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Nonlinear optical experiments in sodium vapor and comparison with Doppler-broadened two-level-atom theory.

John F. Valley

Published Jan 1, 1989• 0 citations

Abstract

Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.

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Physical Review A•Oct 1, 1998•11 citations

Two spectral regions of gain exist for a weak probe beam propagating through a medium of two-level-atoms pumped by a strong near-resonance field. Experimentally a cw ring-dye laser is used to explore this gain at the Na D₂ resonance in a vapor. Plane-wave calculations of probe-gain spectra which include the Doppler broadening inherent in a vapor agree well with experimental spectra obtained with a Fabry-Perot interferometer. Such two-beam-coupling gain might have applications as optical pre- or power amplifiers. The gain is also the primary step in four-wave-mixing. Mixing of the pump and sideband which experiences gain produces the medium polarization from which the fourth-wave arises. For phase-matched propagation the fourth-wave, which is at a frequency that experiences little or negative probe-gain (i.e., absorption), grows at nearly the same rate as the primary sideband. Together the two sidebands extract far more than twice as much energy from the pump than does the primary sideband acting alone. Experimentally four-wave-mixing which arises from noise at the gain-sideband-frequency is sometimes accompanied by conical emission at the fourth-wave sideband. Since this sideband is also seen on axis the explanation cannot be simply phase-matching. Simulations which include the full transverse nature of the experiment are currently running on a CRAY supercomputer. These simulations indicate that the radial variation of the medium index of refraction is responsible for conical emission.

The results of an experimental and theoretical study of the gain (or absorption) experienced by a weak probe beam propagating through a sodium vapor in the presence of an intense pump field that is nearly resonant with the 3s→3p atomic transition are presented. In general, the probe transmission spectrum is found to be comprised of three distinct features, two of which can lead to amplification of the probe wave. The origin of these features can be traced to the modification of the atomic level structure by the ac Stark effect. The experimentally measured spectra are in good agreement with the predictions of a theoretical model based on the solution of the density-matrix equations of motion for a two-level atom and including the effects of Doppler broadening. The dependence of the induced gain on the pressure of a helium buffer gas has been measured and is found to be in good agreement with the predictions of theory. The maximum gain observed in these experiments occurs at one of the Rabi sidebands and leads to a 38-fold increase in the intensity of the probe wave.

We present the results of an experimental and theoretical study of the gain (or absorption) experienced by a weak probe beam propagating through a sodium vapor in the presence of an intense pump field that is nearly resonant with the 3s → 3p atomic transition. The probe-transmission spectrum includes three distinct features that result from the modification of the atomic-level structure by the ac-Stark effect. Two of these features can lead to amplification of the probe wave. We measured the dependence of the probe spectrum on the detuning of the pump beam from resonance and on the pressure of a helium buffer gas. The experimentally obtained spectra are in good agreement with the predictions of a theoretical model based on the solution of the density-matrix equations of motion for a two-level atom and including the effects of Doppler broadening. The maximum gain measured in these experiments occurs at one of the Rabi sidebands and leads to a 38-fold increase in the intensity of the probe wave. Under some experimental conditions, we also observed two additional resonances, which are due to stimulated Raman scattering involving the sodium ground-state hyperfine levels.

We have used a two-wave mixing gain process in sodium vapor to construct a self-pumped phase conjugator. This was done by forming a resonator around a quartz sodium cell equipped with Brewster angle windows. A pump beam is then directed into the sodium cell at a small angle to the longitudinal axis of the resonator. At sufficiently high cw pump intensities, the ac-Stark effect pro- vides sufficient gain to achieve oscillation. Although this gain is unidirectional it occurs on the wings of the sodium resonance so that the backward traveling optical field in the resonator does not experience loss due to sodium absorption. The counterpropagating optical fields in the resonator interact with the pump in an internal four- wave mixing process to produce a fourth optical field (phase conjugate to the pump field). Our experiment was conducted at the sodium D2 resonance. The pump laser was a 699 autoscan single frequency ring dye laser providing pump intensities up to several hundred watts per square centimeter.

We present the results of an experimental and theoretical study of the gain experienced by a weak probe beam propagating through a sodium vapor in the presence of an intense pump field that is nearly resonant with the 3s→3p atomic transition. This interaction provides a means by which the outputs of two lasers can be combined coherently. The probe transmission spectrum is comprised of three distinct features, two of which result in amplification of the probe wave. The origin of these features can be traced to the modification of the atomic level structure by the ac Stark effect. The experimentally measured spectra are in good agreement with the predictions of a theoretical model based on the solution of the density-matrix equations of motion for a two-level atom and including the effects of Doppler broadening. The dependence of the induced gain on the pressure of a helium buffer gas has been measured and is in good agreement with the predictions of theory. The maximum gain observed in these experiments occurs at one of the Rabi sidebands and leads to a 38-fold increase in the intensity of the probe wave.

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.