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Physical Review A

Asymmetry in pulsed four-wave mixing

Harry Friedmann, A. D. Wilson‐Gordon

Published Jun 1, 1998• 9 citations
Publisher

Abstract

The Bloch equations are solved for a two-level system interacting with a strong pulsed laser pump and a weak pulsed laser probe. It is shown that the four-wave-mixing excitation spectrum, which is symmetrical with respect to the pump-probe detuning $\ensuremath{\delta}$ in the steady-state regime, becomes asymmetrical under pulsed conditions. The asymmetry is ascribed mainly to the linewidths of the pump and probe laser pulses.

DOI
10.1103/physreva.57.4854

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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.

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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
The Bloch equations are solved for a two-level system interacting with a strong pulsed laser pump and a weak pulsed laser probe. It is shown that the four-wave-mixing excitation spectrum, which is symmetrical with respect to the pump-probe detuning \ensuremathδ\ensuremath{\delta}\ensuremathδ in the steady-state regime, becomes asymmetrical under pulsed conditions. The asymmetry is ascribed mainly to the linewidths of the pump and probe laser pulses.
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.
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).
It is shown that saturation causes the three-peaked four-wave-mixing (FWM) signal at frequency 2${\ensuremath{\omega}}_{1}$-${\ensuremath{\omega}}_{2}$, obtained from the interaction of a two-level system with a ``probe'' laser of varying frequency ${\ensuremath{\omega}}_{2}$ and a ``pump'' laser of fixed frequency ${\ensuremath{\omega}}_{1}$, to become asymmetrical on increasing the probe-laser intensity. Whereas saturation peaks occur in the population-inversion spectrum at one-photon and multiphoton resonances, this is not so for the FWM spectrum, where often the peaks correspond to nothing more than minima in the population-inversion spectrum.
We study theoretically the phenomenon of pulsed four‐wave mixing in intersubband transitions of a symmetric semiconductor quantum well structure. In the theoretical model we consider two quantum well subbands that are coupled by a strong pulsed pump electromagnetic field and a weak pulsed probe electromagnetic field. For the description of the system dynamics we use the density matrix equations obtained from the effective nonlinear Bloch equations. We calculate the time‐integrated four‐wave mixing spectrum for various pulse shapes and electron sheet densities and study the effects of pulse shape on four‐wave mixing.
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.