中文摘要：

从麦克斯韦方程出发，推导了长周期光栅耦合器在折射率、增益、损耗复合调制下完整的耦合理论模型。在此基础上，详细分析了该复合调制长周期光栅耦合器直通与交叉臂问的功率耦合和多波长滤波特性。结果表明，当增益／损耗调制与折射率调制作用相等时，复合调制长周期光栅耦合器具有单向非互易的功率耦合特性，而且随着多波长复用信号输入光纤和输入方向的不同，具有不同的上下话路滤波特性。在增益调制作用下，满足相位匹配条件的信号不仅可有效地耦合到交叉臂下话路输出，还能得到明显的放大；但当损耗调制时，直通与交叉臂中的信号功率均保持各自的初值，而且不再具备波长选择滤波能力。

英文摘要：

The unified coupled-mode theory for long-period-grating-coupler is obtained by deriving directly from Maxwell＇s equation when all the modulation effects of refractive-index, gain and loss are considered. Then, the characteristics of power coupling and signal filtering between the straight-arm and cross-arm of complex-modulated long-period-grating-coupler are investigated thoroughly. The results demonstrate that monodirectional nonreciprocal power coupling is shown when gain/loss is equal with refractive-index modulation. In addition, the complex- modulated long-period-grating-coupler shows different add/drop filtering characteristics if the multiplexed signals are injected from different fibers or directions. For the gain modulation, the phase-matched signal is coupled into the cross-arm and is amplified simultaneously. But for the loss modulation, the signals in straight-arm and cross-arm remain their respective original input power, and can not be filtered according to their wavelengths any more.