多层“台阶”近似方法中层数与计算误差的关系

多层"台阶"近似方法是将平板波导中折射率随厚度变化的曲线近似地用N层台阶形的折线来代替,使每一个小区域内折射率成为常数,由此得到电磁场分布和传播常数.本文从理论上给出了层数N与计算精度之间的关系.推导出在分割成N层和2N层两种近似下的计算值精度的改进.本文结果适用于任何渐变折射率平板光波导.

THE RELATION OF THE LAYER NUMBER N AND CALCULATING ERROR IN MULTILAYER "STAIRCASE"APPROXIMATION METHOD

In multilayer"staircase"approximation method,a graded refraction index planar waveguide is replaced approximately by a"staircase"of N layers.Within each layer the index value is a contant. In this way the fields of the multilayer structure may be calculated and the propagation constant can be found.In this paper the analytic relation of the layer number and calculating error is presented exactly.The relative error between N-layers and 2N-layers approximations is gven.The result is valid to any planar waveguide with graded refractive index.