A theoretical model based on the ray-transfer matrix is developed for the pulsed cavity ring-down (CRD) technique to numerically investigate the influence of the geometric parameters of the pulsed-CRD arrangement on the CRD signal. By fitting the spatial distribution of the pulsed laser beam to that of the TEM_(00) cavity mode, the geometric parameters are optimized to obtain perfect matching between the laser beam and the ring-down cavity. It is indicated by the numerical simulations that as long as the laser power exiting the ring-down cavity is fully collected, a single exponential-decay signal, identical to the perfectly-matched CRD signal, is obtained in the mismatching case to determine accurately the cavity decay time. Intensity fluctuations appear in the mismatched CRD signal if the laser power exiting the ring-down cavity is not fully collected. Both the conventional exponential decay fitting approach and a linear fitting procedure are employed to analyze these mismatched CRD signals and the latter is recommended to make an accurate pulsed-CRD measurement.
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