中文摘要：

光子晶体结构设计优化是理论研究的一个重要内容。运用平面波展开法对圆柱、方柱及正六边柱构造的二维三角格子光子晶体的禁带进行仿真计算,讨论了介质材料分别为GaAs、Si和Ge情况下,柱子形状、旋转角度、填充比的变化对完全光子禁带的影响。发现：对于二维三角格子光子晶体,相对于介质柱,空气柱更易获得完全光子禁带;而相对于圆柱及方柱,正六边柱得到的完全禁带宽度最大,所以二维三角格子的最优结构为Ge介质背景下的正六边空气柱,最优结构参数为θ=18°,d/a=0.92,最大禁带宽度Δmax=0.116（ωa/2πc）,研究结果可为今后实验制作大带隙二维三角格子光子晶体提供理论上的指导。

英文摘要：

Optimization design of photonic crystals is an important content of theoretically investigation.Plan Wave Expansion Method is used to simulate the photonic band gap（PBG） of 2D triangular lattice photonic crystals of circular column and square column and hexagonal column.When the dielectric materials are GaAs,Si and Ge,the influence of rods shape,rotation angle,filling rations on absolute photonic band gap are discussed.Conclusions as blow： For 2D triangular lattice photonic crystals,air rods are easier to obtain absolute PBG than dielectric rods.And compared with circular rods or square rods,hexagonal rods have the biggest complete PBG width： Δmax=0.116（ωa/2πc）.In a word,for 2D triangular photonic crystals,the optimum structure is hexagonal air rods,where dielectric is Ge,d/a equals to 0.92,θ equals to 18°.This result can provide theoretical instruction for 2D triangular photonic crystals with big photonic band gap.