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

Optics Letters

Saturation splitting in the spectrum of resonant degenerate four-wave mixing

Govind Prasad Agrawal, A. Van Lerberghe, Philippe Aubourg, Jean-Luc Boulnois

Published Nov 1, 1982• 29 citations
Publisher

Abstract

The spectrum of degenerate four-wave mixing on a homogeneously broadened one-photon transition is shown to exhibit line splitting when the pump-intensity difference exceeds the saturation intensity. The splitting arises from a saturation mechanism reinforced by the pump imbalance. Experimental evidence of this effect, using SF(6) as the nonlinear medium, is presented.

DOI
10.1364/ol.7.000540

Related papers

Saturation splitting of phase-conjugate line through resonant degenerate four-wave mixing in SF6

Jean-Luc Boulnois, Philippe Aubourg, A. Van Lerberghe +1 more

Using the isolated P(33)A 12 one-photon resonance in SF6 the degenerate four-wave mixing spectrum is shown to exhibit line splitting below a critical pressure. The dependence of this saturation splitting on the gas pressure and the pump intensity is quantitatively studied.

Applied Physics Letters•Feb 1, 1983•4 citations

Saturation effects in degenerate four-wave mixing on homogeneously broadened coupled transitions

Govind Prasad Agrawal

An analytic nonperturbative treatment of degenerate four-wave mixing is presented to study Zeeman-coherence effects in phase conjugation. The counterpropagating pump waves are taken to be orthogonally circularly polarized and interact with different Zeeman sublevels. The nonlinear medium is modeled in terms of a homogeneously broadened, folded three-level system. Particular attention is paid to the phase-conjugate spectrum obtained by varying the Larmor frequency associated with the Zeeman splitting. A level-crossing resonance is found to occur in the saturation regime and manifests itself as a narrow peak or dip depending on various level decay rates. Even for a purely absorptive system, the Zeeman coupling of the ground-state degenerate sublevels is shown to produce significant phase-conjugate reflectivities at pump intensities much lower than those required for a two-level system.

Physical Review A•Oct 1, 1983•30 citations

Resonant Degenerate Four-Wave Mixing in SO2

Wenqi Wei, Z.Z. Lu, Q. Dong +6 more

We report an experimental investigation of degenerate four-wave mixing spectrum of SO2.A novel beam-split technique is used to compensate the beam drift caused by the laser itself and disturbance from the environment.Degenerate four-wave mixing spectra of the transition B 1 B1 ← X 1 A11 for SO2 are obtained.The degenerate four-wave mixing signal intensity as a function of the total input laser energy is measured.The effects of the laser field intensity on the degenerate four-wave mixing spectrum are analyzed.Our results show that the degenerate four-wave mixing signal intensity rises with laser intensity and tends to saturate.Then, a dip begins to appear at resonance in the profile with increase in laser field.The existence of saturation for degenerate four-wave mixing signal intensity and spectrum profile confirms the prediction of previous theoretical work.

Acta Physica Polonica A•Jun 1, 2020•0 citations

Theory of saturated line shapes in phase-conjugate emission by resonant degenerate four-wave mixing in Doppler-broadened three-level systems

Daniel Bloch, M. Ducloy

We present a theoretical study of phase-conjugate (PC) emission by backward degenerate four-wave mixing (DFWM) processes in a resonant gas medium. In this study, high-intensity (pump) saturation and Doppler broadening are simultaneously taken into account. We develop a general formalism to deal with the saturation effects in the case of a three-level atom (with degenerate frequencies) and obtain analytical expressions of the PC field amplitude (after integration over the velocity distribution) under the following conditions: (1) the probe beam and one of the pump beams have intensities weak enough to be treated at the lowest perturbation order, whereas the other pump intensity is arbitrarily high; (2) the probe crosses the standing pump wave at grazing incidence. It is shown that the saturation induced by the forward pump (copropagating with the probe beam) leads to entirely different behavior of the nonlinear susceptibility from that induced by the backward pump (counterpropagating with the probe beam). This saturation anisotropy is specific to the inhomogeneous broadening of the gas medium, which is also responsible for the frequency splitting experimentally observed in the intensity line shape of the PC emission for large pump intensities. At saturation, this splitting is theoretically shown to be proportional to the Rabi frequency, with a proportionality coefficient critically dependent on the relaxation processes; in the case of a single-relaxation model, the splitting is equal to 1.5 times the Rabi frequency. The PC intensity line shape is demonstrated to be of dispersive origin in the case of backward saturation, whereas for forward saturation, narrow structures are predicted in both real and imaginary parts of the nonlinear susceptibility, also leading to the intensity line-shape splitting. One also finds that the reflectivity of PC mirrors based on resonant DFWM strongly depends on the origin of the saturation. For a saturating forward pump, the PC emission intensity tends toward zero with increasing pump intensities, and it reaches a finite (nonzero) limit in the case of backward saturation. Most of these predictions have been observed experimentally [ BlochD., Phys. Rev. Lett.49, 719 ( 1982)].

Journal of the Optical Society of America•May 1, 1983•67 citations

Saturation splitting of line shapes in noncollinear four-wave mixing in SF_6

O. Di Lorenzo-Filho, Paulo C. de Oliveira, J. R. Rios Leite

Phase-conjugate emission by resonant degenerate four-wave mixing with two counterpropagating weak pump beams and a noncollinear strong object beam was calculated for a Doppler-broadened two-level system. Singlepeak Doppler-free lines with small saturation broadening at a collinear configuration became split for a wide angle. The effect is demonstrated with the use of a CO(2) laser and SF(6). Conversely, calculated line shapes with Stark splitting in a collinear arrangement became single peaked for a wide angle.

Optics Letters•May 1, 1991•4 citations

Resonant degenerate four-wave mixing spectroscopy of transitions with degenerate energy levels: Saturation and polarization effects

Thomas A. Reichardt, Robert P. Lucht

The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.

The Journal of Chemical Physics•Dec 8, 1999•22 citations
The spectrum of degenerate four-wave mixing on a homogeneously broadened one-photon transition is shown to exhibit line splitting when the pump-intensity difference exceeds the saturation intensity. The splitting arises from a saturation mechanism reinforced by the pump imbalance. Experimental evidence of this effect, using SF(6) as the nonlinear medium, is presented.
An analytic nonperturbative treatment of degenerate four-wave mixing is presented to study Zeeman-coherence effects in phase conjugation. The counterpropagating pump waves are taken to be orthogonally circularly polarized and interact with different Zeeman sublevels. The nonlinear medium is modeled in terms of a homogeneously broadened, folded three-level system. Particular attention is paid to the phase-conjugate spectrum obtained by varying the Larmor frequency associated with the Zeeman splitting. A level-crossing resonance is found to occur in the saturation regime and manifests itself as a narrow peak or dip depending on various level decay rates. Even for a purely absorptive system, the Zeeman coupling of the ground-state degenerate sublevels is shown to produce significant phase-conjugate reflectivities at pump intensities much lower than those required for a two-level system.
We report an experimental investigation of degenerate four-wave mixing spectrum of SO2.A novel beam-split technique is used to compensate the beam drift caused by the laser itself and disturbance from the environment.Degenerate four-wave mixing spectra of the transition B 1 B1 ← X 1 A11 for SO2 are obtained.The degenerate four-wave mixing signal intensity as a function of the total input laser energy is measured.The effects of the laser field intensity on the degenerate four-wave mixing spectrum are analyzed.Our results show that the degenerate four-wave mixing signal intensity rises with laser intensity and tends to saturate.Then, a dip begins to appear at resonance in the profile with increase in laser field.The existence of saturation for degenerate four-wave mixing signal intensity and spectrum profile confirms the prediction of previous theoretical work.
We present a theoretical study of phase-conjugate (PC) emission by backward degenerate four-wave mixing (DFWM) processes in a resonant gas medium. In this study, high-intensity (pump) saturation and Doppler broadening are simultaneously taken into account. We develop a general formalism to deal with the saturation effects in the case of a three-level atom (with degenerate frequencies) and obtain analytical expressions of the PC field amplitude (after integration over the velocity distribution) under the following conditions: (1) the probe beam and one of the pump beams have intensities weak enough to be treated at the lowest perturbation order, whereas the other pump intensity is arbitrarily high; (2) the probe crosses the standing pump wave at grazing incidence. It is shown that the saturation induced by the forward pump (copropagating with the probe beam) leads to entirely different behavior of the nonlinear susceptibility from that induced by the backward pump (counterpropagating with the probe beam). This saturation anisotropy is specific to the inhomogeneous broadening of the gas medium, which is also responsible for the frequency splitting experimentally observed in the intensity line shape of the PC emission for large pump intensities. At saturation, this splitting is theoretically shown to be proportional to the Rabi frequency, with a proportionality coefficient critically dependent on the relaxation processes; in the case of a single-relaxation model, the splitting is equal to 1.5 times the Rabi frequency. The PC intensity line shape is demonstrated to be of dispersive origin in the case of backward saturation, whereas for forward saturation, narrow structures are predicted in both real and imaginary parts of the nonlinear susceptibility, also leading to the intensity line-shape splitting. One also finds that the reflectivity of PC mirrors based on resonant DFWM strongly depends on the origin of the saturation. For a saturating forward pump, the PC emission intensity tends toward zero with increasing pump intensities, and it reaches a finite (nonzero) limit in the case of backward saturation. Most of these predictions have been observed experimentally [ BlochD., Phys. Rev. Lett.49, 719 ( 1982)].
Phase-conjugate emission by resonant degenerate four-wave mixing with two counterpropagating weak pump beams and a noncollinear strong object beam was calculated for a Doppler-broadened two-level system. Singlepeak Doppler-free lines with small saturation broadening at a collinear configuration became split for a wide angle. The effect is demonstrated with the use of a CO(2) laser and SF(6). Conversely, calculated line shapes with Stark splitting in a collinear arrangement became single peaked for a wide angle.
The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.