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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。
A simplified iterative algorithm is used to solve the simplified eigenvalue equation of the cladding model. The initial value is selected by the machine. The method does not require human intervention. The core code only needs tens of rows and can be calculated quickly. The effective refractive index (including real number solution and complex number solution) of each cladding mode is calculated, so that the refractive index characteristics of long period fiber grating (LPG) can be numerically simulated over a wide range. Compared with the experimental results, it is proved that this algorithm is a more effective method to solve the super complex transcendental equation with multiple complex roots. This is of great significance for the application of this algorithm to study more cladding gratings and coated fiber gratings A certain meaning.