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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Simultaneous stochastic effects of the solvent and electromagnetic field on the absorptive and dispersive process in a four-wave mixing signal

Francisco Flores, José Luis Paz

Published Aug 14, 2001• 0 citations
Publisher

Abstract

We calculate the non-linear absorptive and dispersive properties in four wave mixing (FWM) signal for a homogeneously broadened molecular two level system with dipole permanent moments interacting with two classical electromagnetic field,, using (omega) 1 equals (omega) 2, considering two sources of noise, the collective effect of the thermal bath, that is modeled as a random Bohr frequency and the effect of the electromagnetic field random amplitude. This assumptions transforms the optical Bloch equations to a system of multiplicative stochastic differential equations whose solution is found though an systematic treatment of cumulant expansion which lead directly to reduce OBE.

DOI
10.1117/12.437208

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We calculate the non-linear absorptive and dispersive properties in four wave mixing (FWM) signal for a homogeneously broadened molecular two level system with dipole permanent moments interacting with two classical electromagnetic field,, using (omega) 1 equals (omega) 2, considering two sources of noise, the collective effect of the thermal bath, that is modeled as a random Bohr frequency and the effect of the electromagnetic field random amplitude. This assumptions transforms the optical Bloch equations to a system of multiplicative stochastic differential equations whose solution is found though an systematic treatment of cumulant expansion which lead directly to reduce OBE.
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.
We have considered the stochastic effect of a thermal reservoir on a two-level system interacting with a classical electromagnetic field. The collective effect of the bath is modelled in this work as a random Bohr frequency whose manifestation is the broadening of the upper level according to a prescribed random function. This assumption transforms the optical Bloch equations to a system of multiplicative stochastic differential equations whose solution is found. After obtaining analytical expressions for the linear absorption coefficient and linear refraction index, numerical results are presented. This is done in the form of tridimensional plots of the optical properties as a function of the pump-frequency detuning factor and the strength or relaxation time of the noise source.
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.
The study of a two-level molecular system with permanent dipole moments (PDM) immersed in a thermal bath and interacting with an electromagnetic field depends on the inclusion of the rotating wave approximation (RWA). 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. With these equations, we have modeled the optical responses for the four-wave mixing signal and we have demonstrated that inside the RWA the PDM cannot be measured.
A study of the effects of relaxation times on the Four-Wave Mixing (FWM) signal response in frequency space for a two-level system is presented where the collisional effects of the solvent and the presence of the electromagnetic field are considered. The model is a generalization of the conventional two-level approach in that it includes a simplified description of the molecular structure associated with the non-zero permanent dipole moments. Significant changes in both the FWM-intensity and nonlinear optical properties are observed, due mainly to changes in the ratio between the longitudinal and transversal relaxation times.
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.