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Laser Applications to Chemical, Security and Environmental Analysis

Theoretical model analysis of the dynamic saturation in cavity ringdown spectroscopy

Jae Yong Lee, Jae Won HAHN

Published Jan 1, 2002• 0 citations
Publisher

Abstract

Transient saturation in cavity ringdown spectroscopy is theoretically modeled with coupled rate equations accounting for the dynamics of intracavity photons and absorber population, which permits a recipe for retrieving original spectra in the saturation regime.
DOI
10.1364/lacea.2002.fd2

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Theoretical quantitative considerations as well as experimental data are presented based on absorption population depletion coupled with cavity ringdown spectroscopy. The absorbing number densities inside the cavity are determined by numerical integration of the coupled rate equations. The number of photons involved in absorption, cavity losses due to mirror reflectivity and stimulated emission are taken into account. The principle is to monitor a first transition by cavity ringdown spectroscopy while a second transition, with a state in common, is resonantly excited by the decaying radiation of different frequency also trapped inside the optical cavity. A numerical example is given for atomic lines of neon and the measurements carried out in a supersonic slit-jet expansion discharge demonstrate the feasibility of the technique. The technique is also proven to work with two resonant transitions of C2. Translational velocity of the jet modifying the rate equations is included in the model.
Cavity Ring Down Spectroscopy has become an important method in gas phase spectroscopy and its uses promise to expand. While previous investigators have considered the decay of the stored energy in the cavity ring down cell following short pulsed excitation, this paper considers the effects of pulse reshaping during cavity ring down. It is found that in order to properly model these effects, one must consider not only the mode dependent loss of the ring down cavity, but also dispersion that shifts the resonant modes of the cavity. Only by considering the latter effect does one get a "causal" result where the free induction decay signal of the absorber occurs after the excitation pulse. It is demonstrated that in the limit that the cavity round trip time is long compared to both the T 2 time of the intracavity absorber and the temporal width of the excitation pulse, the reshaping of the n'th pulse out of the ring down cavity is the same as the reshaping produced by free space propagation over a distance of (2 n + 1) L where L is the separation of the mirrors in the cell. However, when the absorber T 2 becomes comparable to or longer than the cavity round trip time, then discrete modes of the ring down cavity become important. A general expression for the output is given for the important case of a weak absorber, and changes in the output are computed for a single absorption line as a function of the ratio of T 2 to the cavity round trip time for several values of the optical thickness of the sample. Lastly, it is suggested that monitoring changes in the pulse shape of the cavity ring down signal provides a way to characterize an absorption spectrum on a frequency scale of the laser bandwidth down to the cavity free spectral range.
We develop an analytical approach to the dynamics of band populations of reverse saturable absorbers modeled by the three-level approximation of the five-level rate equations. We find high-accuracy approximate solutions to these rate equations, taking into account the temporal shape of the incident laser pulse for different regimes of excitation. The results obtained are confirmed by direct numerical integration of the rate equations and are verified by solution of the full system of the rate and the propagation equations. The validity ranges of the approximations are determined. We also prove that for input pulses that are much longer than the lifetime of the first excited state the ground-state depletion obeys the same functional dependence on the input fluence as in the case of rectangular input pulses. The dynamics of the excited states, however, explicitly depends on the pulse shape. We quantitatively estimate the effect of various parameters on the nonlinear absorption coefficient and discuss implementation of the approach by a beam propagation method to reduce the computational time.
We propose a new simple approximate solution to the two-state rate equation model for analyzing decay signals of saturation cavity ring-down spectrometry in the adiabatic and low-saturation regime. It helps obtain baseline-immune Doppler-free spectra for hyperfine transitions and linear absorption coefficients of a gas in the saturation regime. To demonstrate it, a baseline-immune Lamb dip spectrum of the R1A2 transitions in the 2v2 + v3 band of methane was recorded. The line position was determined to be 6 076.108 457 7(11) cm-1, the relative uncertainty being 1.8 × 10-10.