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Optics Letters

Angular dependence of line shape and strength of degenerate four-wave mixing in a Doppler-broadened system with optical pumping

L. M. Humphrey, J. P. Gordon, P. F. Liao

Published Feb 1, 1980• 44 citations
Publisher

Abstract

Results of experiments investigating the effects of optical pumping and atomic motion on cw degenerate four-wave mixing in atomic sodium vapor are presented. The signal strength is found to decrease as (sin θ)−2, where θ is the angle between the object and pump waves; however, the linewidth for generation is Doppler free and is independent of θ. Agreement is found with a simple model of the mixing process. Distortions of the atomic velocity distribution (produced in our experiments by optical pumping) are found to be essential for efficient cw generation. A new modulation scheme for the discrimination against background is used.

DOI
10.1364/ol.5.000056

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Conference on Lasers and Electro-Optics•Apr 25, 1988•0 citations
Results of experiments investigating the effects of optical pumping and atomic motion on cw degenerate four-wave mixing in atomic sodium vapor are presented. The signal strength is found to decrease as (sin θ)−2, where θ is the angle between the object and pump waves; however, the linewidth for generation is Doppler free and is independent of θ. Agreement is found with a simple model of the mixing process. Distortions of the atomic velocity distribution (produced in our experiments by optical pumping) are found to be essential for efficient cw generation. A new modulation scheme for the discrimination against background is used.
We study phase-conjugate degenerate four-wave mixing in an optically pumped, two-level atomic system (the 3s2S1/2,{3s}^{2}{S}_{1/2},3s2S1/2​, F=2,F=2,F=2, ${m}_{\mathrm{F}}=\stackrel{\ensuremath{\rightarrow}}{2}{3p}^{2}{P}_{3/2},$ F=3,F=3,F=3, mF=3{m}_{\mathrm{F}}=3mF​=3 transition in a diffuse, collision-free, thermal beam of sodium). In this investigation, we study the detailed line shape and strength of the four-wave mixing signal as a function of the intensity of the cw pump waves, and of the velocity of the atoms. Our technique allows us to examine the four-wave mixing interaction under conditions in which the Doppler shift, the natural linewidth of the transition, and the Rabi frequency for the interaction are each comparable with one another. From our experimental measurements and computational results, we show that the line shapes are very complex in this regime, and that they depend sensitively upon the atomic velocity, especially in the case when the intensity of the forward and backward pump beams exceeds the saturation intensity for the transition.
We present experimental observations of phase-conjugate degenerate four-wave mixing in a two-level atomic system (the ${3s}^{2}{S}_{1/2}, F=2, {m}_{F}=\stackrel{\ensuremath{\rightarrow}}{2}{3p}^{2}{P}_{3/2}, F=3, {m}_{F}=3$ transition in a diffuse, collision-free, thermal beam of atomic sodium) driven by cw, narrow-band $(\ensuremath{\sim}250 \mathrm{kHz}),$ stabilized pump and probe fields. The primary measurements that we report are of the peak signal strength of the four-wave-mixing interaction and the bandwidth of the four-wave-mixing spectrum (as the laser frequency is tuned through the resonant frequency) as a function of the intensity of the pump field. We compare these measurements with the predictions of a theoretical analysis in which extension to include the effect of the small transverse velocity $(\ensuremath{\sim}3 \mathrm{m}/\mathrm{s}\mathrm{e}\mathrm{c})$ of the atomic beam is critical. These measurements provide a direct verification of the theory of this important nonlinear interaction.
We present in this paper a theoretical study of the angular dependence of phase-conjugate emission via resonant degenerate four-wave mixing (FWM) in Doppler-broadened gas media. The nonlinear optical polarization is calculated through an expansion of the atomic density matrix up to the third order in the incident fields. One finds that, when the incident frequency is resonant for a single-photon transition, both strength and lineshape of the phase-conjugate emission strongly depend on the angle 0 between standing pump wave and probe wave. The emission intensity, maximum at grazing incidences, decreases rapidly by several orders of magnitude when 0 increases. Simultaneously the emission linewidth increases from homogeneous to Doppler width. Similar effects are predicted for nearly-degenerate FWM (different pump and probe frequencies). In particular, one shows that the bandwidth of the equivalent optical reflection filter undergoes a Doppler-broadening linearly increasing with sin θ. On the opposite, none of the above effects is predicted in two-photon-resonant FWM which does not exhibit any angular dependence.
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.
Degenerate four-wave mixing in sodium vapor is investigated using a flashlamp-pumped dye laser synchronized on a cw dye laser. At low atomic density, the reflectivity versus the pump intensity and the line shapes are in good agreement with theoretical predictions in the case of both plane waves and Gaussian beams. At high atomic density, reflectivities much higher than unity have been observed. The influence of the pump imbalance has been studied as well as the deformation of the wave front of the conjugated beam introduced by the pump beams. In the high-atomic-density case, the theoretical problem is more complex, and our experimental results exhibit only qualitative agreement with theory.