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在多模光纤模式色散求解、光纤耦合模理论分析以及锥形光纤的模式演化等过程中,都涉及到多模阶跃光纤纤芯传导模式的特征方程的求解,计算量很大,从而直接影响整体的计算效率。分析了牛顿迭代法及其收敛速度的优势。求解弱导近似下的标量模式特征方程时,利用第一类贝塞尔函数的零点确定其解区间,再结合牛顿迭代法在区间内快速求解特征方程。将此求解过程引入矢量模式特征方程求解中,并结合上下边界截弦的方式快速判断特征方程尾根与首根的存在性问题。将此方法的计算结果与OptiFiber软件的计算结果作对比,画出光纤的模式色散曲线,验证了该快速求解方法的正确性。
In the process of multimode fiber mode dispersion solution, fiber coupled mode theory analysis and the mode evolution of tapered fiber, it involves the solution of the characteristic equation of multimode step fiber core conduction mode, which has a large amount of calculation and thus has a direct impact on The overall computational efficiency. The advantages of Newton iteration method and its convergence speed are analyzed. When solving the scalar mode characteristic equation with weak guide approximation, the solution interval of the Bessel function of the first kind is determined by its zero point, and then the characteristic equation is solved quickly by the Newton iteration method in the interval. The solution process is introduced into the eigenvalue equation of vector mode, and the existence of the root and the first root of the eigenvalue equation is quickly judged by the truncation of the upper and lower boundary. The calculation results of this method are compared with those of OptiFiber software, and the mode dispersion curve of optical fiber is drawn. The correctness of this method is verified.