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

Effect of propagation on pulsed four-wave mixing

P. Weisman, A. D. Wilson‐Gordon, Harry Friedmann

Published Apr 17, 2000• 11 citations
Publisher

Abstract

We examine the effect of propagation on the resonance Rabi sideband of the four-wave mixing (FWM) spectrum, obtained when short temporally displaced pump and probe pulses interact with an optically thick medium of two-level atoms. We find that the dependence of the time-integrated FWM signal on the pump-probe delay is considerably altered by propagation. In particular, the logarithm of the FWM signal, for the case where the probe precedes the pump, deviates from linearity and may even increase over a range of values. An explanation is given in terms of the overlap of the pump envelope with the coherent response of the atomic system to the probe, both of which are modified on propagation.

DOI
10.1103/physreva.61.053816

Related papers

Effect of propagation on pulsed four-wave mixing

P. Weisman, A. D. Wilson‐Gordon, Harry Friedmann

Summary form only given. It is well-known that the steady-state four-wave mixing (FWM) spectrum, obtained when a two-level atomic system interacts with a coherent pump of arbitrary intensity and a weak probe, is symmetrical and consists of three peaks: a central peak and two Rabi sidebands. Previously, we showed for temporally nonoverlapping pulses, that the spectrum becomes extremely asymmetrical and that only the Rabi sideband near the resonance frequency survives, in the case where the probe precedes the pump. For the opposite case, where the pump precedes the probe, no FWM spectrum is obtained at all. It should be noted that these results hold true provided the pump and probe pulses are much shorter than the transverse relaxation time T/sub 2/ and the pump-probe time delay /spl Delta/t/sub 0/ (/spl Delta/t/sub 0/<0 when the probe precedes the pump). We have also shown that T/sub 2/ can be determined from the slope of the semilog plot of the FWM intensity, near the resonance sideband, versus the pump-probe time delay /spl Delta/t/sub 0/ (for the case /spl Delta/t/sub 0/<0).

Conference on Lasers and Electro-Optics•Aug 29, 2005•0 citations

Effect of four-wave mixing on induced waveguiding

D. Bortman-Arbiv, A. D. Wilson‐Gordon, Harry Friedmann

We study the waveguiding induced in a weak probe propagating in a medium of two-level atoms driven by a copropagating strong pump. We show that when the transverse profile of the pump exhibits solitonlike oscillations, similar oscillations can be induced in the transverse profile of the probe. When the probe waist size is initially narrower than that of the pump, the probe adjusts its width after a short propagation distance, to that of the pump. We show that the effect of the weak beam, which is created during propagation by four-wave mixing, on the waveguiding of the probe, becomes important when the medium is optically thick. This suggests that the importance of four-wave mixing in modifying induced waveguiding should be considered in other waveguiding schemes.

Physical Review A•Feb 11, 2000•7 citations

Spectral response and propagational instability for pump-probe propagation in a two-level medium

Michael E. Crenshaw, C. M. Bowden

The interaction of a strong nearly resonant cw pump laser and a weak cw probe laser in a medium consisting of two-level atoms was studied by numerical integration of the Maxwell-Bloch equations. With propagation into the optically thick medium, the numerically calculated probe gain spectrum deviates substantially from one calculated by a four-wave-mixing formulation of coupled-wave theory with an undepleted pump. For probe frequencies inside the modified gain region, the laser field, initially in an unstable steady-state condition, evolves to a stable solution of the sine-Gordon equation.

Physical Review Letters•Sep 2, 1991•4 citations

Four-Wave Mixing with Short Temporally Nonoverlapping Pulses

A. D. Wilson‐Gordon, Harry Friedmann

We predict that the four-wave mixing (FWM) excitation spectrum for a two-level system becomes extremely asymmetrical when steady-state excitation is replaced by pulsed excitation, using temporally nonoverlapping probe and pump pulses. We also show that when a resonant probe pulse precedes the detuned pump pulse, the FWM signal may become more intense than when the pulses overlap. These effects are attributed to free-induction decay (FID): the coherence induced in the two-level system by a short resonant probe pulse survives the pulse (FID) and replaces it in producing a strong nonlinear signal on interaction with the strong pump pulse. Moreover, by plotting the FWM signal intensity as a function of the delay between the probe and pump pulses, an efficient method is proposed for determining short transverse relaxation times or fast chemical reaction rates.

The Journal of Physical Chemistry A•Nov 1, 1998•2 citations

Anomalous spectral response and propagationl instability for pump-probe propagation in a two-level medium

Michael E. Crenshaw, C. M. Bowden

We investigated the sideband instability by numerical integration of the Maxwell-Bloch equations for propagation of a nearly resonant pump laser and a weak probe laser in a system of two-level atoms. In an optically thick medium, the probe gain (absorption) spectrum becomes a function of propagation distance. We find that the well-known gain resonance at the generalized Rabi frequency Ω' is suppressed and a broad asymmetric gain region forms on each side of the laser frequency. For probe-pump detunings inside these gain regions, the field envelope breaks up into periodic traveling waves that are compared to the polycnoidal solutions of the sine-Gordon equation with periodic boundary conditions.

Quantum Electronics and Laser Science Conference•May 12, 1991•0 citations

Quantum theory of Rabi sideband generation by forward four-wave mixing

G. S. Agarwal, Robert W. Boyd

The predictions of a quantum-mechanical theory of forward four-wave mixing in a homogeneously broadened system of two-level atoms are presented. In the limit of a very short interaction region, the predictions of this theory reproduce those of well-known theories for the spontaneous-emission spectrum of an atom in the presence of an intense laser field. More generally, the theory predicts how the emission spectrum is modified due to propagation effects for a medium of arbitrary length. For long propagation path lengths, the emitted radiation can be quite intense and has a spectrum that is strongly peaked at the Rabi sidebands of the incident laser frequency. The theory shows that Rabi sideband generation in the forward direction can be understood as parametric amplification of weak radiation emitted spontaneously at the Rabi sidebands. The quantum noise that initiates the four-wave-mixing process has contributions both from fluctuations in the incident vacuum radiation field and from fluctuations in the polarization of the atomic dipoles. Both contributions are important for the case of a radiatively broadened medium, although the material fluctuations make the dominant contribution for the case of a medium in which the broadening is largely collisional. Under certain conditions large amounts of squeezing in the radiated field are predicted.

Physical Review A•Oct 1, 1988•41 citations
We examine the effect of propagation on the resonance Rabi sideband of the four-wave mixing (FWM) spectrum, obtained when short temporally displaced pump and probe pulses interact with an optically thick medium of two-level atoms. We find that the dependence of the time-integrated FWM signal on the pump-probe delay is considerably altered by propagation. In particular, the logarithm of the FWM signal, for the case where the probe precedes the pump, deviates from linearity and may even increase over a range of values. An explanation is given in terms of the overlap of the pump envelope with the coherent response of the atomic system to the probe, both of which are modified on propagation.
Summary form only given. It is well-known that the steady-state four-wave mixing (FWM) spectrum, obtained when a two-level atomic system interacts with a coherent pump of arbitrary intensity and a weak probe, is symmetrical and consists of three peaks: a central peak and two Rabi sidebands. Previously, we showed for temporally nonoverlapping pulses, that the spectrum becomes extremely asymmetrical and that only the Rabi sideband near the resonance frequency survives, in the case where the probe precedes the pump. For the opposite case, where the pump precedes the probe, no FWM spectrum is obtained at all. It should be noted that these results hold true provided the pump and probe pulses are much shorter than the transverse relaxation time T/sub 2/ and the pump-probe time delay /spl Delta/t/sub 0/ (/spl Delta/t/sub 0/<0 when the probe precedes the pump). We have also shown that T/sub 2/ can be determined from the slope of the semilog plot of the FWM intensity, near the resonance sideband, versus the pump-probe time delay /spl Delta/t/sub 0/ (for the case /spl Delta/t/sub 0/<0).
We study the waveguiding induced in a weak probe propagating in a medium of two-level atoms driven by a copropagating strong pump. We show that when the transverse profile of the pump exhibits solitonlike oscillations, similar oscillations can be induced in the transverse profile of the probe. When the probe waist size is initially narrower than that of the pump, the probe adjusts its width after a short propagation distance, to that of the pump. We show that the effect of the weak beam, which is created during propagation by four-wave mixing, on the waveguiding of the probe, becomes important when the medium is optically thick. This suggests that the importance of four-wave mixing in modifying induced waveguiding should be considered in other waveguiding schemes.
The interaction of a strong nearly resonant cw pump laser and a weak cw probe laser in a medium consisting of two-level atoms was studied by numerical integration of the Maxwell-Bloch equations. With propagation into the optically thick medium, the numerically calculated probe gain spectrum deviates substantially from one calculated by a four-wave-mixing formulation of coupled-wave theory with an undepleted pump. For probe frequencies inside the modified gain region, the laser field, initially in an unstable steady-state condition, evolves to a stable solution of the sine-Gordon equation.
We predict that the four-wave mixing (FWM) excitation spectrum for a two-level system becomes extremely asymmetrical when steady-state excitation is replaced by pulsed excitation, using temporally nonoverlapping probe and pump pulses. We also show that when a resonant probe pulse precedes the detuned pump pulse, the FWM signal may become more intense than when the pulses overlap. These effects are attributed to free-induction decay (FID): the coherence induced in the two-level system by a short resonant probe pulse survives the pulse (FID) and replaces it in producing a strong nonlinear signal on interaction with the strong pump pulse. Moreover, by plotting the FWM signal intensity as a function of the delay between the probe and pump pulses, an efficient method is proposed for determining short transverse relaxation times or fast chemical reaction rates.
We investigated the sideband instability by numerical integration of the Maxwell-Bloch equations for propagation of a nearly resonant pump laser and a weak probe laser in a system of two-level atoms. In an optically thick medium, the probe gain (absorption) spectrum becomes a function of propagation distance. We find that the well-known gain resonance at the generalized Rabi frequency Ω' is suppressed and a broad asymmetric gain region forms on each side of the laser frequency. For probe-pump detunings inside these gain regions, the field envelope breaks up into periodic traveling waves that are compared to the polycnoidal solutions of the sine-Gordon equation with periodic boundary conditions.
The predictions of a quantum-mechanical theory of forward four-wave mixing in a homogeneously broadened system of two-level atoms are presented. In the limit of a very short interaction region, the predictions of this theory reproduce those of well-known theories for the spontaneous-emission spectrum of an atom in the presence of an intense laser field. More generally, the theory predicts how the emission spectrum is modified due to propagation effects for a medium of arbitrary length. For long propagation path lengths, the emitted radiation can be quite intense and has a spectrum that is strongly peaked at the Rabi sidebands of the incident laser frequency. The theory shows that Rabi sideband generation in the forward direction can be understood as parametric amplification of weak radiation emitted spontaneously at the Rabi sidebands. The quantum noise that initiates the four-wave-mixing process has contributions both from fluctuations in the incident vacuum radiation field and from fluctuations in the polarization of the atomic dipoles. Both contributions are important for the case of a radiatively broadened medium, although the material fluctuations make the dominant contribution for the case of a medium in which the broadening is largely collisional. Under certain conditions large amounts of squeezing in the radiated field are predicted.