将光纤布拉格光栅近似为一维光子晶体,研究光栅的能带结构和光学传输特性。利用平面波展开法对光子晶体进行理论研究,将研究方法移植到光纤布拉格光栅上,并对其进行数值分析,得到光栅的传输特性。研究表明,光栅反射谱有多个反射峰,峰值中心频率是基频的整数倍,而且峰值处存在光子带隙,反射峰带宽对应光子带隙宽度,中心频率和带宽随光栅长度、高介电常量材料占空比、调制深度而变化。结果与传统的耦合模理论一致。

The band structure and the transmission properties of the fiber Bragg grating are investigated in the scope of the photonic crystal. The plane wave expansion method is used to analyze the photonic crystal, and is translated into the scope of the fiber Bragg gratings. The optical properties of the fiber Bragg grating are obtained after plenty of numerical computations. It shows that there are many reflection peak-value frequencies, which are integer times to the fundamental frequency. Every peak-value frequency reflects a photonic band gap, its center frequency and band width are related with the grating parameters, such as the grating length, the index modulation depth, and the duty ratio of the material with high dielectric constant. All results are same as those from the conventional coupling mode theory.