相位修正的耦合模理论用于计算光纤Bragg光栅法布里-珀罗腔透射谱

Phase-modified coupled mode theory for calculation of fiber Bragg grating Fabry-Perot cavity transmission spectrum

基于光纤Bragg光栅(FBG)反射复振幅相移对FBG法布里-珀罗腔透射谱的影响,分析了传统耦合模理论计算均匀FBG反射复振幅相移产生误差的原因.引入折射率分布初始相位参数描述FBG折射率分布纵向的微小偏移,用真实的反透射系数代替简明形式的反透射系数,对传统耦合模理论进行了修正,增加了与折射率分布初始相位参数有关而与波长无关的相位因子.在此基础上进一步对计算非均匀FBG的传输矩阵法的相位进行了修正.修正后的快速计算结果用于FBG法布里-珀罗腔透射谱的计算,可反映折射率分布初始相位参数对透射峰波长位置的影响,与Rouard算法及实验值均有较好的一致性.

Based on the influence of reflection phase of fibre Bragg grating on the transmission spectrum of fibre Bragg grating（FBG） Fabry-Perot cavity, the reason for the error of traditional coupled mode theory when calculating the reflection phase of uniform FBG is analyzed. A parameter of initial phase of effective index distribution is introduced to describe the slight offset of the index distribution of FBG in the longitudinal direction, and the real reflection and transmission coefficients are substituted for the simplified coefficients to modify the traditional coupled mode theory by introducing a phase factor, which is related with the initial phase of effective index distribution and independent of wavelength. The phase of transfer matrix method for nonuniform FBG is further modified. The modified fast calculation results are used to calculate the transmission spectrum of FBG F-P cavity and show the influence of initial phase of effective index distribution on the wavelength offset of FBG Fabry-Perot cavity transmission peaks. The results agree with those of Rouard method and experimental values.