Microscopic dynamics. of materials can be studied by time delayed four-wave mixing spectroscopy. Dephasing constants can be measured by such experiments. Experimental results are easily analysed when the correlation time r of the exciting electric field is much shorter than the dephasing time ''2 However when these quantities are on the same time scale numerical fits are necessary. In the present work we analysed theoretically a time delayed four-wave mixing experiment. The material is described by an ensemble of two-level systems and a large inhomogeneous broadening is assumed. Using the third order term of the density matrix we establish a relation between 1''2 -r and ''Tm the time delay for which the maximum of the diffracted light intensity is observed. The conditions to obtain an estimate of T2 from the measurement of Tm are discussed.
Microscopic dynamics. of materials can be studied by time delayed four-wave mixing spectroscopy. Dephasing constants can be measured by such experiments. Experimental results are easily analysed when the correlation time r of the exciting electric field is much shorter than the dephasing time ''2 However when these quantities are on the same time scale numerical fits are necessary. In the present work we analysed theoretically a time delayed four-wave mixing experiment. The material is described by an ensemble of two-level systems and a large inhomogeneous broadening is assumed. Using the third order term of the density matrix we establish a relation between 1''2 -r and ''Tm the time delay for which the maximum of the diffracted light intensity is observed. The conditions to obtain an estimate of T2 from the measurement of Tm are discussed.
Measurements of the relaxation times T1 and T2 of a two-level system by nonlinear transient spectroscopic methods are discussed, where delayed incident pulses are assumed to have correlation times much shorter than T1 or T2 but varied widths. In particular, a delayed degenerate four-wave mixing (photon echoe) and apump-and-probe type transmission measurement with incoherent long pulses are considered in detail, and a principle of their use for ultrafast spectroscopy is clarified. If the field is steady and T1>>T2, the time resolutionof T2measurement by the delayed four-wave mixlng is determined by the field correlation, therefore by the spectral width of the incident light irrespective of the pulse width. The time resoution of the T1 measurement by the pump-and-probe method is determined by the intensity correlation of the incident light, whereasthe one by the delayed four-wave mixing by a higher order correlation.
We present a time-resolved study of the diffracted pulse in degenerate four-wave mixing experiments with short-response-time materials. The first step is the validation of a theoretical model that takes into account the temporal characteristics of the energy level (relaxation time T1 and dephasing time T2) and of the incident pulse (duration and spectral phase) in a simple particular case. Two methods are used for characterizing the diffracted beam: the amplitude correlation with the reference pulse and the spectrum intensity measurements. We discuss the experimental results, which show good agreement with the theoretical model and evidence the strong influence of the incident pulse characteristics.
A picosecond time-resolved four-wave mixing technique is used to study the dephasing of nonlinear optical resonances in CdSe. At low temperature strong coherent, nonlinear signals at the free exciton resonance, at the biexciton resonance, and at the exciton-biexciton transition are observed. The observed correlation traces, i.e. the diffracted intensity versus the delay between the interfering light pulses, yield information on the dephasing process. Dephasing times for excitons as long as 40 ps, decreasing with increasing excitation density and temperature, are observed. A two-level model is applied to describe theoretically the dynamical behavior of the resonances, and to extract their homogeneous broadening, as well as their inhomogeneous broadening.
A systematic theoretical and computational investigation of the microscopic factors which determine the phase of the signal field in time-resolved quasidegenerate three-pulse scattering experiments is presented. The third-order phase-matched response is obtained by density-matrix perturbation theory using a Green-function formalism for a system composed of two well-separated sets of closely spaced energy levels. Equations for calculating the electric field of four-wave-mixing signals generated by path-length delayed pulses are given. It is found that the phase of the signal field is determined by the excitation pulse phases, the dynamics of the nonlinear polarization decay, the product of four transition dipole matrix elements, and by a pulse-delay-dependent phase modulation at the frequency of the first dipole oscillation in the four-wave-mixing process. Analytic results for a two-level Bloch model show the phase shift from rapid nonlinear polarization decay. The product of dipole matrix elements is real and positive for three-level processes (bleached ground-state absorption and excited-state emission), but can be real and negative for some four-level Raman processes. The pulse-delay-dependent phase modulation treated here is closely related to the interferometric pulse-delay-dependent amplitude modulation observed in some collinear experiments, and plays a role in producing photon echos in inhomogeneously broadened samples. Numerical calculations of phase-resolved electric fields for finite duration pulses using a Brownian oscillator model appropriate for condensed-phase dynamics are presented. The ability of pulse-delay-dependent phase modulation to encode the frequency of the initially excited dipole onto the phase of the signal field can be exploited to examine energy-level connectivity, reveal correlations hidden under the inhomogeneous lineshape, and probe relaxation pathways in multilevel systems.
A multilevel model, including homogeneous and inhomogeneous broadening, is proposed for the study of time-delay four-wave mixing with incoherent light (TDFWM-IL) in absorption bands consisting of a series of vibrational transitions. A theory of TDFWM-IL is developed for this model, and a general formula for the delay-time dependence of the signal intensity Is(τ), considering both the homogeneous and inhomogeneous broadening of the transitions, is deduced. Special analyses are given to the homogeneous and inhomogeneous limits. The differences between Is(τ) derived from multilevel theory and from two-level theory, are pointed out. When the homogeneous broadening of individual transitions is much smaller than the frequency interval of adjacent transitions, Is(τ) in the multilevel theory is modulated periodically and the envelope is close to that in the two-level theory for both the homogeneous and inhomogeneous limits. When the individual transitions are homogeneously broadened enough so that an unresolved continuous band is formed, an effective two-level model can still be used approximately for the studies of TDFWM-IL in this continuous band, with both homogeneous and inhomogeneous broadening. However, the dephasing time [Formula: see text] in the formula of Is(τ) in this effective two-level model is not the real dephasing time of an individual transition of the band, but the effective one which reflects the behavior of the whole band.
A homogeneous broadening multilevel theory of time-delay four-wave mixing with incoherent light is developed for absorption bands that consist of a series of vibrational transitions. A formula for the delay-time dependence of the signal intensity I(τ) is obtained. The differences between I(τ) derived from multilevel theory and from two-level theory are pointed out. It has been demonstrated experimentally that the multilevel theory is more suitable than the two-level theory for this type of absorption band. It is shown, in particular, that when we apply the two-level theory to the analysis of experiments in this type of absorption band, what we determine is not the dephasing time of an individual transition but the effective dephasing time, which reflects the behavior of the total absorption spectrum of the band.