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Physical Review A

Line shapes of saturated absorption spectroscopy in optically thick media

O. Di Lorenzo-Filho, J. R. Rios Leite

Published Aug 1, 1998• 2 citations
Publisher

Abstract

The line shapes of saturation spectroscopy in optically thick two-level media are calculated for atomic and molecular transitions. Line narrowing and distortion effects due to propagation are presented. For Doppler-broadened media it is shown that, due to multiphoton processes, the natural linewidth limits the ultimate narrowing that can be reached. Thus, up to ${\ensuremath{\alpha}}_{0}L=20,$ only when the rate-equation approximation is valid subhomogeneous linewidths are expected.

DOI
10.1103/physreva.58.1139

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The line shapes of saturation spectroscopy in optically thick two-level media are calculated for atomic and molecular transitions. Line narrowing and distortion effects due to propagation are presented. For Doppler-broadened media it is shown that, due to multiphoton processes, the natural linewidth limits the ultimate narrowing that can be reached. Thus, up to \ensuremathα0L=20,{\ensuremath{\alpha}}_{0}L=20,\ensuremathα0​L=20, only when the rate-equation approximation is valid subhomogeneous linewidths are expected.
Saturated absorption spectroscopy linewidths down to half the natural linewidth have been obtained for the sodium D1{\mathit{D}}_{1}D1​ transition in a strongly absorbing gas cell. The strong-line-narrowing effect is achieved by using an experimental ``tandem'' approach with two absorbing cells in series, where the saturated absorption output from the first cell is used as an input beam for a saturated absorption measurement in the second cell. A physical interpretation of the line-narrowing mechanism in highly absorbing media is presented, which, among other things, explains why the narrowing effects are different for crossover transitions. It is further argued that in these experiments the line-narrowing effect is caused by optical pumping and can be appropriately described by rate equations. This is different from several other recent papers on high-contrast transmission spectroscopy, where full Bloch vector models were necessary to fully describe the line shapes. Here a rate equation model, which includes two spatial dimensions, is developed, and reasonable agreement is obtained between experimental and theoretical data. \textcopyright{} 1996 The American Physical Society.
We present an empirical formula for linewidth in saturated absorption spectroscopy for two-level atoms with cycling transition lines, taking the coherence term in the Doppler-broadened limit into account. The full width at half-maximum is obtained as (1+(1+as0)b)γt, where s0 is the on-resonance saturation parameter, γt is the transverse decay rate, and a and b are the parameters that depend on γt. We find that as γt increases, a and b approach 1 and 1/2, respectively. These are the typical values in the case without the coherence term.
Saturation effects affecting absorption and fluorescence spectra of an atomic vapor confined in an extremely thin cell (cell thickness $L<1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$) are investigated experimentally and theoretically. The study is performed on the D2{D}_{2}D2​ line $(\ensuremath{\lambda}=852\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ of Cs and concentrates on the two situations $L=\ensuremath{\lambda}∕2$ and $L=\ensuremath{\lambda}$, the most contrasted ones with respect to the length dependence of the coherent Dicke narrowing. For $L=\ensuremath{\lambda}∕2$, the Dicke-narrowed absorption profile simply broadens and saturates in amplitude when increasing the light intensity, while for $L=\ensuremath{\lambda}$, sub-Doppler dips of reduced absorption at the line-center appear on the broad absorption profile. For a fluorescence detection at $L=\ensuremath{\lambda}$, saturation induces narrow dips, but only for hyperfine components undergoing a population loss through optical pumping. These experimental results are interpreted with the help of the various existing models and are compared with numerical calculations based upon a two-level modeling that considers both a closed and an open system.
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."
We calculate the line shape and linewidths for electromagnetically induced transparency (EIT) in optically thick, Doppler broadened media (buffer gasses are also considered). In generalizing the definition of the EIT linewidth to optically thick media, we find two different linewidth definitions apply depending on whether the experiment is pulsed or continuous wave (cw). Using the cw definition for the EIT line shape we derive analytic expressions describing the linewidth as a function of optical depth. We also review the EIT line shapes in optically thin media and provide physical arguments for how the line shapes change as a function of various parameters.