平面光波导器件时域有限差分束传输法分析中边界和初始条件的处理

从慢变包络（SVEA）时域光传输方程出发，对比了综合道格拉斯（GD）和传统的中心差分（CN）两种离散化格式，指出GD法比CN法精度有了很大提高.重点讨论了GD法的TD-BPM边界处理问题，给出了吸收边界和透明边界离散的显式和隐式表达式，分析并确定了交替方向隐式法（ADIM）的边界处理方式;同时，对激励源加入的连接边界进行了仔细讨论.结果表明对于隐式GD-TD-BPM法边界处理应采用隐式，中间激励更能反映光波导反射场的情况.

Boundary Condition and Initial Condition in the Time-domain Beam Propagation Methods Applied to Study Planar Waveguides

Based on time-domain beam propagation methods (TD-BPM) with the slowly varying envelope approximation (SVEA), both schemes of generalized Douglas(GD)and conventional central-difference(CN)have been respectively used to disperse lightwave transmission equation, and have been compared each other. The results showed that the former is more accurate. The explicit and implicit expressions of absorbing and transparent boundary condition have been derived for the GD scheme in TD-BPM, respectively. The boundary condition based on the alternating-direction implicit method(ADIM)was also established. Meanwhile, incident wave and connecting condition have been discussed in details. As a result, the boundary condition of implicit GD-TD-BPM must apply implicit expression, and settling incident wave in computational region may effectively detail the reflected field.