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Physical Review A

Nonlinear selective reflection in cascade three-level atomic systems

F. Schuller, O. Gorceix, M. Ducloy

Published Jan 1, 1993• 38 citations
Publisher

Abstract

We study the cascade three-level selective-reflection spectroscopy for normal incidence at a dielectric--atomic-vapor interface in a pump-probe scheme. Taking into account the effects of spatial dispersion arising from deexcitation by collisions with the interface and the transient response of atoms leaving the surface, we evaluate the modification of the probe-field reflection induced by the presence of the pump field in terms of a nonlocal nonlinear susceptibility. The dependence of this susceptibility on the probe frequency for various given pump frequencies is calculated. Sub-Doppler structures in the selective reflection spectrum are obtained and analyzed. Potential applications to the study of the interaction of highly excited atomic states with the surface are indicated.

DOI
10.1103/physreva.47.519

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We study the cascade three-level selective-reflection spectroscopy for normal incidence at a dielectric--atomic-vapor interface in a pump-probe scheme. Taking into account the effects of spatial dispersion arising from deexcitation by collisions with the interface and the transient response of atoms leaving the surface, we evaluate the modification of the probe-field reflection induced by the presence of the pump field in terms of a nonlocal nonlinear susceptibility. The dependence of this susceptibility on the probe frequency for various given pump frequencies is calculated. Sub-Doppler structures in the selective reflection spectrum are obtained and analyzed. Potential applications to the study of the interaction of highly excited atomic states with the surface are indicated.
We evaluate the emission into a dielectric induced by the dipole polarization of an atomic vapor, in the case where two light beams are incident on the dielectric-vapor interface. These beams are a weak signal beam and a pump beam. Effects of spatial dispersion, arising from deexcitation of the vapor particles at collisions with the interface, are accounted for. The reflected radiation contains sub-Doppler structures arising from combinations of the effects of velocity-dependent transient behavior and the nonlinear response of the vapor. We express the modification of the signal-field reflection due to the pump field in terms of an effective susceptibility of the signal field. This susceptibility explicitly depends on the incidence angles and the frequencies of both beams. We present explicit simplified expressions for this effective susceptibility, valid in special cases. We also give some numerical results.
We consider nonlinear selective reflection on the interface between dielectric media and dilute vapors of three-level atoms. Assuming a pump-probe scheme with cascade-type excitation, we study the modification \ensuremath{\Delta}R of the reflection coefficient of the probe induced by the presence of the pump. We extend previous calculations of the frequency spectrum of \ensuremath{\Delta}R made for low probe power to the case of arbitrary probe power. One then obtains a strong resonance which has already been observed experimentally. Moreover, for the two-photon resonance present in the low-intensity spectrum, a power splitting can be predicted with increasing intensity \textcopyright{} 1996 The American Physical Society.
We present an experimental study of nonlinear selective reflection at a dielectric--Cs-vapor interface, in a three-level cascade-up scheme. The nonlinear reflection at the Cs D2{\mathit{D}}_{2}D2​ resonance line is monitored in the presence of resonant irradiation at 621 nm or 658 nm (6P3/2{\mathit{P}}_{3/2}P3/2​\ensuremath{\rightarrow}8D5/2{\mathit{D}}_{5/2}D5/2​,9S1/2{\mathit{S}}_{1/2}S1/2​). Experimental reflection spectra with either counterpropagating or copropagating light beams are analyzed and compared with the theoretical predictions of F. Schuller et al. [Phys. Rev. A 47, 519 (1993)]. For a blue-detuned pump and copropagating geometry an alternative type of three-level coherent reflection resonances, specifically associated with desorbing atoms, is observed. Also observed is the nonlinear reflection associated with the off-resonant, two-photon dispersion of atoms moving parallel to the window surface. Probe beam saturation is responsible for the appearance of additional resonant features in reflection spectra. Finally we analyze crossover spectral resonances which arise from nondegenerate, four-wave-mixing processes induced by the combined influence of counterpropagating pump and probe beams, and the pump beam being partially reflected by the window.
We calculate the reflection coefficient for a light beam incident on the interface between a dielectric and a resonant atomic vapor to first order in the dipole polarization in the vapor. The angle of incidence and the polarization direction are chosen arbitrarily, and saturation is fully accounted for. The atoms are supposed to get deexcited at collisions with the surface. The resulting transient behavior of atoms leaving the surface is responsible for a nonlocal response. This spatial dispersion near the surface is known to produce a natural-linewidth-limited resonance in the vapor reflection coefficient at normal incidence. Our analysis shows that this sub-Doppler structure is broadened by the residual Doppler effect for non-normal incidence. This structure disappears at the critical angle for total internal reflection, where one predicts a conventional Voigt-type dispersion response, based on the complex-refractive-index approach. We also calculate the saturation broadening of the atomic response for large intensities. Beyond the critical angle, the spectral response suddenly shifts from dispersion to absorption line shapes. In the case of total internal reflection, the spatial dispersion leads to an additional Lorentzian broadening, which results from an effective imaginary Doppler shift at passage through the evanescent wave (transit-time broadening).
We study internal selective reflection from a dielectric-vapor interface, where three levels of the vapor atoms in a \ensuremath{\Lambda} configuration are connected by two light frequencies. The reflectivity contains then both a sub-Doppler structure due to spatial dispersion in the boundary layer and the dark resonance arising from coherent population trapping. We derive analytical expressions for the reflectivity of either one of the two light beams. The contributions from atoms approaching or leaving the interface are strongly different, whereas they are identical for the case of two-state atoms.
We report on recent developments in selective reflection spectroscopy at a vapor interface. In FM linear spectroscopy, the long range van der Waals surface interaction, responsible for lineshapes distortions and shifts, is quantitatively well understood with respect to the nature of the dielectric surface. Pump‐probe saturation effects in reflection spectroscopy on a two‐level system offer alternate ways of probing surface interaction, while nonlinear reflection spectrsocopy on a three‐level cascade system provides a unique tool for probing in a vapor cell the velocity distribution of desorbing atoms.