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Optica Pura y Aplicada

Propagation of the Four-Wave Mixing signal in a molecular system: stochastic considerations of the thermal bath

José Luis Paz

Published Sep 21, 2015• 3 citations
Publisher

Abstract

This work studies the spatial propagation of the Four-Wave Mixing (FWM) signal of a molecular system (malachite green) with two electronic levels immersed in a thermal bath, under a perturbative treatment at all order in the pump field and to first order in the probe and signal fields.Using the Optical Stochastic Bloch Equations OSBE, we present three approximations, two of them with analytical solutions and the third with a numerical approach, where the effects of the variation of pump intensity through the path optical are considered.We compare these results with the analogous in absence of the thermal reservoir.The stochastic effects induced by the solvent, due to the experimental conditions as relaxation times, chemical concentration of the solution and optical frequencies of the fields, diminishes the intensity responses compared with the same in absence of the bath.

DOI
10.7149/opa.48.3.225

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This work studies the spatial propagation of the Four-Wave Mixing (FWM) signal of a molecular system (malachite green) with two electronic levels immersed in a thermal bath, under a perturbative treatment at all order in the pump field and to first order in the probe and signal fields.Using the Optical Stochastic Bloch Equations OSBE, we present three approximations, two of them with analytical solutions and the third with a numerical approach, where the effects of the variation of pump intensity through the path optical are considered.We compare these results with the analogous in absence of the thermal reservoir.The stochastic effects induced by the solvent, due to the experimental conditions as relaxation times, chemical concentration of the solution and optical frequencies of the fields, diminishes the intensity responses compared with the same in absence of the bath.
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.
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.
The stochastic effects of a thermal bath on a two-level molecular system interacting with a classical electromagnetic field are considered. The collective effects are modeled as a random Bohr frequency, whose manifestation is the broadening of the upper level according to a prescribed random function. A methodology based in cumulant expansions to obtain the average in the Fourier components associated with the coherence and populations, calculated by Optical Stochastic Bloch Equations (OSBE), is employed. The Four-wave mixing signal intensity as a function of the detuning of the pump beam, parametrized by the ratio of the relaxation times and other variables, is analyzed.
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.
A strong pump-power dependence of the four-wave mixing (FWM) signal for an aqueous solution of Malachite green is reported. The characteristics of the pump-power dependence of the nonlinear signal are reproduced by a theoretical model based on the coupling between pump-probe, considering signal fields and propagation effects. The effect of the intramolecular coupling on the nonlinear intensity of the FWM signal is studied using a model molecule consisting of two-coupled harmonic curves of electronic energies with minima displaced in energy and nuclear positions. Two-vibrational states are considered while including non-adiabatic effects for the two-state model. Moreover, the coupling among the field components, as well as the propagation effects, are studied by considering a constant pump-intensity. Our calculation scheme, considering both the intramolecular coupling effects in the description of the molecular structure and the effects produced by the propagation of the FWM signal along the optical length, allows the exponential dependence of the latter, as the intensity of the pumping beam increases. Our treatments do not require the inclusion of other non-resonant processes outside the RWA approximation, due to the consideration of an adiabatic basis.
In this work are 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. The solvent induces a random shift of the Bohr frequency in the molecular system. A methodology based in cumulant expansions is employed to obtain the average of the coherences, populations, and susceptibilities of Fourier components associated, calculated by the optical stochastic Bloch equations. These symmetry properties show the dependence of the measured spectra with the variations in the frequencies of the incident fields. Our results show 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 the absence of the bath.