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International Journal of Modern Physics B

OPTICAL PROPERTIES OF MOLECULAR SYSTEM COUPLED TO THE SOLVENT

A. Romero-Depablos, José Luis Paz, Adriana Mendoza‐Garcia, P. Martín, E. Castro

Published Dec 20, 2009• 4 citations
Publisher

Abstract

Analytic approximations for the absorption coefficient and refraction index have been obtained for a two-level molecular system in the presence of a four-wave mixing signal. Stochastic collisions among solute–solvent molecules produce a broadening of the upper level of energy. In this work, we have used four generalized Lorentzian approximants of the Voigt function as probability distribution, calculated by the two-point quasi-rational approximant method previously denoted as asymptotical Padé technique, for the evaluation of the average values of the Fourier components associated to the induced coherences. The innovation of this type of distributions allows us, by taking appropriate limits, to find similar profiles of optical properties as those using Gaussian and Lorentzian distribution functions.

DOI
10.1142/s021797920905434x

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Analytic approximations for the absorption coefficient and refraction index have been obtained for a two-level molecular system in the presence of a four-wave mixing signal. Stochastic collisions among solute–solvent molecules produce a broadening of the upper level of energy. In this work, we have used four generalized Lorentzian approximants of the Voigt function as probability distribution, calculated by the two-point quasi-rational approximant method previously denoted as asymptotical Padé technique, for the evaluation of the average values of the Fourier components associated to the induced coherences. The innovation of this type of distributions allows us, by taking appropriate limits, to find similar profiles of optical properties as those using Gaussian and Lorentzian distribution functions.
Nonlinear optical properties of a two-level molecular system immersed in a thermal bath have been studied in the present work. Solvent effects were explicitly considered by modeling the non-radiative interaction with the solute as a random variable. The innovation of this treatment is that it allows us to take into account the environment, inducing quantum effects not considered by classical treatment. The major contribution of the methodology proposed in this work, is the implementation of an approximant to the Voigt function as a probability distribution, because it allow us to cover a wider range of possible interactions among the solvent and the molecular system by simple changing the parameters [Formula: see text] and [Formula: see text], associated to the variances of the Lorentzian and Gaussian distributions, respectively.
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.
Propagation of a four wave mixing through a molecular system interacting with thermal reservoir was carried out. From that, analytical expressions to the absorption coefficient at different frequencies were obtained. Surfaces to that property and to the refractive index were exhibited. Saturation effect due the field can be viewed as well as the attenuation of the optical properties when the molecule-solvent coupling increases. That permit us to define an effective relaxation time which includes a parameter that measures the molecule-solvent interaction.
The solvent effects over optical properties of a two level system in presence of an electromagnetic field was modeled in this work. The system-field interaction was considered by using the dipolar-electric approximation, assuming negligible the molecular permanent dipole moments. The solvent effects were included in the formalism in a stochastic form, through the induced shifts over the Bohr molecular frequency. The coherence was calculated from the optical stochastic Bloch equations (OSBE), and later, it was averaged over all realizations of the stochastic molecular variable. To do that, it was applied the convolution theorem, which was resolved using direct and inverse Fourier transforms.
It was studied the solvent influence over a two level system interacting with an electromagnetic field using an stochastic treatment. It was considered a high-intensity electromagnetic field which is capable to produce local saturations. The induced coherence in the two electronic states, was averaged in the usual form, through both, Lorentzian and Gaussian probability density. From that, analytical expressions for susceptibility and optical properties were obtained. Numerical calculations were carried out to construct surfaces corresponding to this properties as a function of the field variables and the distributions parameters.
It was studied the solvent influence over a two level system in the four wave mixing spectroscopy. the solvente effect was incorporated to the model in a stochastic form, through the broadening of the upper molecular level. Two intense waves of the same frequency, ω1, and another wave with minor intensity and ω2 frequency, were considered coupled to the nonlinear system, generating a new signal whose frequency is ω3, and where the wave-vectors follow the relation vector k1 + vector k1 = vector k2 + vector k3. Using the dipolar-electric and the rotating wave approximations, it was calculated the average of the coherence at the ω1, ω2 and ω3 frequencies. From that results, analytical expressions to the susceptibilities at the studied frequencies were obtained. Linear, coherent and coupled processes were identified.