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The nonlinear optical susceptibilities are analyzed in their optical propagation length considering the incoherent-coherent contributions with the dependence on the relaxation times. In addition, some symmetry properties of the Four-Wave mixing (FWM) signal concerning the frequency detuning exchange are used in the study, without restricting ourselves to the maxima of population oscillations. We analyze the behaviors of these optical responses in a vibronic coupling scheme using a molecule model consisting of two coupled harmonic curves of electronic energies with displaced minima in position and nuclear energies. The solvent effect in our model is treated through the natural Bohr frequency shift to a time-dependent function, with explicit manifestations in its comparison as if the upper state were broadened. Our results for both FWM signal propagation and nonlinear optical susceptibilities are sensitive to the intramolecular coupling parameters, solvent stochasticity, and perturbation order for the treatment of the weak probe beam. The consideration of a second-order probe beam in FWM would not represent a significant contribution to the predicted results, since its percentage contribution is negligible within the model development framework; however, this contribution becomes important when increasing the ratio between longitudinal and transverse relaxation times.

In this work, we analyze different levels of propagation of the Four-wave mixing signal in a strongly driven two-level system when the stochastic effects of the thermal bath, are considered. First approximation level, given by an analytical solution valid only for constant pump intensity along the optical path; a second approximation level as an analytical solution valid for a lineal variation of the pump intensity, and finally, a third level as numerical solution, which represent the exact case. In all cases, high dependence of the nonlinear propagation with the chemical concentration, stochastic noise parameters, relaxation times, are studied. Keywords: Propagation, Four-wave mixing, Optical susceptibilities