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Journal of the Optical Society of America B

Analytic solutions for the saturated absorption spectra

Geol Moon, Heung‐Ryoul Noh

Published Apr 10, 2008• 54 citations
Publisher

Abstract

We present analytic solutions for saturated absorption spectra. The analytic forms of all the ground- and excited-state populations were obtained, and the absorption of a counterpropagating probe beam was calculated by solving the rate equations in the presence of a pump laser beam. The analytic solutions were compared with the numerical, experimental results, and Nakayama's model and good agreement was found between them. We found that the analytic theory could provide accurate spectra at an arbitrary pump beam intensity and diameter.

DOI
10.1364/josab.25.000701

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We present analytic solutions for saturated absorption spectra. The analytic forms of all the ground- and excited-state populations were obtained, and the absorption of a counterpropagating probe beam was calculated by solving the rate equations in the presence of a pump laser beam. The analytic solutions were compared with the numerical, experimental results, and Nakayama's model and good agreement was found between them. We found that the analytic theory could provide accurate spectra at an arbitrary pump beam intensity and diameter.
In this study, we examined the effect of pump laser beam diameter on saturated absorption spectra. The rate equations describing the dynamics of the population of each sublevel were solved and the time evolution of the signals was obtained theoretically. With the exception of some signals, the experimental results showed good agreement with the calculated results, which were analyzed using the calculation based on rate equations. Furthermore, the beam diameter dependence of the spectra was examined for several pump beam intensities, and the results matched the calculated results.
We present the analytic solutions of the saturated absorption spectrum for an atomic medium composed of two-level atoms and describe the effects of saturation and optical pumping on the spectrum. The background-subtracted Doppler-free spectrum is Lorentzian-shaped with an amplitude and width given by 1 − {1 + s 0 [1 + (γ 2 t /2)]} −1/2 and γ t [1 + {1 + s 0 [1 + (γ 2 t /2)]} 1/2 ], respectively, where γ t is the transverse decay rate, γ 2 is the decay rate to energy levels other than the ground state, s 0 is the saturation parameter and t is the interaction time of the atoms with laser beams. Analytic results are compared with numerical results and show good agreement with one another. This paper is intended for graduate students who have started to study basic atomic physics.
We studied the nonstationary phenomena for the saturated absorption spectra peaks of the 87Rb D2 line by varying the diameter and the intensity of a pump laser beam. We found that the dependence of the magnitude of the signals on the variation of the beam diameter was almost equivalent to that of the pump beam intensity both experimentally and theoretically. However, we observed that the signals for the cycling transition line Fg=2→Fe=3 were different from each other, which could be explained by the saturation effect. We compared the experimental results with theoretical calculations based on the rate equation model. We observed good agreement between them.
We present an analytic calculation for linear susceptibility in pump-probe spectroscopy for a Doppler broadened atomic vapor. The analytic form of the population of each magnetic sublevel of a 87Rb^{87}\mathrm{Rb}87Rb atom, illuminated by a weak circularly polarized pump beam, was calculated for the lowest order of laser intensity and used in the calculation for the susceptibility of a counterpropagating (copropagating) probe beam. The obtained analytic results for the susceptibility can be used for calculating the absorption or the refractive index of the probe beam as functions of pump beam diameter and intensity.
An analytic solution for the intensity distribution of two counterpropagating pump waves within a saturable absorber is derived. From this distribution, the spatial variation of the nonlinear absorption and coupling constants that appear in the coupled-amplitude equations for the probe and the signal (i.e., conjugate) waves are determined. These coupled-amplitude equations are solved numerically in a noniterative manner, leading to a prediction for the phase-conjugate reflectivity. The results of the exact theory are compared with those of previously published theories. It is found that at large values of the input-pump intensities, the predicted phase-conjugate reflectivity is larger when pump-absorption effects are included in the theory.
This paper presents a simple analytical theory for the velocity-dependent pump-probe laser spectroscopy of 87Rb^{87}\mathrm{Rb}87Rb and 85Rb^{85}\mathrm{Rb}85Rb atoms where the pump and the probe beams are circularly or linearly polarized. The analytical solutions of the line shapes of the velocity-selective optical pumping spectroscopy [G. Moon and H. R. Noh, Phys. Rev. A 78, 032506 (2008)] and saturated absorption spectroscopy [G. Moon and H. R. Noh, J. Opt. Soc. Am. B 25, 701 (2008); 27, 1741 (2010)] obtained in the previous reports, expressed as a sum of several Lorentzian functions, could be approximated as one (or in some cases, two) Lorentzian function(s). In particular, the contributions of the saturation and optical pumping effects could be discriminated explicitly in these simple analytical solutions, which is not possible in existing theories such as Nakayama's model. The simple analytical results for the saturation spectroscopy were compared with experimental results, and good agreement between them was observed.