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Conference on Lasers and Electro-Optics

Effect of propagation on pulsed four-wave mixing

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

Published Aug 29, 2005• 0 citations
Publisher

Abstract

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).

DOI
10.1109/iqec.2000.907816

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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 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.
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 present results of our experimental investigations of phase-conjugate four-wave mixing in a nearly Doppler-free, collisionless, two-level quantum system with a partially coherent non-Markovian laser field. The two components of the laser field---an intense pump and a weak, time-delayed probe---are derived from a single narrow-band cw laser source on which phase and frequency fluctuations conforming to the phase diffusion model are superimposed. We carry out these measurements using the D2{D}_{2}D2​ transition in an optically pumped diffuse beam of atomic sodium. We vary the pump intensity, laser bandwidth, and temporal delay between the pump and probe, and measure the peak signal strength, the bandwidth, and the asymmetry of the four-wave-mixing spectrum. For comparison with our experimental results of the peak signal strength, we also analyze the same interaction numerically, through direct integration of the optical Bloch equations. The numerical results are in good agreement with the measurements.
We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the 3s2S1∕23s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}3s2S1∕2​, F=2F=2F=2, ${m}_{F}=2\ensuremath{\rightarrow}3p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$, F=3F=3F=3, mF=3{m}_{F}=3mF​=3 transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the ``local'' DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.
A study has been made of the effect of relaxation times on the four-wave mixing (FWM) signal response in frequency space for a two-level system where intramolecular coupling is explicitly taken into account within a vibronic model. The model is a generalization of the conventional two-level approach in that it includes a simplified description of the molecular structure and the explicit consideration of permanent dipole moments. Significant changes in both the intensity and shape of the peaks of the FWM spectrum are observed, due mainly to changes in the ratio between the longitudinal and transversal relaxation times, T 1/T 2.