In this work we studied the symmetry properties of the Rayleigh-type optical mixing signal, of a two-level molecular system immersed in a thermal bath and irradiated by a classical electromagnetic field. Taking into account that the solvent produces an inhomogeneous displacement of the Bohr frequency and, employing a cumulant expansion to solve the stochastical equations derived, we obtained the mean values of the coherence, populations and susceptibilities Fourier components of the molecular system, from the optical stochastical Bloch equations (OSBE). These symmetry properties are used to show the dependence of the spectra with the frequency shifts of the incident fields, and we obtained that the inclusion of the thermal bath diminishes the intensity response as well it promotes the loss of the symmetry properties, compared with the same results in absence of the bath.
The inclusion of the permanent dipole moments and the solvent on the optical conventional Bloch equations (OCBE) allowed us to obtain analytical expressions for the optical properties of a two-level molecular system. We employed the methodology developed by Colmenares <i>et al.</i><sup>1</sup>, in which they model the collisional effect of the solvent through a stochastical function, ξ(<i>t</i>) = ω<sub>0</sub> + σ(<i>t</i>), so the OCBE become a set of coupled integro-differential stochastical equations that we solved, up to third order in the incident field, employing the perturbation theory. Once obtained the analytical expressions for the density matrix elements, macroscopic polarization and effective susceptibility of the system, we studied the optical properties derived in the frequency space, inside and outside the rotating wave approximation.
This work studies the spatial propagation of the four-wave mixing signal of a molecular system with two electronic levels immersed in a thermal bath. Using the optical Bloch-Maxwell equations, we present three approximations, two of them are analytical solutions and the other is a numerical approach, where the effects of the variation of pump intensity through the optical path are considered. Also, we compare these results with the analogous in absence of the thermal reservoir and it is shown that the stochastic effect induced by the solvent, due to the experimental conditions as relaxation times, concentration of the solution and optical frequencies of the pumps, diminishes the intensity responses compared with the same in absence of the bath.