Resonant degenerate four-wave mixing spectroscopy of transitions with degenerate energy levels: Saturation and polarization effects

The physics of the degenerate four-wave mixing process for resonant transit ions between two degenerate energy levels is investigated by direct numeric al integration of the time-dependent density matrix equations. The Zeeman s tructure of the upper and lower energy levels is included in a multistate f ormulation of the density matrix equations. The inclusion of the Zeeman str ucture enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pu mp, and probe beams. Saturation curves and lineshapes are calculated for di fferent polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agree ment with perturbation theory in terms of the relative intensities of the d egenerate four-wave mixing signal for linear polarization configurations. A s the laser intensity increases and the resonance starts to saturate, we fi nd in general that the relative degenerate four-wave mixing reflectivity in creases for the crossed polarization configurations compared to the paralle l polarization configuration because the saturation intensity is higher. Ho wever, for some resonance transitions, some of the crossed polarization con figurations saturate at lower laser intensities than the parallel polarizat ion configuration, even though the reflectivity for these crossed polarizat ion configurations is much lower than for the parallel polarization configu ration in the perturbative intensity limit. This result is explained in ter ms of the coupling of the various Zeeman states during the degenerate four- wave mixing interaction for specific polarization configurations. The effec t of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculat ions are performed for resonances that are Doppler broadened as well as col lision broadened. The effect of saturation on the reflectivity of the cross ed polarization configurations compared to the parallel polarization config uration is even more significant for resonances with comparable Doppler and collisional broadening. (C) 1999 American Institute of Physics. [S0021-960 6(99)00246-9].