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Journal of Nonlinear Optical Physics & Materials

Solvent effects in the nonlinear optical properties using the Voigt function

José Luis Paz, Luis G. Rodríguez, J. Cardenas, César Costa Vera

Published Jun 1, 2016• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s0218863516500168

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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.
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.
"Higher order effects of the electric field on the optical susceptibilities of a molecular system immersed in a thermal bath is studied in the present work. The molecule is viewed as a two level system, whose Bohr frequency is shifted randomly due to the interaction with the solvent. The optical Bloch equations were solved using the perturbation expantion of the field, and we have averaged over all realizations of the stochastic variable using gaussian and lorentzian distributions. Analytical expressions to the optical susceptibilities were found, which incorporte molecular and noise parameters. Susceptibilities surfaces are obtained as a fucntion of the detuning factor and the perturbation field."
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.
The nonlinear optical properties are studied theoretically of a molecular system immersed in a thermal bath and interacting with a four-wave mixing signal. A methodology based on cumulant expansions to obtain the average in the Fourier components associated with the coherences and populations, calculated by the optical stochastic Bloch equations, is employed. The system properties are analyzed as a function of the frequency detuning of the high-intensity pump beam and parameterized by the frequency detuning of the probe beam, both with respect to the Bohr frequency of the system. The longitudinal and transversal relaxation times and the bath effects, modeled as white noise, are also included as parameters in the calculation. Different cases, with degenerate and non-degenerate optical frequencies are examined and compared, resulting in differences related to the maximum in the population pulsation effects.
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.
Absorptive and dispersive nonlinear optical properties have been studied considering a two-level molecular system with permanent dipole moments immersed in a thermal reservoir interacting with a classical electromagnetic field. Our model is based in a stochastic description, where the system–solvent interaction induces random shifts in the Bohr frequency (ω0) that transforms ω0 into a stochastic variable ξ(t). Our results show that it is necessary to neglect the rotating-wave approximation in order to measure the effect of the permanent dipole moments. The two-photon transitions over those with one-photon are favored when the permanent dipole moments are considered.