Numerical investigation on the cavity ring-down signal produced by a pulsed laser excitation of a Fabry-Perot cavity

In the presence of pulsed laser excitations, a Fabry-Perot cavity produces an optical signal transmission which decays out exponentially with a time rate proportional to the cavity loss. The signal is thus referred to as a ring-down signal and its feature provides a simple physical background for cavity ring-down spectroscopy (CRDS) to measure the ultralow absorption of a sample contained in the cavity. Numerical calculations are performed on temporal profile, intensity modulation behavior, and output coupling efficiency of the ring-down signal. The assumption made for the investigation is that a Fourier-transform-limited Gaussian laser pulse be injected to a stable empty cavity with complete mode-match to the lowest cavity transverse mode. It is found that the ring-down signal is generally superimposed by an inherent intensity modulation and a transient peak. The behavior dramatically changes depending on the excitation pulse duration and the cavity parameters such as the cavity free-spectral-range and the frequency detuning. Intuitive and straight forward time domain pictures are provided to allow understanding of the features in the context of time domain interference characterized by the amount of temporal overlap and the phase shift between the interfering fields. Also predicted is the superluminal transmission in a Fabry-Perot cavity which is confirmed by both the numerical calculation of the transmitted pulse profile in time domain and theoretical analysis based on the frequency domain description.