Optical Stochastic Bloch Equations Research Articles

Propagación de la señal de Mezcla de cuatro ondas en un sistema molecular: Consideraciones estocásticas del baño térmico

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

Rotating wave approximation effects on the nonlinear optical responses of complex molecular systems using a four-wave mixing signal

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.

SYMMETRY PROPERTIES IN THE STUDY OF THE RAYLEIGH-TYPE OPTICAL MIXING SIGNAL IN PRESENCE OF A THERMAL BATH

In this work are studied the symmetry properties of the Rayleigh-type optical mixing signal of a two-level molecular system immersed in a thermal bath and irradiated by a classical electromagnetic field. The solvent induces a random shift of the Bohr frequency in the molecular system. A methodology based in cumulant expansions is employed to obtain the average of the coherences, populations, and susceptibilities of Fourier components associated, calculated by the optical stochastic Bloch equations. These symmetry properties show the dependence of the measured spectra with the variations in the frequencies of the incident fields. Our results show that the inclusion of the thermal bath diminishes the intensity response as well it promotes the loss of the symmetry properties, compared with the same results in the absence of the bath.

SOLVENT COLLISIONAL EFFECTS IN FOUR-WAVE MIXING

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.

Solvent influence on the nonlinear optical properties of molecular systems in the presence of degenerate and non-degenerate four-wave mixing

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.

THEORETICAL MODEL FOR THE CALCULATION OF OPTICAL PROPERTIES OF GOLD NANOPARTICLES

We have developed an analytical method to describe the optical properties of nanoparticles, whose results are in agreement with the observed experimental behavior according to the size of the nanoparticle under analysis. Our considerations to describe plasmonic absorption and dispersion are based on the combination of the two-level molecular system and the two-dimensional quantum box models. Employing the optical stochastic Bloch equations, we have determined the system's coherence, from which we have calculated expressions for the absorption coefficient and refractive index. The innovation of this methodology is that it allows us to take into account the solvent environment, which induce quantum effects not considered by classical treatments.

Determination of nonlinear optical properties using the Voigt function: Stochastic considerations

In this work, the absorptive and dispersive profiles of a molecular system have been calculated through a methodology based on the averaging of the coherence obtained by the resolution of the optical stochastic Bloch equations. To this aim, a generalized Lorentzian approximation to the Voigt function has been used as a probability distribution, which allows a more generalized analysis of the interactions between the solvent and the molecule. This has been modeled with the parameters of the standard organic dye Green Malaquite, which exhibits a nonlinear behavior under the interaction with a high intensity electric field.

Absortive and dispersive optical properties in molecular systems

Solute–solvent collisions for a two-level molecular system interacting with a four-wave mixing signal are analyzed in the present contribution. The system is described using the optical stochastic Bloch equations (OSBE), where Bohr’s frequency is treated a stochastic variable due to the random collisions with the solvent. The resulting equations for the Fourier components associated to the coherence are averaged over all the realizations of the stochastic variable, using an approximant for the Voigt’s function as a probability distribution. In this model we were able to calculate the optical susceptibilities at different frequencies, depicted as numerical surfaces for the behavior of the optical properties.

COLLISIONAL EFFECT OF THE SOLVENT ON THE OPTICAL RESPONSES OF A TWO-LEVEL SYSTEM

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.

Analysis of the stochastic effects of the solvent and high-pump-power on the nonlinear optical properties in four-wave mixing spectroscopy

Using the Optical Stochastic Bloch equations (OSBE), and considering a two-level molecular system interacting with a thermal reservoir (modeled as an Ornstein–Uhlenbeck process) in four-wave mixing spectroscopy, we derive analytical expressions for the nonlinear optical properties (absorptive and dispersive processes). Here, we have widened the previous formalism [(J.L. Paz et al., Phys. Lett. A 226 (1997) 365)] to consider the solvent effects and high-pump-power in the four-wave mixing (FWM) technique. The saturation effects introduced by including high-pump-power are explicitly considered. These results are very useful when laser-beams of moderate or high-intensity are employed for the determination of relaxation mechanisms in molecular systems interacting explicitly with their environment.

Simultaneous stochastic effects of a thermal reservoir and an electromagnetic field on the optical susceptibility of a two-level system

In this paper we derive analytical expressions for the optical susceptibility of a two-level system immersed in a thermal bath and interacting with an external electromagnetic field, where both of them are considered as noise sources. The dynamics of the system is described by a set of optical stochastic Bloch equations. The noise sources are modeled as Ornstein-Uhlenbeck processes. The optical stochastic Bloch equations are perturbatively solved up to second order in the external field. We found that each noise affects the dynamics in a different manner. Thus, at first order, the bath modifies the transverse relaxation time, whereas the effect of a random field can only be appreciated if the expansion is calculated up to second order, where correlations begin to be important.

On the optical stochastic Bloch equations

We present a methodology, based on the use of a theorem due to Novikov, to solve the optical stochastic Bloch equations for a two-level system up to first order in the external field in the presence of a heat reservoir. Two cases are studied. In the first, a white noise bath is considered, while in the second colored noise (Ornstein-Uhlenbeck process) is analysed.