利用BPM对MEMS波分复用系统中的渐变折射率波导的性能进行分析。详细推导了BPM的微分方程, 并给出了BPM微分方程的有限差分解的形式。并根据FDBPM对已知折射率分布的径向渐变折射率波导进行数值计算分析, 其结果表明, 在波长为1.55 μm的高斯光束垂直入射的情况下, 中心折射率为1.5901, 聚焦参数为0.052 μm-1, 并且半径为3 μm的平方律渐变波导中具有快速稳定的、高传输率的高斯基模分布。

The performance of gradient index waveguides in wavelength division multiplexer (WDM) based on Micro Electro-Mechanical System (MEMS) is analyzed. The BPM differential equation is deduced in detail, at the same time, its finite difference solution is put forward. According to the finite difference beam propagation method (FDBPM), radial gradient refractive index waveguides whose refractive index profile is offered are calculated numerical and analyzed. The results indicate that there has fast stable and high transfer rate Gaussian mode in the waveguides when the vertical incident light beam is Gaussian beam with wavelength of 1.55 μm, that waveguides have center refractive index of 1.5901, focusing parameter of 0.052 μm-1 and radius of 3 μm.