由于具有复杂的折射率分布,光子晶体光纤一般需要采用数值方法进行研究。有效折射率方法最早用来研究光子晶体光纤的模式特征及其色散特性,但是一般采用标量近似的方法。建立了研究光子晶体光纤的矢量有效折射率方法,并用于计算光子晶体光纤的色散常数。类比于阶跃型折射率光纤,只需将电磁场所满足的相应的贝塞尔函数代入阶跃型折射率光纤所满足的矢量特征方程即可求解光子晶体光纤包层的有效折射率。采用矢量有效折射率方法的计算结果与基于有限元方法求解的数值结果和测量结果吻合得更好。

The complex refractive index distribution of photonic crystal fibers makes a numerical algorithm necessary. An effective index method based on weak-guidance approximation is often used to study the modal properties of such fibers including their dispersion properties. In this paper, a fully vectorial effective index method is formulated for photonic crystal fibers based on the solution of the vectorial characteristic equation and is used to compute the dispersion parameters of photonic crystal fibers. In analogy with step-index fibers, the effective index of the photonic crystal fiber cladding can be calculated simply by substituting the appropriate Bessel functions of the electromagnetic field into the vectorial characteristic equation for step-index fibers. The result obtained by the vectorial effective index method is in better agreement with those by the finite element methods and measured data.