从耦合模理论和传输矩阵方法出发, 介绍了一种设计复杂光纤光栅的有效的简单方法。该方法只考虑光栅内部的一级反射, 发现滤波器的反射谱和FBG的耦合函数间存在近似的傅里叶变换关系, 能简单快速地对弱反射光栅进行设计。该方法的有效性通过设计光纤通信系统中常用的两种色散补偿器得以体现：第一种色散补偿器的色散值在3dB带宽内恒为17ps/nm, 另一种则为具有线性色散斜率的色散补偿器。数值仿真结果表明：此方法可以有效地从反射信息中提取光纤光栅参数, 能够应用在利用光纤光栅反射特性的复杂滤波器的设计中。

The approach of inferring the grating profile from its reflection spectrum is referred to as fiber Bragg grating (FBG) synthesis algorithm. Synthesis of FBG is of great significance for the design of special FBG to have desired characteristics. A simple and efficient method based on the coupled-mode theory and transfer matrix method for the design of complex FBG was proposed. The method takes into account only the first reflection, exploiting the approximate Fourier transform relation that exists between the filter spectral response and the coupling function. Its low algorithmic complexity enables the fast synthesis of weak reflection FBG. The method is illustrated by designing two types of dispersion compensators for the applications of optical fiber communication systems, constant dispersion coefficient with 17ps/nm in its 3dB passband and linear dispersion slope coefficient compensators. Numerical simulation results show that the method is very effective for parameter reconstruction of fiber gratings according to desired reflectivity characteristics and can be applied in the design of complex filter based on the reflectivity characteristics of fiber gratings.