Analytic models of spectral responses of fiber-grating-based interferometers on FMC theory

In this paper the analytic models (AMs) of the spectral responses of fiber-grating-based interferometers are derived from the Fourier mode coupling (FMC) theory proposed recently. The interferometers include Fabry-Perot cavity, Mach-Zehnder and Michelson interferometers, which are constructed by uniform fiber Bragg gratings and long-period fiber gratings, and also by Gaussian-apodized ones. The calculated spectra based on the analytic models are achieved, and compared with the measured cases and those on the transfer matrix (TM) method. The calculations and comparisons have confirmed that the AM-based spectrum is in excellent agreement with the TM-based one and the measured case, of which the efficiency is improved up to ~2990 times that of the TM method for non-uniform-grating-based in-fiber interferometers.