为了对折射率型1维光子晶体缺陷波导中的光传输进行有效数值模拟, 采用此类型波导的厄米-高斯函数展开方法进行了研究。首先给出了计算方法的详细理论推导, 然后利用该方法计算了偏振态不同、结构参量不同的情况下波导本征模式的色散关系、模场空间分布、能量控制因子及等效折射率。结果表明, 1维光子晶体缺陷波导与阶跃平面光波导主要差别在于高阶模式, 且可通过调节1维光子晶体的结构参量来有效调控高阶模式的传输。

In order to simulate the light propagation in 1-D refractive-index-typed photonic crystal (PC) defect waveguide effectively, Hermite-Gaussian function expansion method was adopted. At first, the detailed theoretical derivations of the calculation method were presented. And then, dispersion relation, mode field patterns, energy control factor and equivalent refractive index of 1-D PC waveguides with different polarizations and different structural parameters were calculated. The results show that there are significant differences in the high-ordered modes between 1-D PC defect waveguides and step planar waveguides. The transmission of high-order modes can be controlled effectively by adjusting the structural parameters of 1-D PC.