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提出了一种用于分析光子晶体光纤的正交函数模型。采用一种新型超格子的构造方法 ,将光子晶体光纤的横向介电常量表示为两种周期性结构叠加。将横向电场以厄密高斯函数展开 ,利用正交函数的性质 ,将全矢量波动方程转化为矩阵本征值问题 ,求解本征值问题可得到模式的传输常量及模场分布。利用此模型举例讨论了椭圆孔三角格子光子晶体光纤的模场分布和偏振特性以及三角格子光子晶体光纤的色散特性和有效面积等传输特性。作为一种普适的模型 ,此方法还可适用于四方结构、蜂窝结构及椭圆孔等多种结构光子晶体光纤。
An orthogonal function model for analyzing photonic crystal fibers is proposed. A new type of superglass construction method is used to represent the transverse dielectric constant of photonic crystal fiber as two periodic structure superpositions. The transverse electric field is developed by Hermitian Gaussian function. By using the properties of orthogonal function, the full vector wave equation can be transformed into the matrix eigenvalue problem. For the eigenvalue problem, the transmission constants and mode field distribution can be obtained. The model is used to discuss the mode field distribution and polarization characteristics of elliptical triangular lattice photonic crystal fiber and the transmission characteristics of the triangular lattice photonic crystal fiber such as dispersion characteristic and effective area. As a universal model, this method can also be applied to a variety of structured photonic crystal fibers such as tetragonal structures, honeycomb structures and elliptical holes.