FMC-based Analysis Method For Phase Spectra Of Fiber Bragg Gratings And Its Applications

Fiber Bragg gratings(FBGs)have been widely used in the field of optical fiber communication and sensing,and will play an important role in the all-optical communication networks and modern optical fiber sensing technologies.With the deepening of theoretical research and the continuous innovation of manufacturing methods,FBGs have become the most promising and representative passive fiber components,and are mainly applied based on the amplitude spectrum.At the same time,the phase spectrum of FBGs are extremely sensitive to their structural changes,and are closely related to their delay and dispersion,which make FBGs applicable to high-sensitivity sensing,RF photon filtering,dispersion compensation for ultrafast fiber lasers,micro-distributed sensing,and signal processing.Therefore,it is of great practical significance and academic reference value to study the phase spectrum characteristics of FBGs.In this paper,the analysis theory of the phase spectrum characteristics of FBGs is deeply studied based on Fourier mode coupling(FMC)theory.And the theory is applied to analyzing the phase spectrum of FBGs and designing arbitrary FBGs.The main contents include:(1)The development of FBGs are briefly described.And the applications about phase spectrum of FBGs in the field of fiber-optic communication and fiber-optic sensing are also roughly summarized.In addition,the theoretical analysis methods for phase spectrum and the design method of FBGs are comparatively analyzed,respectively.(2)The FMC theory of FBGs is introduced in detail.Based on FMC theory,the phase characteristics of FBGs and the general solution that is suitable for analyzing the phase responses of arbitrary FBGs are expounded,and the analytical solutions for the phase spectrum of some common non-uniform FBGs are obtained.On the basis of the above theoretical research,the reverse designed theory of arbitrary complex FBGs is proposed.(3)According to the general solution and analytical solutions of the phase spectrum,the phase spectrum of different non-uniform FBGs,such as phase shift,apodized,superstructure and chirp gratings,are simulated and analyzed,and compared with the results obtained by the transmission matrix(TM)analysis method and the multilayer film analysis method.The comparison results show that the phase spectrum analysis method based on the FMC theory has high accuracy,efficiency and universality.(4)According to the general solution of the phase spectrum of FBGs,the delay anddispersion characteristics of different non-uniform FBGs are analyzed and calculated,and compared with the results of the TM method.(5)According to the FMC theory and phase spectrum characteristics,the design theory and algorithm of FBGs are established,which can be used to design FBGs with arbitrary spectrum.FBGs with arbitrary triangular,double triangular,Gaussian and comb-like reflectivites are designed respectively,and the design results were analyzed and verified by using the direct Fourier transform(FT)analysis method.The analysis and verification results show that the designed FBGs have desired response spectrum accurately.