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Journal of Nonlinear Optical Physics & Materials

Four-wave mixing signal intensity: Relaxation time effects on the absorptive and dispersive optical properties in a two-level system

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

Published Jun 1, 2015• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s021886351550023x

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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.
A study has been made of the effect of relaxation times on the four-wave mixing (FWM) signal response in frequency space for a two-level system where intramolecular coupling is explicitly taken into account within a vibronic model. The model is a generalization of the conventional two-level approach in that it includes a simplified description of the molecular structure and the explicit consideration of permanent dipole moments. Significant changes in both the intensity and shape of the peaks of the FWM spectrum are observed, due mainly to changes in the ratio between the longitudinal and transversal relaxation times, T 1/T 2.
We consider the Four-Wave mixing (FWM) signal and the effects of the pump beam on the nonlinear optical responses of a two-level system where intramolecular coupling is modelled by two coupled harmonic electronic potentials, displaced both in their equilibrium minimum position and energy. We investigate the modifications introduced in the FWM signal, considering a simple representation for the vibrational structure and including molecular electronic states with nonzero permanent dipole moments. The critical quantities for this analysis are the transition and permanent dipole moments, which depend strongly on the intramolecular coupling. Our results show how both absorption and dispersion are affected by the vibronic coupling.
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.
We study the nonlinear absorptive and dispersive optical properties of molecular systems immersed in a thermal reservoir interacting with a four-wave mixing (FWM) signal. Residual spin-orbit Hamiltonians are considered in order to take into account the internal structure of the molecule. As system parameters in the dissipation processes, transverse and longitudinal relaxation times are considered for stochastic solute–solvent interaction processes. The intramolecular coupling effects on the optical responses are studied using a molecule model consisting of two coupled harmonic curves of electronic energies with displaced minima in nuclear energies and positions. In this study, the complete frequency space is considered through the pump–probe detuning, without restricting the derivations to only maximums of population oscillations. This approach opens the possibility of studying the behavior of optical responses, which is very useful in experimental design. Our results indicate the sensitivity of the optical responses to parameters of the molecular structure as well as to those derived from the photonic process of FWM signal generation.
In this work we have studied the changes in the Four-Wave Mixing (FWM) signal with the changes in the ratio between the longitudinal and transversal relation times T1/T2. Moreover, we have studied too the modifications in the FWM signal with the changes in the strength constant of the crossed harmonic potential curves that describe the two- levels system employed to this study. We have included the permanent dipolar moments of the states in the uncoupled basis. The rotating wave approximation is neglected to observe the process out of the resonance region. We observed changes in the shape, intensity and position in the resonances of the FWM signal spectra, with the changes in the ratio T1T2 and the strength constant (delta) .© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
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.