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

Solvent effects on the optical properties of two-level systems with permanent dipole moments

A. Mastrodoménico, M. A. Izquierdo, José Luis Paz, Pedro J. Colmenares

Published Nov 18, 2013• 0 citations
Publisher

Abstract

The inclusion of the permanent dipole moments and the solvent on the optical conventional Bloch equations (OCBE) allowed us to obtain analytical expressions for the optical properties of a two-level molecular system. We employed the methodology developed by Colmenares et al.1, in which they model the collisional effect of the solvent through a stochastical function, ξ(t) = ω0 + σ(t), so the OCBE become a set of coupled integro-differential stochastical equations that we solved, up to third order in the incident field, employing the perturbation theory. Once obtained the analytical expressions for the density matrix elements, macroscopic polarization and effective susceptibility of the system, we studied the optical properties derived in the frequency space, inside and outside the rotating wave approximation.

DOI
10.1117/12.2021368

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The inclusion of the permanent dipole moments and the solvent on the optical conventional Bloch equations (OCBE) allowed us to obtain analytical expressions for the optical properties of a two-level molecular system. We employed the methodology developed by Colmenares et al.1, in which they model the collisional effect of the solvent through a stochastical function, ξ(t) = ω0 + σ(t), so the OCBE become a set of coupled integro-differential stochastical equations that we solved, up to third order in the incident field, employing the perturbation theory. Once obtained the analytical expressions for the density matrix elements, macroscopic polarization and effective susceptibility of the system, we studied the optical properties derived in the frequency space, inside and outside the rotating wave approximation.
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.
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.
The optical properties of a two-level molecular system immersed in a thermal reservoir and irradiated by an electromagnetic field were studied using the optical stochastic Bloch equations. The effect of the solvent is modeled as a stochastical shift of the system's Bohr frequency and the electromagnetic field includes both pump and probe fields. The resulting analytical expressions were studied by means of two and three dimensional graphics of the optical properties as a function of the pump-frequency detuning factor and the strength of the noise source.
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.
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.