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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。
The dispersion characteristics of photonic crystal fiber (PCF) were studied by the finite difference method based on half vector wave equation. The central difference scheme is used to transform the semi-vector wave equation into the eigenvalue problem of the matrix, and the mode characteristics and propagation constants of the fiber are obtained. The calculation results are also analyzed. Numerical results show that the semi-vector finite difference method is in good agreement with the numerical results and the measured results obtained by the finite difference method and the finite element method of the full vector and is more accurate than the effective refractive index model based on the scalar equation , Which provides theoretical calculation tools for further designing photonic crystal fibers with proper dispersion characteristics.