Using the z-scan technique, we have measured the self-induced absorptive and refractive nonlinear behavior of hot atomic rubidium vapor within the Doppler profile of the D2 line. We observe large nonlinear amplitude and phase effects with only tens of microwatts of incident power. Our results are in good agreement with numerical calculations based on an analytic model of a Doppler-broadened two-level system.

arXiv:physics/0309017Journal of the Optical Society of America BDec 1, 200318 citations

Optics Express

Measuring the group velocity dispersion in near resonant hot atomic vapors

Alix Merolle, Quentin C. Glorieux

Published Feb 12, 2026• 1 citation

Publisher

Abstract

DOI: 10.1364/oe.587198

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Measuring the group velocity dispersion in near resonant hot atomic vapors

Merolle, Alix, Quentin C. Glorieux

Group velocity dispersion (GVD) in near-resonant hot atomic vapors is difficult to measure with standard pulse broadening or interferometric techniques, as absorption, pulse distortion and nonlinearities strongly affect the probe and reduce the signal-to-noise ratio. We introduce a simpler method using a continuous-wave laser with weak phase modulation and a slow photodetector, directly inspired by Bragg-like spectroscopy in fluids of light. During propagation, the red and blue-detuned sidebands accumulate different dispersive phase shifts, leading to oscillations in the transmitted modulation contrast as the modulation frequency is scanned. Vanishing contrast at well-defined frequencies directly yields the GVD. We apply this technique to hot rubidium vapors and observe the strong frequency dependence of the GVD across a broad detuning range of the D2 line at different temperatures.Group velocity dispersion (GVD) in near-resonant hot atomic vapors is difficult to measure with standard pulse broadening or interferometric techniques, as absorption, pulse distortion and nonlinearities strongly affect the probe and reduce the signal-to-noise ratio. We introduce a simpler method using a continuous-wave laser with weak phase modulation and a slow photodetector, directly inspired by Bragg-like spectroscopy in fluids of light. During propagation, the red and blue-detuned sidebands accumulate different dispersive phase shifts, leading to oscillations in the transmitted modulation contrast as the modulation frequency is scanned. Vanishing contrast at well-defined frequencies directly yields the GVD. We apply this technique to hot rubidium vapors and observe the strong frequency dependence of the GVD across a broad detuning range of the D2 line at different temperatures.

arXiv:2512.07954Dec 8, 20250 citations

Pulse delay and group velocity dispersion measurement in V-type electromagnetically induced transparency of hot 85 Rb atom

Bankim Chandra Das, Dipankar Bhattacharyya, Arpita Das +3 more

Abstract Pulse delay with the group velocity dispersion (GVD) characteristics was studied in the V-type electromagnetically induced transparency in the hyperfine levels of 85 Rb atoms with a closed system configuration. The phase coherency between the pump and the probe laser beams was maintained. We studied the pulse delay and the GVD characteristics with the variation of the pump Rabi frequency taking optical density (OD) as a parameter. We observed a maximum of 268 ns pulse delay for 21.24 MHz pump Rabi frequency at OD 5.04 of the Rb vapor cell. For a better understanding of the experimental results, we have derived an analytical solution for the delay characteristics considering the thermal averaging. The analytical solution was derived for a three level V-type system. The theoretical plots of the delay and the GVD show the same characteristics as we observed in the experiment. This analytical approach can be further generalized for the higher level schemes to calculate different quantities such as susceptibility, group velocity delay or GVD characteristics.Abstract Pulse delay with the group velocity dispersion (GVD) characteristics was studied in the V-type electromagnetically induced transparency in the hyperfine levels of 85 Rb atoms with a closed system configuration. The phase coherency between the pump and the probe laser beams was maintained. We studied the pulse delay and the GVD characteristics with the variation of the pump Rabi frequency taking optical density (OD) as a parameter. We observed a maximum of 268 ns pulse delay for 21.24 MHz pump Rabi frequency at OD 5.04 of the Rb vapor cell. For a better understanding of the experimental results, we have derived an analytical solution for the delay characteristics considering the thermal averaging. The analytical solution was derived for a three level V-type system. The theoretical plots of the delay and the GVD show the same characteristics as we observed in the experiment. This analytical approach can be further generalized for the higher level schemes to calculate different quantities such as susceptibility, group velocity delay or GVD characteristics.

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Saturable nonlinear refraction in hot atomic vapor

Colin F. McCormick, Daniel R. Solli, R. Y. Chiao +1 more

Atomic vapors make flexible and useful nonlinear optical media when light is detuned far from resonances. However, few direct measurements of their nonlinear coefficients have been performed to date. We present a measurement of the Kerr coefficient for various detunings to both the red and blue of the $D2$ line in hot atomic rubidium vapor. Saturation effects complicate the interpretation of the standard z-scan method, but a simple saturation model agrees well with our data. We find values of ${n}_{2}\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}{10}^{\ensuremath{-}7}{\mathrm{cm}}^{2}/\mathrm{W}$ for 1 GHz detunings from the $D2$ line.Atomic vapors make flexible and useful nonlinear optical media when light is detuned far from resonances. However, few direct measurements of their nonlinear coefficients have been performed to date. We present a measurement of the Kerr coefficient for various detunings to both the red and blue of the $D2$ line in hot atomic rubidium vapor. Saturation effects complicate the interpretation of the standard z-scan method, but a simple saturation model agrees well with our data. We find values of ${n}_{2}\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}{10}^{\ensuremath{-}7}{\mathrm{cm}}^{2}/\mathrm{W}$ for 1 GHz detunings from the $D2$ line.

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Adiabatic Following and Slow Optical Pulse Propagation in Rubidium Vapor

D. Grischkowsky

Short pulses of narrow-line low-intensity dye-laser light nearly resonant with the Zeeman-split $^{2}P_{\frac{1}{2}}$ resonance line (7948 \AA{}) of rubidium were observed to propagate through dilute rubidium vapor as slowly as $(\frac{1}{14})c$ . These slow pulse velocities showed that most of the energy in the propagating wave was contained by the vapor as coherent atomic excitation. The observed pulse velocities ${v}_{p}$ are in good agreement with the equation ${v}_{p}=\frac{d\ensuremath{\omega}}{\mathrm{dk}}$ for the group velocity obtained from linear-dispersion theory. Also, the experimental results are quantitatively explained by adiabatic following, in which the pseudomoments of the atoms remain aligned along the effective field of the laser light. The adiabatic-following model allows for a direct comparison of our results with the work on self-induced transparency. For high-intensity light, adiabatic following predicts a nonlinear pulse velocity and the possibility of observing self-steepening.Short pulses of narrow-line low-intensity dye-laser light nearly resonant with the Zeeman-split $^{2}P_{\frac{1}{2}}$ resonance line (7948 \AA{}) of rubidium were observed to propagate through dilute rubidium vapor as slowly as $(\frac{1}{14})c$. These slow pulse velocities showed that most of the energy in the propagating wave was contained by the vapor as coherent atomic excitation. The observed pulse velocities ${v}_{p}$ are in good agreement with the equation ${v}_{p}=\frac{d\ensuremath{\omega}}{\mathrm{dk}}$ for the group velocity obtained from linear-dispersion theory. Also, the experimental results are quantitatively explained by adiabatic following, in which the pseudomoments of the atoms remain aligned along the effective field of the laser light. The adiabatic-following model allows for a direct comparison of our results with the work on self-induced transparency. For high-intensity light, adiabatic following predicts a nonlinear pulse velocity and the possibility of observing self-steepening.

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Control of group velocity dispersion in single mode fiber based on stimulated Brillouin scattering

Nor Ain Husein

Slow light study is discussed in various methods of generation, materials and approaches. In this study, the control of group velocity, Vg and group velocity dispersion (GVD) of a pulse propagating in optical fiber is simulated and demonstrated. The slow light generation, which is closely related to Vg of a light pulse for this study is based on stimulated Brillouin scattering (SBS), the most efficient approach as reported by previous researchers. By using Matlab R2011b software, the slow light generation is simulated for the slow light structure in the form of hollow conical shape resonator, focusing on the geometrical parameters. The simulation work is extended to the control of Vg and GVD, to investigate the influences of refractive index of the materials and wave number of the light pulses. While most of slow light researches neglect the effect of dispersion, this study explicitly includes the second term of the wave number’s expansion to represent GVD. Therefore, the experimental work investigates the creation of a strongly dispersive material with large chirp and small group delay via SBS in a highlynonlinear optical fiber as opposed to previous SBS experiments which mainly focus on the creation of a slow light material with minimum dispersion and chirp. To demonstrate the control of Vg and GVD, a two-frequency pump field which consists of two distributed feedback lasers with the relative frequency separation nearly twice the Brillouin frequency and a slow light medium in the form of a 2-km high nonlinear single mode optical fiber are employed. For input field with slowly varying amplitude, the experiment obtained output pulses with large GVD and decreased intensity. All-optical control of the GVD is demonstrated by measuring the linear frequency chirp impressed on a 28-nanosecond-duration optical pulse and it is tunable over the range of ± 7.8 ns2 m-1. In addition, the maximum observed value of GVD is 109 times larger than that obtained in a typical single-mode silica optical fiber. The simulation results for Gaussian pulses as input signal are in good agreement with the experimental ones, and therefore the control of Vg and GVD for different shapes of input pulses using the developed system can be predicted.Slow light study is discussed in various methods of generation, materials and approaches. In this study, the control of group velocity, Vg and group velocity dispersion (GVD) of a pulse propagating in optical fiber is simulated and demonstrated. The slow light generation, which is closely related to Vg of a light pulse for this study is based on stimulated Brillouin scattering (SBS), the most efficient approach as reported by previous researchers. By using Matlab R2011b software, the slow light generation is simulated for the slow light structure in the form of hollow conical shape resonator, focusing on the geometrical parameters. The simulation work is extended to the control of Vg and GVD, to investigate the influences of refractive index of the materials and wave number of the light pulses. While most of slow light researches neglect the effect of dispersion, this study explicitly includes the second term of the wave number’s expansion to represent GVD. Therefore, the experimental work investigates the creation of a strongly dispersive material with large chirp and small group delay via SBS in a highlynonlinear optical fiber as opposed to previous SBS experiments which mainly focus on the creation of a slow light material with minimum dispersion and chirp. To demonstrate the control of Vg and GVD, a two-frequency pump field which consists of two distributed feedback lasers with the relative frequency separation nearly twice the Brillouin frequency and a slow light medium in the form of a 2-km high nonlinear single mode optical fiber are employed. For input field with slowly varying amplitude, the experiment obtained output pulses with large GVD and decreased intensity. All-optical control of the GVD is demonstrated by measuring the linear frequency chirp impressed on a 28-nanosecond-duration optical pulse and it is tunable over the range of ± 7.8 ns2 m-1. In addition, the maximum observed value of GVD is 109 times larger than that obtained in a typical single-mode silica optical fiber. The simulation results for Gaussian pulses as input signal are in good agreement with the experimental ones, and therefore the control of Vg and GVD for different shapes of input pulses using the developed system can be predicted.

Jun 1, 20150 citations

Nonlinear absorption and refraction in near-detuned rubidium vapor

Colin F. McCormick, Daniel R. Solli, R. Y. Chiao +1 more

arXiv:physics/0309017Journal of the Optical Society of America BDec 1, 200318 citations

D2

line in hot atomic rubidium vapor. Saturation effects complicate the interpretation of the standard z-scan method, but a simple saturation model agrees well with our data. We find values of ${n}_{2}\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}{10}^{\ensuremath{-}7}{\mathrm{cm}}^{2}/\mathrm{W}$ for 1 GHz detunings from the

D2

line.

Short pulses of narrow-line low-intensity dye-laser light nearly resonant with the Zeeman-split

^{2}P_{\frac{1}{2}}

resonance line (7948 \AA{}) of rubidium were observed to propagate through dilute rubidium vapor as slowly as

(\frac{1}{14})c

. These slow pulse velocities showed that most of the energy in the propagating wave was contained by the vapor as coherent atomic excitation. The observed pulse velocities

{v}_{p}

are in good agreement with the equation ${v}_{p}=\frac{d\ensuremath{\omega}}{\mathrm{dk}}$ for the group velocity obtained from linear-dispersion theory. Also, the experimental results are quantitatively explained by adiabatic following, in which the pseudomoments of the atoms remain aligned along the effective field of the laser light. The adiabatic-following model allows for a direct comparison of our results with the work on self-induced transparency. For high-intensity light, adiabatic following predicts a nonlinear pulse velocity and the possibility of observing self-steepening.