Modeling of active fiber loop ring-down spectroscopy considering non-linear effects of EDFA gain

Non-linear effects of erbium-doped fiber amplifier (EDFA) gain have been significant factors in deteriorating the performance of active fiber loop ring-down spectroscopy (FLRDS). The non-linear effects involve two aspects: the gain saturation and the non-uniformity of the gain spectrum. The gain saturation of EDFA induces pulse-to-pulse gain fluctuations, which causes ring-down decays to deviate from the exponential law. The non-uniform gain spectrum introduces measurement errors in the active FLRDS systems operating in wavelength-tuning or wavelength-switching modes. A theoretical model of active FLRDS that integrates both non-linear gain effects is presented in this paper. It can be used for qualitative and quantitative analysis of the measurement errors introduced by the non-linear gain effects on the active FLRDS. The model provides theoretical guidance to the performance prediction and optimization of the active FLRDS systems.