Theoretical analysis on the dynamic absorption saturation in pulsed cavity ringdown spectroscopy

We perform a theoretical analysis on the transient dynamics of absorption saturation in pulsed cavity ringdown spectroscopy. Based on a coupled rate equation approach, modelling of the dynamic saturation is carried out to account for time-evolving intracavity photon density and absorbing population. Master equations are derived in terms of normalized system parameters, which enables one to systematically study the non-exponential feature of saturated cavity ringdown signals. Erroneous quantification of sample absorbance by the conventional ringdown time analysis is numerically simulated, and the saturated spectral feature showing a Lamb dip is obtained for a Doppler broadened sample. Finally a novel numerical recipe is proposed to handle saturated ringdown signals and retrieve unsaturated spectra, allowing relevant absorption parameters without degrading the measurement signal-to-noise ratio.