光子晶体光纤模式截止特性的理论分析

"无限单模传输"特性是光子晶体光纤最引人注目的特性,Birks等用有效折射率模型对其进行了合理的解释,但定量分析误差很大,而且由于进行了标量近似,填充比较大时不适用.我们仍采用该法,但作了改进:(1)有效纤芯半径和二阶模截止的归一化频率的选取更准确;(2)采用了全矢量方法.研究了光子晶体光纤的模式截止特性,得到了在不同结构参量下归一化频率与相对波数的依赖关系和二阶模截止的相对波数与结构参量的依赖关系,并由后一关系曲线及其渐近线将光子晶体光纤的工作区域划分为无限单模、单模和多模区域.结果与其它数值方法的结果一致性很好,而且方法较其它方法更为简便.

Theoretical analysis of mode cutoff in photonic crystal fibers

" Endlessly single-mode " operation is the most remarkable characteristic of photonic crystal fibers. Birks et al. explained it reasonably by effective index model, but considerable error was engender in quantitative analysis, and the properties of photonic crystal fibers with larger filling ratio can't be analyzed by this method because of its scalar approximation. Effective index model is applied for modeling photonic crystal fibers, but improvement is made: (1) effective core radius and the normalized frequency which determines the second modal cutoff are more exact; (2) full vector method is used. The characteristic of mode cutoff of photonic crystal fibers is studied. The normalized frequency is calculated for a range of fiber parameters and wavelengths. Relative cutoff wave number for some fiber parameters is obtined, and the relative cutoff wave number and its asymptotic bound are used to determine the boundary of three operation regimes of photonic crystal fibers with endlessly single-mode, single-mode and multi-mode operation. The result obtained is in good agreement with numerical methods, and calculation is more convenient than numerical methods.