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

Abstract

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.