提出应用“超格子构造法”研究光子晶体光纤(PCF)的传输特性。电场用正交完备的厄米-高斯(Hermite-Gauss)函数展开,有中心缺陷的周期性分布的介电常数用两组不同周期的介电常数分布迭加构成超格子,每组介电常数都用余弦函数展开,然后利用波动方程及厄米-高斯函数的正交性,得到光子晶体光纤的传输特性(模场分布、双折射、色散)。模式双折射的大小可用以衡量该算法的精度。

A novel supercell lattice method (SLM), induced from both the plane wave expansion method (PWM) and the semi vector method, is presented to analyze the photonic crystal fibers (PCF). The electric field is still expanded with the Hermite-Gaussian function, the dielectric constant of the PCF missing the center air hole can be considered as the sum of two perfect PCFs, which have different dielectric constant and different structure parameters (the hole pitch, the hole diameter). The periodical dielectric structures of the two perfect PCFs are expanded in cosine function with different periods. From the wave equation and the properties of Hermite-Gaussian function, the propagation characteristics of the PCF, such as the mode field distribution, birefringence, the dispersion property, can be obtained. The accuracy of the SLM can be scaled by the birefringence because the ideal triangular lattice PCF has no birefringence based on the group theory.