中文摘要：

从麦克斯韦方程组出发，通过将光纤波导扰动和光栅折射率调制扰动效应转换成等效的耦合系数，推导出光纤布拉格光栅耦合器的统一特征方程。采用打靶法并结合朗格一库塔（Runge-Kutta）数值积分对两种光纤布拉格光栅耦合器型上下话路滤波器的传输特性进行了详细的分析。结果表明，对于光栅破坏耦合器，利用光栅引入的强色散效应，滤波器的波长选择能力得到极大的提高，低于1nm的带宽能够满足波分复用（WDM）系统的需求，并且当光栅调制的等效耦合远远超过两光纤消逝场间的耦合效率时，不仅有效地抑制了反射信号。使满足布拉格匹配条件的信号透射输出，还消除了旁瓣纹波；而对于光栅辅助耦合器。其非干涉本质使得器件性能更加稳定，并可通过调整光栅长度进一步改善滤波响应。

英文摘要：

The unified coupled-mode equation for Bragg-grating-coupler was obtained by deriving directly from Maxwell＇s equations when both the fiber perturbation and grating-induced refractive index modulation were transferred into the equivalent coupling coefficients. Utilizing the shooting method and Runge~Kutta numerical integral, two types of add-drop filter based on fiber-Bragg-grating（FBG） coupler were investigated thoroughly. The results demonstrated that for grating-frustrated-coupler, the filter＇s wavelength selectivity was improved obviously by the grating-induced strong dispersion and the spectral bandwidth could be less than 1nm to satisfy the wavelength division multiplexing （WDM） system. In addition, when grating coupling coefficient was far larger than evanescent field coupling coefficient, the grating-frustrated coupler transmitted the signal at Bragg wavelength and suppressed back-reflected and sidelobe ripple effectively. For the grating-assisted-coupler, the inherent noninterferometric made it very stable, and allowed to improve the spectral response of the filter by adjusting grating length.