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。

The solution of characteristic equation of multimode step-index fiber core conduction mode is involved in many cases, such as the mode dispersion solution of multimode fiber, the theory analysis of optical fiber coupled-mode, and the mode evolution of tapered fiber. The large computation capability of this solution affects the whole computational efficiency directly. The Newton-Raphson iteration method is analyzed and it has obvious advantage in convergence speed. In the solving process of scalar mode characteristic equation under the weak-guidance approximation, we use the zero point of the type I Bessel function to determine the interval of roots, then solve the characteristic equation quickly in the interval by combining the Newton-Raphson iteration method. The solving process is introduced in the solving of vector mode characteristic equation, and its first root and last root are determined quickly by combining the way of upper and lower boundary chord intercept. Finally, we compare the calculation results of our method with the results of OptiFiber software, draw the mode dispersion curve of fiber, and verify the accuracy of our method.