Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Strong amplification of sidebands in self-focused laser beams in an atomic vapor

A. C. Tam

Published May 1, 1979• 62 citations
Publisher

Abstract

A cw dye-laser beam tuned to the high-frequency wing of the Na ${D}_{2}$ line (at 2-6 GHz from the center of the ${D}_{2}$ line) is focused into a Na vapor, forming a self-focused laser filament. The incident laser beam, which is mainly single frequency, contains very weak sidebands at about \ifmmode\pm\else\textpm\fi{} 1 GHz from the main frequency and of intensity \ensuremath{\sim} ${10}^{\ensuremath{-}3}$ of the main frequency. Such sidebands are found to be strongly amplified by the vapor. Amplification factors in excess of 100 have been observed at suitable Na density, laser power, and detuning. Such strong sideband amplification, previously unknown, is explained as an off-resonant stimulated Raman scattering process.

DOI
10.1103/physreva.19.1971

Related papers

cw Self-Focusing and Self-Trapping of Light in Sodium Vapor

John E. Bjorkholm, Arthur Ashkin

We report steady-state self-focusing, self-trapping, and self-defocusing of a cw dye laser beam in sodium vapor for frequencies within several Doppler widths of the $D$-line resonance transitions. We measured the variation of the beam profile as the light propagates through the vapor. We observed a 20-mW beam self-trapped in a 12-cm-long filament having a half-power diameter of 70 \ensuremath{\mu}m.

Physical Review Letters•Jan 28, 1974•321 citations

CW self-focusing and self-trapping of light in sodium vapor

John E. Bjorkholm, Arthur Ashkin

We report steady-state self-focusing, self-trapping, and self-defocusing of a cw dye laser beam in sodium vapor for frequencies within several Doppler widths of the $D$-line resonance transitions. We measured the variation of the beam profile as the light propagates through the vapor. We observed a 20-mW beam self-trapped in a 12-cm-long filament having a half-power diameter of 70 \ensuremath{\mu}m.

IEEE Journal of Quantum Electronics•Sep 1, 1974•11 citations

Four-wave mixing resonantly enhanced by ac-Stark-split levels in self-trapped filaments of light

Donald J. Harter, Robert W. Boyd

It is observed that when an intense, nearly resonant laser beam propagates through a dilute ($N<5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$) vapor of sodium atoms, a four-wave-mixing process occurs, leading to the generation of strong, coherent radiation in the forward direction at frequencies symmetrically detuned from that of the exciting laser by the generalized Rabi frequency. This phenomenon is explained as resulting from a nearly phase-matched mixing process utilizing the nonlinear response of the sodium atom. Our analysis is based on a solution of the density-matrix equations of motion that includes the effect of level shifts induced by the ac Stark effect, which can be as great as 10 \AA{} for our experimental conditions, and which leads to gain due to the stimulated three-photon effect at one Rabi sideband and to strong coupling due to a parametric mixing process between radiation at the two sideband frequencies. It is also observed that at larger sodium densities ($N\ensuremath{\gtrsim}5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$), self-focusing of the laser beam can occur, leading to several complicating effects. We find experimentally that the on-resonance Rabi frequency $\ensuremath{\Omega}$ within a self-trapped filament lies preferentially within the range from 1 to 3 times the laser detuning from resonance $\ensuremath{\Delta}$ and we explain this result as a consequence of strong saturation of the refractive index that occurs for $\ensuremath{\Omega}\ensuremath{\gtrsim}\ensuremath{\Delta}$. Four-wave mixing is found to occur within these self-trapped filaments. The high-frequency sideband thus generated is trapped within the filament, whereas the lower-frequency sideband is ejected as a consequence of Snell's law and forms a cone surrounding the transmitted laser beam.

Physical Review A•Feb 1, 1984•102 citations

Frequency correlated laser beam generation in sodium vapor: sodium-density and pump-intensity dependence

Prem Kumar, Bernard Matthew Poelker

When sodium vapor is irradiated with a single-frequency dye laser (pump) tuned in the vicinity of either of the Doppler-broadened D lines and enclosed in an optical cavity, Raman shifted oscillation builds up, which is blue shifted for a blue-detuned pump and red shifted for a red-detuned pump by 1.772 GHz (sodium ground-state hyperfine splitting).1 The gain mechanism responsible for this Raman-laser action can be understood by modeling sodium as a three-level atom. The Raman laser frequency is highly correlated with that of the pump as demonstrated earlier by observing a beat frequency bandwidth between the two lasers of as low as 17 kHz.2 (The pump had rms frequency fluctuation of the order of 10 MHz.) For spectroscopic applications, for example, frequency correlated laser beams are commonly generated using acoustooptic techniques which are difficult to implement beyond the gigahertz region. The Raman laser technique is extendable, in principle, even to the millimeter range. Here we present measurements of the sodium-density and pump-intensity dependence of the Raman-laser output and compare the results with those predicted by the three-level-atom model.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Nonlinear optical experiments in sodium vapor and comparison with Doppler-broadened two-level-atom theory.

John F. Valley

Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.

•Jan 1, 1989•0 citations

Instabilities in the Propagation of Laser Beams Through Atomic Vapors

Robert W. Boyd, Daniel J. Gauthier, Michelle S. Malcuit

There are several nonlinear optical processes that can lead to instabilities in a laser beam as it propagates through a nonlinear optical medium. Self focusing effects, for instance, can lead to the growth of new spatial frequency components in a laser beam. A laser beam can also be unstable to the growth of new spectral components. Stimulated Raman scattering is a well-known example of a process that can lead to this sort of instability. In this paper, we present the results of a series of experiments on the somewhat different instabilities that occur for the case of the propagation of a laser beam through an atomic vapor. We find that these instabilities become particularly pronounced when the frequency of the incident laser is near to that of a one- or two-photon resonance of the atom. In either case, we find that the laser beam is unstable to the growth of new frequency components, and that in general these new frequencies are not emitted collinearly with the incident laser. These instabilities are important because they place a limit on the laser intensity that can be used to drive nonlinear optical processes.

International Meeting on Instabilities and Dynamics of Lasers and Nonlinear Optical Systems•Jan 1, 1985•0 citations
A cw dye-laser beam tuned to the high-frequency wing of the Na D2{D}_{2}D2​ line (at 2-6 GHz from the center of the D2{D}_{2}D2​ line) is focused into a Na vapor, forming a self-focused laser filament. The incident laser beam, which is mainly single frequency, contains very weak sidebands at about \ifmmode\pm\else\textpm\fi{} 1 GHz from the main frequency and of intensity \ensuremath{\sim} 10\ensuremath−3{10}^{\ensuremath{-}3}10\ensuremath−3 of the main frequency. Such sidebands are found to be strongly amplified by the vapor. Amplification factors in excess of 100 have been observed at suitable Na density, laser power, and detuning. Such strong sideband amplification, previously unknown, is explained as an off-resonant stimulated Raman scattering process.
We report steady-state self-focusing, self-trapping, and self-defocusing of a cw dye laser beam in sodium vapor for frequencies within several Doppler widths of the DDD-line resonance transitions. We measured the variation of the beam profile as the light propagates through the vapor. We observed a 20-mW beam self-trapped in a 12-cm-long filament having a half-power diameter of 70 \ensuremath{\mu}m.
We report steady-state self-focusing, self-trapping, and self-defocusing of a cw dye laser beam in sodium vapor for frequencies within several Doppler widths of the DDD-line resonance transitions. We measured the variation of the beam profile as the light propagates through the vapor. We observed a 20-mW beam self-trapped in a 12-cm-long filament having a half-power diameter of 70 \ensuremath{\mu}m.
It is observed that when an intense, nearly resonant laser beam propagates through a dilute ($N<5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$) vapor of sodium atoms, a four-wave-mixing process occurs, leading to the generation of strong, coherent radiation in the forward direction at frequencies symmetrically detuned from that of the exciting laser by the generalized Rabi frequency. This phenomenon is explained as resulting from a nearly phase-matched mixing process utilizing the nonlinear response of the sodium atom. Our analysis is based on a solution of the density-matrix equations of motion that includes the effect of level shifts induced by the ac Stark effect, which can be as great as 10 \AA{} for our experimental conditions, and which leads to gain due to the stimulated three-photon effect at one Rabi sideband and to strong coupling due to a parametric mixing process between radiation at the two sideband frequencies. It is also observed that at larger sodium densities ($N\ensuremath{\gtrsim}5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$), self-focusing of the laser beam can occur, leading to several complicating effects. We find experimentally that the on-resonance Rabi frequency $\ensuremath{\Omega}$ within a self-trapped filament lies preferentially within the range from 1 to 3 times the laser detuning from resonance $\ensuremath{\Delta}$ and we explain this result as a consequence of strong saturation of the refractive index that occurs for $\ensuremath{\Omega}\ensuremath{\gtrsim}\ensuremath{\Delta}$. Four-wave mixing is found to occur within these self-trapped filaments. The high-frequency sideband thus generated is trapped within the filament, whereas the lower-frequency sideband is ejected as a consequence of Snell's law and forms a cone surrounding the transmitted laser beam.
When sodium vapor is irradiated with a single-frequency dye laser (pump) tuned in the vicinity of either of the Doppler-broadened D lines and enclosed in an optical cavity, Raman shifted oscillation builds up, which is blue shifted for a blue-detuned pump and red shifted for a red-detuned pump by 1.772 GHz (sodium ground-state hyperfine splitting).1 The gain mechanism responsible for this Raman-laser action can be understood by modeling sodium as a three-level atom. The Raman laser frequency is highly correlated with that of the pump as demonstrated earlier by observing a beat frequency bandwidth between the two lasers of as low as 17 kHz.2 (The pump had rms frequency fluctuation of the order of 10 MHz.) For spectroscopic applications, for example, frequency correlated laser beams are commonly generated using acoustooptic techniques which are difficult to implement beyond the gigahertz region. The Raman laser technique is extendable, in principle, even to the millimeter range. Here we present measurements of the sodium-density and pump-intensity dependence of the Raman-laser output and compare the results with those predicted by the three-level-atom model.
Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.
There are several nonlinear optical processes that can lead to instabilities in a laser beam as it propagates through a nonlinear optical medium. Self focusing effects, for instance, can lead to the growth of new spatial frequency components in a laser beam. A laser beam can also be unstable to the growth of new spectral components. Stimulated Raman scattering is a well-known example of a process that can lead to this sort of instability. In this paper, we present the results of a series of experiments on the somewhat different instabilities that occur for the case of the propagation of a laser beam through an atomic vapor. We find that these instabilities become particularly pronounced when the frequency of the incident laser is near to that of a one- or two-photon resonance of the atom. In either case, we find that the laser beam is unstable to the growth of new frequency components, and that in general these new frequencies are not emitted collinearly with the incident laser. These instabilities are important because they place a limit on the laser intensity that can be used to drive nonlinear optical processes.