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Physical Review A

Nonlinear selective reflection from an atomic vapor at arbitrary incidence angle

Gerard Nienhuis, F. Schuller, M. Ducloy

Published Nov 1, 1988• 116 citations
Publisher

Abstract

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).

DOI
10.1103/physreva.38.5197

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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 calculate the modulation of the reflection coefficient for a frequency-modulated (FM) light beam incident on the interface between a dielectric and an atomic vapor. The vapor is described as a gas of resonant, Doppler-broadened, two-level systems, with transition frequency and linewidth arbitrarily depending on the atom-dielectric distance. The atoms are supposed to get deexcited at collisions with the surface. The transient atomic response is calculated to first order in the incident field, for both incoming and desorbed atoms. The reflection coefficient, evaluated to first order in the vapor dipole polarization, leads to a formal expression of the reflectivity modulation, valid for arbitrary atom-surface interaction potentials. One first discusses the reflection signal in absence of wall interactions, for arbitrary modulation frequencies. At large frequencies, it allows one to monitor both vapor absorption and dispersion. Second, the formal theory is applied to the case of a Van der Waals-London surface attraction exerted on the atomic vapor. Both normal and oblique beam incidences are considered. One shows how the vapor dispersion signal is red-shifted and strongly distorted by the appearance of vapor-surface long-range interactions, and how it can be used to monitor these interactions. At non-normal incidences, the lineshapes get Doppler-broadened.
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 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.
Up to now, Doppler-free nonlinear spectroscopy has been applied to atoms inside a gas medium (volume spectroscopy). We have extended these methods to atoms in the vicinity of a surface. The basic principle consists of monitoring reflectivity changes produced when a laser beam, incident on a glass–vapor interface, is brought into resonance with an atomic transition. For Doppler-free spectroscopy, two counterpropagating beams are used to operate velocity selection. If these two beams are under normal incidence in the glass—velocity selection perpendicular to the surface—one observes saturated dispersion (selective reflection sensitive to the real index). For incidence angles in the glass (prism) larger than the critical angle (total internal reflection), a standing evanescent wave is produced in the gas (velocity selection along the surface), and saturated absorption is detected. Experimental demonstration was performed on the Na resonance line; high sensitivity (10−4 relative reflectivity change) and spectral resolution as good as 20 MHz were obtained. The main limitation to better resolution comes from the short atomic transit time in the evanescent wave (typical extension ~λ). Relevant applications of these techniques should also concern the diagnostics of optically thick media, as analysis of interaction between gas-phase atoms and the surface, notably atom–wall collisions, and modification of the spontaneous emission characteristics.
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.
Intense light incident on a dense-gas--dielectric interface, from the dielectric side, is reflected because of the combined effect of the discontinuities in the index of refraction at the interface and at the transition region in the gas where the degree of atomic saturation changes abruptly. This latter discontinuity gives rise to a self-reflected wave. At low intensities this self-reflected wave is weak, the problem is linear, and the net reflected wave intensity taken as a function of frequency has a simple shape that should allow measurement of the hitherto undetected self-induced frequency shift in a collision-broadened gas at an absorption resonance. Calculations show that in the weak intensity regime, r'', the imaginary part of the reflection coefficient, is quasi-Lorentzian and shifted by an amount comparable to its width. At high light intensity r'' broadens, shifts, and distorts. The distortion, which nonuniformly modulates the Lorentzian shape, comes from an interference of the forward and self-reflected waves. In the wings of the resonance line the self-reflected wave can be neglected, and the shape of r'' although not distorted is shifted from where it would be if there were no local field correction.