用平面波展开法研究了介质矩形柱二维正方格子光子晶体的能带结构，正方晶格的晶格常数为a，当介质矩形柱边长为0.3633a，相对介电常数为11.56时，光子晶体的能带在布里渊区的中心点获得一个三重简并态，包括在同一频率接触构成狄拉克锥的两个线性能带，一个穿过狄拉克点的平的能带，光子晶体等效为介电常数和磁导率都为零的零折射率材料。用有限元法仿真电磁波在光子晶体中的传输特性，仿真结果表明，狄拉克点频率的电磁波通过光子晶体时相位不发生变化，传输特性与零折射率材料相同，用这种光子晶体设计的凹透镜可以实现焦点的半峰全宽为波长λ的0.63倍，焦距为λ的4.12倍的亚波长聚焦。

Based on the plane wave expansion method, the band structure of a square lattice two dimensional (2D) photonic crystal (PC) with rectangular dielectric rods in the air background is studied. When the length and relative permittivity of the rectangular rods are set as 0.3633a and 11.56, respectively, a triply degenerate state is found at the center of the Brillion zone in the band structure. The triply degenerate state consists of two linear bands that generate Dirac cones and an additional flat band intersecting at the Dirac point. This 2D PC can be related to a zero index material with effective permittivity and permeability equal to zero simultaneously. The finite element method is used to simulate the transmission characteristics of electromagnetic waves in photonic crystals. The simulation results show that the phase of the electromagnetic waves at the Dirac point frequency does not change, and their transmission characteristics are the same as those in zero refractive index material. With a concave lens made of such kind of PC, a sub-wavelength focusing with 0.63 λ half-peak width of focus and a 4.12 λ focal length is realized.