采用基于半矢量波动方程的有限差分法研究了光子晶体光纤(PCF)的色散特性。利用中心差分格式将半矢量波动方程转化为矩阵的特征值问题,进而得到光纤的模式特征和传播常数,并对计算结果进行了分析。数值计算结果表明,半矢量的有限差分法与全矢量的有限差分法和有限元方法求解的数值结果以及测量结果吻合得很好,而比基于标量方程的有效折射率模型得到的结果更为精确,为进一步设计具有适当色散特性的光子晶体光纤提供了理论计算工具。

A finite difference scheme based on semi-vectorial wave equations is used to study the dispersion properties of photonic crystal fibers (PCF). Using a central difference scheme, the semi-vectorial wave equations are cast into algebraic eigenvalue problems, from which modal fields and propagation constants are obtained. The results obtained by the semi-vectorial finite difference method are coincided well with those by the full-vectorial finite difference method and the finite element method as well as experimental results, and are more accurate than those by the scalar effective index model. It can be shown that the semi-vectorial finite difference method is an effective numerical tool for the design of photonic crystal fibers with desirable dispersion.