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Fortschritte der Physik

Theoretical Aspects of High Resolution Spectroscopy in the Presence of Strong Doppler Broadening

Helmut Paul

Published Jan 1, 1974• 7 citations
Publisher

Abstract

Abstract Some important types of spectroscopic experiments which allow to detect substructures masked by the Doppler width of the lines are discussed within a unified theoretical framework. It is pointed out that, in case of a three‐ or more‐level system, besides saturation effects also processes of Raman type play an essential role. The effect of high intensity of one (monochromatic) partial wave on the shape and width of the resonances (inverted Lamb dip) is studied in detail taking fully into account the dynamic Stark effect in addition to the power‐broadening of the holes burnt into the absorption profile.

DOI
10.1002/prop.19740220102

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Physical Review A•Feb 1, 1978•36 citations
Abstract Some important types of spectroscopic experiments which allow to detect substructures masked by the Doppler width of the lines are discussed within a unified theoretical framework. It is pointed out that, in case of a three‐ or more‐level system, besides saturation effects also processes of Raman type play an essential role. The effect of high intensity of one (monochromatic) partial wave on the shape and width of the resonances (inverted Lamb dip) is studied in detail taking fully into account the dynamic Stark effect in addition to the power‐broadening of the holes burnt into the absorption profile.
We consider in this paper the Doppler-broadened absorption by two-level molecules of a gas from a weak traveling electromagnetic plane wave in the presence of an oppositely traveling strong plane wave at the same frequency. Here the absorption spectrum exhibits a dip that broadens and deepens as the gas is increasingly saturated by the strong wave. This saturation effect has been employed in the recent experiments on the fine structure of atomic hydrogen performed by H\"ansch, Shahin, and Schawlow (HSS). The form, linewidth, and strength of saturation dips in the fine-structure lines are studied for experimental parameters appropriate to the hydrogen experiment. In addition, saturation line-shape curves are calculated for experimental situations in which the strengths of the stronger field give rise to stronger or weaker saturation of the gas medium and varying degrees of Doppler broadening exist. The calculation of shape of the saturation dip and absorption curves for a Doppler-broadened gas of two-level atoms is made exactly; in effect, the strong field is treated as arbitrarily strong by avoiding a perturbation-theory treatment in favor of the exact solutions for a driven two-level system. The general behavior found is in accord with intuition and experimental observations by HSS. There is an optimum saturation power which gives a prominent dip and beyond which the dip suffers "power broadening."
A previously developed diagrammatic method for calculating the nonlinear response of a dilute gas at near resonance with strong classical radiation fields is extended to include velocity-dependent homogeneous and inhomogeneous broadening phenomena. The method is applied to two-level saturated-absorption (Lamb-dip) spectroscopy. Expressions are obtained for the collision-broadened Lamb dip probed by a weak field in the presence of an arbitrarily strong saturating field and are compared to the usual infinite-Doppler-width, weak-saturation expression. We study the effects of velocity and momentum transfer on the line-shape parameters and discuss the effect of phase-changing and strong inelastic collisions on the intensity.
The review deals with resonance phenomena resulting from saturation of low-pressure-gas absorption lines by a coherent optical field, when the spectral lines are inhomogeneously broadened by the Doppler effect. Principal attention is paid to narrow resonances of width much smaller than the Doppler widths, which are produced upon saturation of the absorption by light waves under various experimental conditions (inside and outside the laser resonator, in traveling and standing waves, in spatially separated waves, etc.), owing to different effects (absorption saturation, mode interaction in the laser). Each of the phenomena is considered from both the theoretical and the experimental points of view. The phenomena considered serve as a basis of a new branch of optical spectroscopy, namely nonlinear laser spectroscopy of ultrahigh resolution.
For pt.I see ibid., vol.8, p.1795 (1975) where the theory of Doppler-free two-photon transitions was discussed for the case of one single laser frequency. Here, the effects of two different frequencies are considered. When the residual Doppler width of the two-photon transition is less than the natural linewidth, the previous results are essentially regained. For large residual Doppler shifts, the absorption profile is a power-broadened Lorentzian if the frequency of the probe field is larger than the frequency of the strong field. In the opposite case, the absorption peak splits because of the AC Stark effect. The high-intensity distortions are minimized when equal frequencies can be used. Power-dependent shifts do not ordinarily occur with a resonantly tuned intermediate level. Some modifications of the spectra are introduced by phase-disturbing collisions.
The review systematizes the experimental material and reports the fundamental theoretical results on the study of nonlinear resonance effects in spectra of atomic systems situated in the radiation field of lasers. The theoretical part explains the topics of greatest importance and significance for understanding of the experimental studies: the Stark effect in an optical field; the nonequilibrium velocity distribution of the atoms; the shape of the spectral line for a transition adjacent to a transition combining with a strong field; the simultaneous manifestation of the Stark effect and of Doppler broadening in the form of a very sharp structure on the line contour; a brief mention of the influence of collisions, recoil, and other factors on the sharp structure in spectra. The experimental part reports the results of experiments on the observation of the Stark effect in the optical region of the spectrum, the fine structure of the profile of a Doppler-broadened line and its properties, namely the dependence on the observation direction, the anisotropy in the field of a standing wave, the polarization properties, etc. in spectra of spontaneous or stimulated emission, absorption, and generation.
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.