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Scientific Reports

Rubidium vapor cell spectroscopy by selective reflection approach

A. Mirzaei, S.M. Hamidi

Published Aug 7, 2026• 0 citations
Publisher

Abstract

Selective-reflection ellipsometry from miniaturized rubidium vapor cells is investigated numerically and experimentally as a phase-sensitive extension of conventional selective-reflection spectroscopy. While most previous studies of selective reflection have mainly focused on scalar reflectivity and line-shape analysis, the present work analyzes the reflected p- and s-polarized fields through the ellipsometric parameters \(\:{\Psi\:}\) and \(\:{\Delta\:}\) . The reflected field from a finite rubidium vapor layer is calculated using a Fourier-series expansion of the coupled field–polarization equations for vapor-layer thicknesses ranging from \(\:L=\lambda\:/2\) to \(\:L=9\lambda\:/4\) , where \(\:\lambda\:=795\:\text{n}\text{m}\) . The numerical results show that wavelength-scale changes in the vapor-layer thickness modify the selective-reflection spectrum and produce thickness-dependent resonant features. The calculated \(\:{\Psi\:}\) and \(\:{\Delta\:}\) spectra exhibit inverse-like behavior at complementary incidence angles, including \(\:{30}^{\circ\:}{,60}^{\circ\:}\) and \(\:{37}^{\circ\:},{53}^{\circ\:}\) . This behavior is interpreted as the combined result of angle-dependent optical path, wavelength-scale phase accumulation, Fabry–Pérot-type thin-layer interference, and resonant near-surface atomic polarization associated with selective reflection. Experimentally, the ellipsometric parameters are extracted from p- and s-polarized reflection measurements performed on a fabricated \(\:50\:\mu\:\text{m}\) rubidium microcell. The experimental spectra support the physical observability of the complementary-angle ellipsometric response in a real miniaturized vapor-cell geometry. These results show that selective-reflection ellipsometry can provide a useful phase-sensitive approach for studying resonant optical responses in confined atomic vapor layers and offers a useful platform for compact spectroscopy, laser stabilization, and atom–surface interaction studies.

DOI
10.1038/s41598-026-66196-8

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Selective-reflection ellipsometry from miniaturized rubidium vapor cells is investigated numerically and experimentally as a phase-sensitive extension of conventional selective-reflection spectroscopy. While most previous studies of selective reflection have mainly focused on scalar reflectivity and line-shape analysis, the present work analyzes the reflected p- and s-polarized fields through the ellipsometric parameters (:{\Psi:}) and (:{\Delta:}) . The reflected field from a finite rubidium vapor layer is calculated using a Fourier-series expansion of the coupled field–polarization equations for vapor-layer thicknesses ranging from (:L=\lambda:/2) to (:L=9\lambda:/4) , where (:\lambda:=795:\text{n}\text{m}) . The numerical results show that wavelength-scale changes in the vapor-layer thickness modify the selective-reflection spectrum and produce thickness-dependent resonant features. The calculated (:{\Psi:}) and (:{\Delta:}) spectra exhibit inverse-like behavior at complementary incidence angles, including (:{30}^{\circ:}{,60}^{\circ:}) and (:{37}^{\circ:},{53}^{\circ:}) . This behavior is interpreted as the combined result of angle-dependent optical path, wavelength-scale phase accumulation, Fabry–Pérot-type thin-layer interference, and resonant near-surface atomic polarization associated with selective reflection. Experimentally, the ellipsometric parameters are extracted from p- and s-polarized reflection measurements performed on a fabricated (:50:\mu:\text{m}) rubidium microcell. The experimental spectra support the physical observability of the complementary-angle ellipsometric response in a real miniaturized vapor-cell geometry. These results show that selective-reflection ellipsometry can provide a useful phase-sensitive approach for studying resonant optical responses in confined atomic vapor layers and offers a useful platform for compact spectroscopy, laser stabilization, and atom–surface interaction studies.
Abstract Various efforts have been made to overcome Doppler broadening in hyperfine measurement limitations in the atomic vapors spectroscopy and associated applications. The present study measured and calculated hyperfine resolved ellipsometric parameters through the near-normal reflectance spectra of the rubidium vapor cell in two experimental setups based on continuous and modulated pathway. The results indicated that valuable information could be extracted from the ellipsometric parameters about the atomic medium. Change in the ellipsometric parameters in each transition line confirms the existence of the elliptical polarization of the reflected light when it is exposed to the alkali metal vapor. Our results show that the ellipticity at 5S1/2 (Fg = 1, 2) → 5P1/2 (Fe = 1, 2) hyperfine transitions of 87Rb (D1 line) is small, and accordingly hyperfine transitions between the ground 5S1/2 (Fg = 2, 3) and excited 5P1/2 (Fe = 2, 3) states of the 85Rb isotope are considerable. These ellipsometric parameters, as phase difference, can trace the behavior of the relative orientation of the electric field and atom velocity in the interface based on van der Waals dipole–dipole interaction and is directly proportional to the strength of the light-matter interaction which extremely useful instead complicated atomic spectroscopic methods.
The features of the effect of selective reflection from rubidium vapor in a nanocell with the thickness L ≈ λ/2 and L ≈ λ/4, where λ = 795 nm is the wavelength of laser radiation resonant with the Rb D 1 line, are studied. It is shown that, because of the behavior of the nanocell as a low-Q-factor Fabry–Pérot etalon, the sign of the derivative of the selective reflection spectra changes near L ≈ λ/2 from negative at L > λ/2 to positive at L < λ/2. The simplicity of the experimental implementation, large amplitude, and sub-Doppler width (40MHz) of a detected signal at an atomic transition frequency are appropriate for applications in metrology and magnetometry. In particular, selective reflection from the nanocell is a convenient frequency marker of atomic transitions; in this case, the amplitudes of peaks are proportional to the transition probabilities. The remote optical monitoring of a magnetic field with a spatial resolution L = λ/4 ≈ 199 of nm is possible on the basis of the splitting of selective reflection peaks in a strong magnetic field (up to 3 kG). A theoretical model describes well the experimental results.
Sub-Doppler nature of atomic spectra in alkali metal vapor cells of nanometric thickness L (nanocells) allows one to study peculiarities of magneto-optical processes, which occur in a magnetic field for the case when L is of the order of λ (λ is a laser resonant wavelength). We particularly address the issues of practical implementation of the studied processes. The following results are presented. i) A "λ-Zeeman technique" exploiting velocity-selective optical pumping resonances in L = λ Rb cell placed in a B-field, which allows direct determination frequency shifts and modification of transition probabilities of individual Zeeman transitions in magnetic field and is applicable for development of wide-range (~ 0.1 - 1000 mT) optical magnetometers and tunable frequency reference. ii) A technique for locking the laser radiation frequency, B-field-tunable in ~ 500 MHz range, which is based on selective reflection of a circularly-polarized laser beam from Rb vapor cell with thickness L ≈ λ/2.
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.
Various efforts have been made to determine the polarization state of evanescent waves in different structures. The present study shows the reliability of magneto-optical spectroscopy of D1 and D2 lines of rubidium metal and polarization-dependent transitions to investigate and trace the changes in the polarization state of evanescent fields during total internal reflection over different angles. For this purpose, we design and fabricate atomic- evanescent Rb vapor cells and examine the effect of polarization changes of evanescent waves, depending on the propagation direction of evanescent waves in anisotropic rubidium vapor media under 88 mT external magnetic field by different configurations theoretically and experimentally. The results confirm the dependency of allowed [Formula: see text] transitions on the magneto optical configuration as a tool to determine changes in the polarization of evanescent waves in more complicated wave states in anisotropic media.
Selective reflection is a high-resolution spectroscopic method that allows the probing of atomic and molecular gases in the near field of dielectric cell windows. It is a sensitive technique for measuring interactions between excited atoms and surfaces, thus providing a unique tool to probe resonant effects in Casimir-Polder physics. The theoretical modelling of selective reflection spectra has thus far employed the infinite Doppler approximation which assumes that the Doppler shift dominates over the atom-surface interactions as well as the homogeneous transition linewidth. Here we extend the theoretical treatment of selective reflection spectra to include the effects of finite Doppler width. This allows us to analyse the regime of very large Casimir-Polder interactions, relevant for Rydberg atom spectroscopy, and revisit previous analyses of experiments with low-lying excited states. Further, this will aid in determining the signatures of quantum friction in vapor cell spectroscopy.