用等效经验关系法研究光子晶体光纤的非线性

Study on the Nonlinear Parameter of Photonic Crystal Fiber by Empirical Relations

运用具有三角形孔格子结构的光子晶体光纤(PCF)的近似经验关系与等效折射率模型相结合的方法来研究PCF的非线性。总结更为简捷的经验关系式进行计算,避开复杂的全矢量计算,得到了PCF基模和空间填充基模的有效折射率。利用等效折射率模型,以传统的阶跃光纤等效替代PCF,以光纤的数值孔径作为两个模型的关联点,得到了PCF的有效纤芯面积的简洁表达式。并在此基础上全面讨论了PCF的非线性与其结构参数及材料参数之间的关系,得到了与实际材料非线性相吻合的结论。

The nonlinear parameter of photonic crystal fiber （PCF） with triangular lattice structure is studied by using the empirical relations and the effective-index model of PCF. More simple empirical relations are summed up, the problems of requiring large computational resources and time in full-vector analysis are resolved by using the empirical relations, and the effective index of the fundamental guided mode and space-filling mode in the triangular air-hole lattice are calculated with it. With the effective-index model of PCF, the PCF with triangular lattice structure is replaced by an equivalent conventional fiber, an effective core area of a PCF of simple expressions is obtained, in which the fiber numerical aperture is used as an association point of the two models. Based on the simple formula, the nonlinear parameter of photonic crystal fibers with different structural/material parameters are fully discussed, and several conclusions coincide with the actual material nonlinearity （the known conclusions） are expressed.