采用正交函数算法,提出了一种新型椭圆孔光子晶体光纤的本地正交函数模型。采用两种周期性结构的叠加构造超格子,用以表征光子晶体光纤(PCF)的横向折射率分布,同时将横向电场展开为Hermite-Gaussian函数。从电磁场的波动方程出发得到关于传播常数的本征方程。进而得到光子晶体光纤的传播常数、模场分布、偏振特性等传输特性。应用此模型讨论了椭圆孔光子晶体光纤基模两个偏振模式的双折射和群速度走离特性。研究表明,椭圆孔光子晶体光纤具有较大的模式双折射和群速度走离,双折射、群速度走离与频率的依赖关系和普通保偏光纤不同。另外椭圆孔光子晶体光纤还可实现在单模区同时保持高双折射和零群速度走离,可用于研究光纤的非线性。

A novel model for light propagation in elliptical-hole photonic crystal fibers (PCF) is developed with localized orthogonal function method. The dielectric constant of the PCF missing the central air hole is considered as the sum of two different periodic dielectric structures of virtual perfect photonic crystals, and the electric field is decomposed using the localized Hermite-Gaussian functions. From the wave equations and the orthonormality of Hermite- Gaussian functions, the propagation characteristics of the PCF, such as the mode field distribution, the effective area, the birefringence, and the dispersion properties are obtained. The birefringence and group velocity walkoff parameters of elliptical-hole PCF are analyzed with this model. It is shown that the birefringence and group velocity walkoff parameters are typically stronger than that of the conventional fibers for comparable parameters, and exhibit frequency dependence quite unlike conventional birefringence systems. Moreover the unusual combination of strong birefringence with zero group velocity walkoff can be obtained, which may allow the novel nonlinear applications.