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Results in Physics

Three levels of propagation of the Four-wave mixing signal

José Luis Paz, Ysaías J. Alvarado, Luis Lascano, César Costa Vera

Published Sep 25, 2018• 6 citations
Publisher

Abstract

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.

DOI
10.1016/j.rinp.2018.09.041

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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.
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.
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.
In a propagation treatment at all orders in the pump field and to first order in the probe and signal fields, for a homogeneously broadened line, we obtain three approximation levels for the Rayleigh-type optical mixing signal intensity: the first level is an analytical solution valid only for constant pump intensity; the analytical solution corresponding to the second approximation level considers pump propagation and yields good results for a large number of cases; the third level is an exact but numerical solution. We present and compare the results obtained with the different approximations.
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 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.