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Physical Review A

Four-wave mixing resonantly enhanced by ac-Stark-split levels in self-trapped filaments of light

Donald J. Harter, Robert W. Boyd

Published Feb 1, 1984• 102 citations
Publisher

Abstract

It is observed that when an intense, nearly resonant laser beam propagates through a dilute ($N<5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$) vapor of sodium atoms, a four-wave-mixing process occurs, leading to the generation of strong, coherent radiation in the forward direction at frequencies symmetrically detuned from that of the exciting laser by the generalized Rabi frequency. This phenomenon is explained as resulting from a nearly phase-matched mixing process utilizing the nonlinear response of the sodium atom. Our analysis is based on a solution of the density-matrix equations of motion that includes the effect of level shifts induced by the ac Stark effect, which can be as great as 10 \AA{} for our experimental conditions, and which leads to gain due to the stimulated three-photon effect at one Rabi sideband and to strong coupling due to a parametric mixing process between radiation at the two sideband frequencies. It is also observed that at larger sodium densities ($N\ensuremath{\gtrsim}5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$), self-focusing of the laser beam can occur, leading to several complicating effects. We find experimentally that the on-resonance Rabi frequency $\ensuremath{\Omega}$ within a self-trapped filament lies preferentially within the range from 1 to 3 times the laser detuning from resonance $\ensuremath{\Delta}$ and we explain this result as a consequence of strong saturation of the refractive index that occurs for $\ensuremath{\Omega}\ensuremath{\gtrsim}\ensuremath{\Delta}$. Four-wave mixing is found to occur within these self-trapped filaments. The high-frequency sideband thus generated is trapped within the filament, whereas the lower-frequency sideband is ejected as a consequence of Snell's law and forms a cone surrounding the transmitted laser beam.

DOI
10.1103/physreva.29.739

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Physical Review A•Jun 1, 1986•6 citations
It is observed that when an intense, nearly resonant laser beam propagates through a dilute (N<5\ifmmode×\else\texttimes\fi1014N<5\ifmmode\times\else\texttimes\fi{}{10}^{14}N<5\ifmmode×\else\texttimes\fi1014 cm\ensuremath−3{\mathrm{cm}}^{\ensuremath{-}3}cm\ensuremath−3) vapor of sodium atoms, a four-wave-mixing process occurs, leading to the generation of strong, coherent radiation in the forward direction at frequencies symmetrically detuned from that of the exciting laser by the generalized Rabi frequency. This phenomenon is explained as resulting from a nearly phase-matched mixing process utilizing the nonlinear response of the sodium atom. Our analysis is based on a solution of the density-matrix equations of motion that includes the effect of level shifts induced by the ac Stark effect, which can be as great as 10 \AA{} for our experimental conditions, and which leads to gain due to the stimulated three-photon effect at one Rabi sideband and to strong coupling due to a parametric mixing process between radiation at the two sideband frequencies. It is also observed that at larger sodium densities (N\ensuremath≳5\ifmmode×\else\texttimes\fi1014N\ensuremath{\gtrsim}5\ifmmode\times\else\texttimes\fi{}{10}^{14}N\ensuremath≳5\ifmmode×\else\texttimes\fi1014 cm\ensuremath−3{\mathrm{cm}}^{\ensuremath{-}3}cm\ensuremath−3), self-focusing of the laser beam can occur, leading to several complicating effects. We find experimentally that the on-resonance Rabi frequency \ensuremathΩ\ensuremath{\Omega}\ensuremathΩ within a self-trapped filament lies preferentially within the range from 1 to 3 times the laser detuning from resonance \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ and we explain this result as a consequence of strong saturation of the refractive index that occurs for \ensuremathΩ\ensuremath≳\ensuremathΔ\ensuremath{\Omega}\ensuremath{\gtrsim}\ensuremath{\Delta}\ensuremathΩ\ensuremath≳\ensuremathΔ. Four-wave mixing is found to occur within these self-trapped filaments. The high-frequency sideband thus generated is trapped within the filament, whereas the lower-frequency sideband is ejected as a consequence of Snell's law and forms a cone surrounding the transmitted laser beam.
Four-wave optical parametric amplification enhanced by the ac Stark effect has been observed, with the use of a dye laser tuned near the D2{D}_{2}D2​ line of sodium. This process leads to the generation of sidebands displaced from the laser frequency by the generalized Rabi frequency. Under certain experimental conditions, the emitted radiation is in the form of a cone surrounding the transmitted laser beam. A theoretical model that describes these effects is presented.
Experimental studies have been made of conjugate wave generation in a Na metal vapor heat pipe. Detailed measurements of gain profiles, pump beam absorption, and parametric wave generation at infrared frequencies for phase conjugation near the two-photon resonance with the Na 4d2D5/2 state, yield details of the effects of parasitic processes on degenerate four-wave mixing. Studies are conducted with an excimer-pumped dye laser system with ~4 ns pulses of < 10mJ/pulse, traversing Na vapor heat pipe. Included in the measurements are pump beam depletion, probe and conjugate beam intensities, and infrared light which is generated by the strong pump beams through stimulated Raman (SR) and amplified spontaneous emission processes. The role of ac Stark shifting in degenerate four-wave mixing near the 4d level is studied. We find a new effect involving a large contribution to the ac Stark effect from the internally generated SR photons. We observe a rapid onset with pressure of stimulated Raman emission accompanied by a dramatic increase in the ac Stark profile of the 4d level, and the sharp onset of gain saturation for the phase conjugate signal, due to the competition of these two processes. This effect results in an ac Stark coefficient which can be very nonlinear in laser power and Na pressure.
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 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.
Two laser beams at frequencies ${\ensuremath{\nu}}_{1}$ and ${\ensuremath{\nu}}_{2}$ are used to produce nonlinear scattering (wave mixing) in I2{\mathrm{I}}_{2}I2​ vapor at frequency 2${\ensuremath{\nu}}_{1}$+${\ensuremath{\nu}}_{2}$. The scattering results from near-resonant allowed transitions in I2{\mathrm{I}}_{2}I2​ molecules and is observed to be anomalously strong when both laser beam frequencies are detuned in the same direction from frequencies corresponding to resonance in the free molecule. The strong scattering is interpreted in terms of a resonantly enhanced ac Stark shift caused by a configuration interaction between the ``dressed molecular levels.'' By tuning the two pulses simultaneously, a tuning range of approximately 2 A\r{} (50 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) is achieved in the mixed wave. The scattering process should therefore have practical application in the efficient generation of tunable coherent radiation in the ultraviolet and vacuum-ultraviolet range of the spectrum. Some of the spectroscopic properties of the three-quantum state at E\ensuremath{\sim}53 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ are studied.