为了研究光场在二维光子晶体中的传播特性,本文应用平面波展开法,得到了二维三角晶格光子晶体的能带结构,在此基础上,运用时域有限差分法,分析了在一定入射角度下,特定频率的光束在光子晶体中的负折射现象,由于应用光子晶体的自准直效应,光束束腰在传播过程中展宽较小。研究了由于能带交折、重叠而产生的特殊色散特性和超棱镜效应,给出了光子晶体内外的磁场强度的分布,得到了极高的角色散度。文章的研究结果对研究基于光子晶体超棱镜效应的波分复用器,具有指导意义。

To research the propagation of electromagnetic fields in a two-dimensional (2D) photonic crystal, we investigate the negative refraction phenomenon of an incident Gaussian beam with some wavelengths and incident angles by means of numerical simulations,where the plane wave expansion (PWE) and 2D Finite Difference Time Domain (FDTD) methods are applied, and because of self-guiding in photonic crystal, the width of the beam will not be expanded. Moreover, we study the unique dispersive properties and super-prism effect in a 2D triangle lattice photonic crystal, these dispersive properties are caused by band folding, band crossing, and band deformations in the vicinity of mode gaps and bandgaps. The results obtained in this paper are of great significance to wavelength demultiplexers based on the superprism phenomena.