采用分步迭代算法对简化的包层模式本征方程进行数值求解, 这种方法由机器选取初值, 整个过程无需人工干预, 核心代码只需几十行且计算速度快, 可求解任意环境折射率下各次包层模式的有效折射率(包括实数解和复数解), 从而可在很宽的范围内对长周期光纤光栅(LPG)的折射率特性进行数值仿真。与实验结果进行了对比, 证明了该算法对求解拥有多个复数根的超复杂超越方程是一种比较有效的方法, 这对于应用该算法研究更多包层光栅及镀膜光纤光栅的其他特性具有一定的意义。

The simplified eigenvalue equation of cladding modes is numerically solved with step iterative method (SIM). For this method, the initial value is chosen by the machine and requires no manual intervention. The core codes can be computed rapidly in only tens of lines, and the effective refractive index of each sub-cladding can be solved with arbitrary refractive index. The simulations of the refractive properties of long period fiber grating(LPG) can be performed in a wide range. Comparative results indicate that this method is effective for solving ultra-complex transcendental equation with several complex roots.