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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Four-wave mixing in V-type atoms in a nonresonant light field

Л. С. Гайда, V. Kartazaev, V. Savchik

Published Jul 22, 2002• 0 citations
Publisher

Abstract

The angular and spectral nature of the emission spectra of sodium atoms driven by the laser tuned near the dispersion- free point of the main doublet has been studied. The experiment shows strong angular dependence of parametrically generated waves. The main features of the registered emission spectra can be explained as a result of FWM in a V- type system. Experimental results show that self- filamentation does not play critical role in forming cone radiation.

DOI
10.1117/12.475900

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The angular and spectral nature of the emission spectra of sodium atoms driven by the laser tuned near the dispersion- free point of the main doublet has been studied. The experiment shows strong angular dependence of parametrically generated waves. The main features of the registered emission spectra can be explained as a result of FWM in a V- type system. Experimental results show that self- filamentation does not play critical role in forming cone radiation.
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.
The parametric and nonparametric nonlinear processes responsible for generation of directional infrared radiation in sodium vapors, excited to the 4D 5/2 energy level by resonant laser radiation, are identified by the transfer of orbital angular momentum from the pump radiation to the generated fields. We show that the optical fields generated by amplified spontaneous emission (ASE) simultaneously participate in several loops of four-wave mixing (FWM) generating new directional emission. The measured spectral linewidth of the FWM emission at 819.7 nm sets an upper limit to the linewidth of two fields resulting from ASE at 2338.6 and 9093.0 nm, assuming their spectra are uncorrelated. Understanding details of the new-field generation is central to applications such as directional laser guide stars, stand-off magnetometry, and entangled field generation.
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.