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

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.