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Physica Scripta

Probe Spectroscopy of Standing Wave Induced Saturation

Erkki Kyrola

Published May 1, 1981• 3 citations
Publisher

Abstract

A gas of two-level atoms is strongly saturated by a standing wave field. The same transition is probed by a weak tunable field. The observed probe absorption displays features due to both population modifications and coherences induced by the strong field. The probe spectrum is evaluated and interpreted in terms of coherent and incoherent multiphoton processes, power shifts and Stark splittings. Specific standing wave effects are identified and discussed. The relations to previous treatments are clarified.

DOI
10.1088/0031-8949/23/5a/006

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Physical Review A•Oct 1, 1972•293 citations
A gas of two-level atoms is strongly saturated by a standing wave field. The same transition is probed by a weak tunable field. The observed probe absorption displays features due to both population modifications and coherences induced by the strong field. The probe spectrum is evaluated and interpreted in terms of coherent and incoherent multiphoton processes, power shifts and Stark splittings. Specific standing wave effects are identified and discussed. The relations to previous treatments are clarified.
The effects of a strong standing wave field on the absorption behaviour of a weak probe field are studied. An absorptive medium is assumed to consist of stationary two-level atoms with arbitrary decay and pumping scheme. The spectrum with a resonant saturator does not exhibit emissive behaviour as in the travelling wave cases. With a detuned saturator the spectrum closely resembles the corresponding three-level spectrum. These features are explained from the standing wave induced spatial selectivity and inhomogeneity. The connections to Doppler-broadened spectra are discussed.
We study inhomogeneously broadened three-level atoms ($\ensuremath{\Lambda}$ configuration). Two energy levels are strongly coupled by an intense standing wave. A weak laser field at an adjacent transition is used as a probe. The probe response is calculated by Green's functions involving continued fractions. The general solution is extendable to other three-level configurations as well to other types of multimode saturators. The connection of various approximate solutions to the exact one is discussed. We concentrate on the Doppler-free case where both transitions have nearly equal frequencies. For this we derive a reasonably accurate closed-form solution, the parameter dependencies of which are investigated in detail. In addition to its average changes the dynamics of the saturated transition plays an important role in the steady-state probe response. The spectra show sharp resonances which cannot be explained in terms of traveling wave superposition models. The width of the velocity distribution has a strong effect on the shape of the spectrum---some resonances are smeared away because of incomplete Doppler dephasing. The relaxation processes influence differently the resonances, which facilitates their interpretation.
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 theory of saturation spectroscopy in three-level gas-vapor systems, including collisional effects, is presented. Using a model of collisions in which they are phase interrupting in their effect on level coherences and velocity changing in their effect on level population densities, the authors calculate the absorption profile of a weak probe field on a given transition when an arbitrarily strong pump field acts on a coupled transition. Line shapes are derived for an arbitrary collision kernel describing the velocity-changing collisions, and these line shapes are evaluated for the collision kernel proposed by Keilson and Storer. Various limiting forms for the line shapes are derived and representative line shapes are displayed. Several new features of the line shapes, including collisionally induced increased probe absorption are discussed. The line shapes are seen to reflect the various collisional processes that may occur in atomic or molecular systems.
A general theory of the saturated-absorption phenomenon in a two-level atomic system is developed, in which the phase relationships between the oscillating atomic dipoles as well as the population differences between energy levels are taken into account. The absorbing gaseous medium considered in this theory is subjected to irradiation by a quasi-running-wave composed of a strong pump field and a weak probe field propagating in opposite directions. Some new interesting results, not predicted by the so-called hole-burning or rate-equation model, are obtained. In particular, the probe-field-transmission peak line shape is found to be markedly different from what is expected according to the rate equations. For finite Doppler widths and a strong saturating pump field, absorption of the probe field can even change sign, and amplification of this field can actually occur. All these features are explained by a close inspection of the evolution of each atomic ensemble of given velocity. Detailed comparison with similar phenomena already observed in rf experiments is presented and permits us to clarify the new predicted effects.