基于平方根算符的2维广角有限差分波束传播法

有限差分波束传播法 (FD BPM)是模拟光在光波导器件中行为特性的重要数值方法 ,它的模拟精度决定于它的帕德 (Pad啨)展开阶数以及计算步长 ,阶数越高或计算步长越小精度就越高 ,但是计算时间就越长。为了在比较低的阶数和适中的步长下获得较高的计算精度 ,从平方根算符出发 ,运用了一些试探性的展开方法对平方根算符进行处理 ,得到 3种 2阶广角波束传播法计算公式 ,数值计算表明这些公式比传统广角波束传播法的 2阶计算公式具有更高的精度 ,而且可以将该试探性处理方法推广到更高阶的广角波束传播法。

Two-Dimensional Wide-Angle Finite Difference Beam Propagation Method Based on the Square Root Operator

The finite difference beam propagation method(FD-BPM)is very powerful and has been widely used for optical waveguide design. The precision of the method is decided by the order of Padé approximation and the step of calculation, which means higher order and smaller step will introduce smaller error, but the calculation time will be longer. For the purpose to obtain higher precision and shorter calculation time, some trial methods are used, and some new second order formulas expanded from the square root operator for BPM are got, and the numerical simulations show that the coefficients of those new second order formulas are more precise than that of the conventional one. Furthermore, the analysis also indicates that those trial methods can be applied to the higher order formulas for the FD-BPM.