds of linear dispersion relation were put forward successively, such as semi-Dirac point and Double Dirac point etc. In the center of the BZ, dispersion is linearly along one high symmetry direction, but it is quadratic along the vertical direction, this kind of dispersion relation was called semi-Dirac point. For the Double Dirac point, there are four bands intersect in one point. We will study the dispersion relation in PC system in depth and the following is the mainly research contents and results:(1) We designed a two dimensional three component PC, through adjust the material parameters we realized the semi-Dirac point in the center of the BZ. The dispersion relation is linearly along the ΓX direction, but it is nonlinearly along the ΓY direction. When increase or decrease the diameter of scatters, the intersecting bands will lifted and becomes nonlinearly. We also found that the semi-Dirac point is obtained by the coupling of quadrupole and dipole modes. In the vicinity of the semi-Dirac point, PC showing many singular features, such as anisotropic transmission, acoustic diode, unidirectional wave-front shaping.(2) In the earlier reports, the Dirac or Dirac-like point were all located in the center or boundary of the BZ, but have little reports about Dirac point located in the M point of BZ. As we all known, the wave vector of the M point is distinct from the Γ or K point, so the underlying physics should also be different. We designed a two dimensional square PC structure and achieved Dirac-like point at the M point of BZ. When the plane wave transmitting through PC in Dirac-like point frequency, the spatial phase will not experiences any change. This behavior is very like the zero-refraction material.. Similarly, PC also have many special properties in the vicinity of the Dirac-like point, such as acoustic cloaking, wave-front shaping.