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Molecular Physics

Three-level depletion by cavity ringdown absorption spectroscopy: proof of concept

Fabio J. Mazzotti, Lizandra Barrios, Ranjini Raghunandan, John Paul Maier

Published Sep 10, 2012• 1 citation

Abstract

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.

DOI: 10.1080/00268976.2012.724458

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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.

Laser spectroscopy experiments are reported on rubidium atoms by using two or three external cavity diode lasers to study multiple resonance transitions in Λ- and V-type systems as well as on (Λ+V)-type system. Electromagnetically induced transparency (EIT) peaks having sub-natural line-widths are found on the Doppler broadened transmission backgrounds with velocity selective enhanced absorption dips. In the presence of a pump laser, probe spectrum shows enhancement of EIT signal by tuning the control laser frequency when the Λ- and V-type EIT signals are made to overlap. Theoretical analysis is carried out by solving the optical Bloch equations for five-level atomic model under Λ configuration. With the numerically simulated spectra, variation of EIT transmission peak with ground state decay rate and excited state spontaneous decay rate are investigated. Effect of pump Rabi frequency on the transmission peak is also shown.

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.