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Optics Letters

Conical emission due to four-wave mixing enhanced by the ac Stark effect in self-trapped filaments of light

Donald J. Harter, Robert W. Boyd

Published Oct 1, 1982• 15 citations
Publisher

Abstract

Experimental evidence is presented that shows that the conical emission often found surrounding a near-resonant laser beam after it passes through an atomic vapor is due to nondegenerate four-wave mixing enhanced by the ac Stark effect. We demonstrate self-trapping of a pulsed dye-laser beam in sodium vapor for wavelengths 0.04 to 10 A shorter than that of the D(2) resonance and show that the four-wave mixing process leading to conical emission occurs within these self-trapped filaments.

DOI
10.1364/ol.7.000491

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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.

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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.

International Laser Science Conference•Jan 1, 1986•2 citations
Experimental evidence is presented that shows that the conical emission often found surrounding a near-resonant laser beam after it passes through an atomic vapor is due to nondegenerate four-wave mixing enhanced by the ac Stark effect. We demonstrate self-trapping of a pulsed dye-laser beam in sodium vapor for wavelengths 0.04 to 10 A shorter than that of the D(2) resonance and show that the four-wave mixing process leading to conical emission occurs within these self-trapped filaments.
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.
A detailed study on yellow conical emission observed in dense sodium vapor following near-resonant one-photon excitation of the Na 42P levels was performed. The origins of conical emission are suggested to be due to Raman resonant four-wave parametric mixing processes. In order to describe spectral and spatial features of off-axis emission, we introduce self-phase modulation and induced-phase modulation as important additional nonlinear processes, explaining the nonmonotonic detuning of the wavelength of the conical radiation with the exiting laser wavelength in the vicinity of resonance transitions. The spatial evolution of emission generated via four-wave mixing is modeled by solving the two-dimensional nonlinear Schrödinger equation describing the spatial evolution of light beams in a nonlinear media. Experimental and theoretical results are presented and discussed.
An experimental and theoretical investigation is made of the angular spectrum of a near-resonant femtosecond laser pulse propagating through sodium vapor. A directional fluorescence emission corresponding to single-photon sodium transition $3S\ensuremath{\rightarrow}3{P}_{1∕2,3∕2}$ has been registered for the pump wavelength ranging from 540to605nm540\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}605\phantom{\rule{0.3em}{0ex}}\mathrm{nm}540to605nm. It is found that such emission can be detected under the conditions of single-photon (enhanced by two-photon) resonance of pump frequency with relevant atomic states. Theoretical treatment of the field-matter interaction by means of the nonperturbative (semiclassical) approach revealed conical components of the cylindrically symmetric beam spectrum originating both from the fluorescence induced by coherent atomic polarization and four-wave mixing.
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.