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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。
Due to the complicated refractive index distribution, photonic crystal fibers generally need to be studied numerically. The effective refractive index method was first used to study the mode characteristics and dispersion characteristics of photonic crystal fiber, but generally the method of scalar approximation. The method of vector effective refractive index for photonic crystal fiber is established and used to calculate the dispersion constant of photonic crystal fiber. Analogously to the step index optical fiber, the effective refractive index of the photonic crystal optical fiber cladding can be solved simply by substituting the corresponding Bessel function that the electromagnetic field satisfies into the vector characteristic equation satisfied by the step index optical fiber. The calculated results using the vector effective refractive index method are in good agreement with the numerical and numerical results based on the finite element method.