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Physical Review A

Transit-time effects in power-broadened Doppler-free saturation resonances

John E. Thomas, M. J. Kelly, J.‐P. Monchalin, Norman A. Kurnit, Ali Javan

Published Jun 1, 1977• 17 citations
Publisher

Abstract

A density-matrix calculation of the line shape for a Doppler-broadened two-level system subjected to a plane-standing-wave laser field with a Gaussian intensity profile is presented to fifth order in perturbation theory. The primary new result is that, for fixed pressure and intensity, the power-broadening contribution to the linewidth is at a minimum when the beam radius is approximately equal to the mean free path. In addition, an analytic solution for the linewidth in the collision-dominated regime is presented for general collision parameters.

DOI
10.1103/physreva.15.2356

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Physical Review A•Feb 1, 1978•36 citations
A density-matrix calculation of the line shape for a Doppler-broadened two-level system subjected to a plane-standing-wave laser field with a Gaussian intensity profile is presented to fifth order in perturbation theory. The primary new result is that, for fixed pressure and intensity, the power-broadening contribution to the linewidth is at a minimum when the beam radius is approximately equal to the mean free path. In addition, an analytic solution for the linewidth in the collision-dominated regime is presented for general collision parameters.
A weak excitation transit-time resolution limited analytic line shape is derived for a Doppler broadening-free degenerate two-photon transition from a standing wave with a TEM00 transverse profile. This approximation is appropriate when the collisional mean free path is much larger than the transverse width of the TEM00 beam. It is considerably simpler than the two-photon absorption line shape previously published, Bordé, C. R. Hebd. Seances Acad. Sci., Ser. B 282, 341–344 (1976), which was derived for more general experimental conditions. The case of a saturating field, with an intensity-dependent shift of the resonance frequency, is treated and expressed in reduced units. Numerical calculations are presented for the line shape for a range of the reduced intensity and light intensity shifts values.
A density-matrix calculation of the line shape for an optically pumped coupled three-level system subjected to two traveling wave-laser fields with Gaussian intensity profiles is presented to third-order in perturbation theory. A closed-form expression for the line shape in the extreme transit-time limit is obtained. The line shape of the narrow resonance (Raman-type processes) is found to be an exponential function of the detuning, with half-width at half maximum ${\ensuremath{\Delta}}_{\mathrm{HWHM}}^{(\mathrm{Hz})}\ensuremath{\simeq}0.98(\frac{u}{2\ensuremath{\pi}D})$ (DDD is the intensity 1e\frac{1}{e}e1​ diameter and uuu is the thermal speed). The saturation intensity is also modified by the transit rate ${\ensuremath{\gamma}}_{t}=\frac{\sqrt{2}u}{D}$ (rad/sec).
The interaction of two closely spaced resonances in degenerate four-wave-mixing spectra is investigated theoretically. Degenerate four-wave-mixing spectra for the phase-conjugate geometry (counterpropagating pump beams) are calculated by integrating the time-dependent density-matrix equations at numerous grid points along the phase-matching axis and summing the polarization contribution from each of these grid points. Both purely homogeneously broadened resonances and resonances that are both collision and Doppler broadened are considered. The homogeneously broadened results are found to agree with the results of the widely used Abrams–Lind expression for the case of stationary absorbers exposed to a steady-state excitation. We examine the effects of power broadening, pressure broadening, transition dipole moment, and population on the spectra of two neighboring homogeneously broadened resonances. As the laser power is increased, the real parts of the resonance susceptibilities destructively interfere with each other in the region between the lines, resulting in a significant and persistent dip in reflectivity. When Doppler broadening is included in the calculations, similar interference effects are observed, although at first the interference dip begins to disappear until the homogeneous part of the line shapes is broadened significantly by saturation. Using this numerical approach, we obtain good agreement with experimental results of primarily Doppler-broadened neighboring resonances.
This paper describes a new class of techniques, called time-delayed laser saturation spectroscopy, which combine frequency- and time-domain methods of laser spectroscopy to provide a way of studying a molecular system as it evolves from an initially prepared stationary state to a second, final state. The specific example analyzed here is three-level free induction decay, in which the time-dependent gain of a Doppler-broadened molecular transition is probed after the sudden termination of an intense field resonating with a coupled transition. The theoretical calculation is based on the coupled density-matrix equations of motion in the slowly-varying envelope approximation. The time-delayed line shapes, which may be studied in either transmission or side fluorescence, exhibit linewidth asymmetries, line-shape deformations, Ramsey-type fringes, power broadening and dephasing, and dynamic Stark splittings and oscillatory decays. The technique provides a unique way of distinguishing the influence of Raman-type processes from that of population saturation and a means to separately measure the associated decay rates. The relationship of the present work to other studies is also discussed.