基于六角形晶格的光子晶体零折射率特性及其光学应用研究

运用色散特性分析的方法,在六角形晶格光子晶体能带结构的布里渊区中心找到了狄拉克点,用等效媒质理论验证了在这一点上光子晶体的等效介电常量和等效磁导率同时为零,即存在狄拉克频点,用此六角形晶格光子晶体可以实现零折射率材料.随后运用有限元数值仿真方法,研究了此六角形晶格结构在狄拉克频点及其附近所呈现的零折射率特性.将此种六角形晶格光子晶体经过合理设计用以制作凹透镜,发现可以实现远场的亚波长聚焦.此外在凹透镜的入射面处引入防反射结构可以在一定程度上增强聚焦效果,提高了系统的分辨率.

Zero Index Characteristic of Hexagonal Lattice Photonic Crystals and Its Optical Application

Based on the method of dispersion characteristics analysis, the Dirac point was found at the center of the Brillion zone in the band structure of the hexagonal lattice photonic crystals, and the phenomenon that both the effective permittivity and permeability approach zero simultaneously at the Dirac point was verified by using the effective medium theory, so that the zero index material can be achieved by the hexagonal lattice photonic crystals at that point. Then, by using the finite element method to perform the numerical simulation, the zero index characteristic presented at or near the Dirac point of the hexagonal lattice photonic crystals was studied. In addition, by designing the concave lens which is made from the hexagonal lattice photonic crystals properly, the results of the sub-wavelength and far-field focusing can be obtained. It is useful to improve the focusing by introducing an antireflection structure to the incident interface of the concave lens, and can improve the effect of focusing and increase the resolution to some extent.