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

It is observed that when an intense, nearly resonant laser beam propagates through a dilute ($N<\mathrm{}5\mathrm{}\times {10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$) 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 Å 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 ($N\gtrsim 5\times {10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$), self-focusing of the laser beam can occur, leading to several complicating effects. We find experimentally that the on-resonance Rabi frequency $\Omega$ within a self-trapped filament lies preferentially within the range from 1 to 3 times the laser detuning from resonance $\Delta$ and we explain this result as a consequence of strong saturation of the refractive index that occurs for $\Omega \gtrsim \Delta$. 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.