一类带PML光波导中的共轭特征算子构造

将无界三层带有不平坦界面的光波导经坐标变换和完美匹配层截断近似转化为有界且带有平坦界面的光波导,利用复Helmhotz方程求解波的传播计算问题,推导出了该复偏微分方程的共轭特征函数所满足的方程,并论证了方程的特征函数与共轭特征函数正交之性质,同时给出局部基下坐标计算的简便公式.

Construction of Conjugate Characteristic Operator for a Class of the Optical Waveguides with PML

The unbounded optical waveguide with three curved interfaces were converted into the bounded optical waveguide with flat interfaces by coordinate transform and terminated by the perfectly matched layer.The paper used the improved and complex Helmholtz equation to solve the wave propagation problem,deduced the equation for the conjugate eigenfunctions of improved and complex Helmholtz equation,proved the orthogonal property between the characteristic eigenfunctions and the conjugate eigenfunctions,and provided a simple formula for calculating the coordinates under the local bases.