A detailed theoretical analysis is given for the ultrafast relaxation study using polarization spectroscopy in the frequency domain to clarify the effect of cross relaxation on the measured results. It is shown that the calculated nonlinear spectral response function reflects the inhomogeneous width rather than the homogeneous one if the rate of cross relaxation of the transition becomes so singnificant. This prevents us from precise determination of phase relaxation Time T 2 of the transition by the stationary polarization spectroscopy. It is further shown that the cross relaxation effect onto the measured spectral response function can effectively be diminished by introducing a partially transient condition. An experiment using picosecond light pulses is presented to demonstrate this fact.
A detailed theoretical analysis is given for the ultrafast relaxation study using polarization spectroscopy in the frequency domain to clarify the effect of cross relaxation on the measured results. It is shown that the calculated nonlinear spectral response function reflects the inhomogeneous width rather than the homogeneous one if the rate of cross relaxation of the transition becomes so singnificant. This prevents us from precise determination of phase relaxation Time T 2 of the transition by the stationary polarization spectroscopy. It is further shown that the cross relaxation effect onto the measured spectral response function can effectively be diminished by introducing a partially transient condition. An experiment using picosecond light pulses is presented to demonstrate this fact.
The effect of cross relaxation on the third-order nonlinear susceptibility, χ(3) (−ω2, ω1, −ω1, ω2), describing polarization spectroscopy experiments is calculated with a density matrix formalism. By using a model of inhomogeneously broadened two-level systems with a reservoir state and allowing for cross relaxation within the inhomogeneous line, we find that both the ratio of the maximum signal at ω1 = ω2 to the background and the broad component resembling the absorption band depend on the cross-relaxation rate. Also, one additional component with a characteristic width of the order of the spectral-diffusion rate Γ3 is expected to appear, depending on the value of this parameter. Furthermore, we estimate from published data [ Phys. Rev. A17, 1439 ( 1978)] the product of the transverse-relaxation time times the cross-relaxation time T2T3 to be 0.014 psec2 for cyanine dye and 0.0009 psec2 for malachite green oxalate.
A comprehensive theory of a new type of three-wave optical mixing (${\ensuremath{\omega}}_{3}=2{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$) is given for the spectroscopic purpose of determining ultra-short relaxation times (picoseconds or less) associated with excited states of condensed matter. Two incident light frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ are chosen so that they are both resonant with an inhomogeneously broadened optical transition and $|{\ensuremath{\omega}}_{2}\ensuremath{-}{\ensuremath{\omega}}_{1}|$ is in the vicinity of inverse relaxation times. The theory is developed for its major application to broad-band electronic transitions. The nonlinear susceptibility ${\ensuremath{\chi}}_{R}^{(3)}$ for this process (named resonant Rayleigh-type mixing) is calculated by a density-matrix formalism with the model of a two-level atomic system incorporating the distribution of resonance frequencies and longitudinal (T1) and transverse (T2) relaxation times. The result shows a frequency characteristic depending only on T1, T2, and ${\ensuremath{\omega}}_{2}\ensuremath{-}{\ensuremath{\omega}}_{1}$ in a broad-band limit, which serves for the determination of T1 and T2 in the frequency domain. The analysis is further extended to include the various effects as follows. The calculation of the saturation effect in the lowest order reveals that it modifies the shape of the frequency characteristic of the nonlinear susceptibility but does not affect seriously the determination of relaxation times. The effect of spectral cross relaxation within the inhomogeneous broadening is incorporated by a generalized density-matrix formalism. The resultant ${\ensuremath{\chi}}_{R}^{(3)}$ consists of two terms. The dominant term is the same as before except that T1 is replaced by a combined relaxation time ${T}_{1}^{\ensuremath{'}}={({T}_{1}^{\ensuremath{-}1}+{T}_{3}^{\ensuremath{-}1})}^{\ensuremath{-}1}$, where T3 is the cross-relaxation time. The other term originates from the inverse spectral-diffusion process. The effect of other energy levels located between the two levels under study is analyzed with a simple three-level model. The resultant ${\ensuremath{\chi}}_{R}^{(3)}$ also consists of two terms, the dominant one being the same as that for the two-level model except that ${T}_{1}^{\ensuremath{-}1}$ should be interpreted as total population decay rate of the upper level. For accurate derivation of ${\ensuremath{\chi}}_{R}^{(3)}$ from experiment, we discuss the interference between the resonant and nonresonant susceptibility terms and the light-wave propagation effect. Finally, the close analogy between this type of optical mixing and the photon echo is discussed.
The nonlinear absorption of intense laser light is used to obtain information about the times required for spectral cross relaxation (T3) and collisional dephasing (T2) in organic-dye solutions. The steady-state transmission experiment of Huff and DeShazer indicates that T2 is in the range 0.1-1 psec for cryptocyanine-methanol, while T3 is in the range 1-10 psec. For DDI-glycerin (1, 1\ensuremath{'}-diethyl-2, 2\ensuremath{'}-dicarbocyanine-iodide-glycerin), measurements of ultrashort-pulse transmission as a function of incident energy and optical polarization suggest a value ${T}_{2}=0.4\ifmmode\pm\else\textpm\fi{}0.2$ psec for that system. These results are based on a new set of rate equations for absorption by inhomogeneously broadened organic-dye solutions. The equations display the effects of spectral cross relaxation and are not limited to light intensities less than those at which coherent interaction effects become important. For the case of ultrashort incident pulses, the equations are extended to account for excited-state absorption, the dependence of absorption on optical polarization, and the existence of a multiplicity of interacting excited states.
A novel transient three-pulse scattering technique for measuring ultrafast dephasing times in condensed matter is analyzed using a perturbative solution of the density matrix equation. The advantages of this technique include subpulsewidth resolution, a clear distinction between homogeneous and inhomogeneous broadening, and sensitivity to spectral cross-relaxation. Its application to the case of a multilevel resonance is also considered. We report results of femtosecond dephasing experiments with dye molecules in liquids and in a polymer host. The dephasing time is determined to be less than 20 fsec for dyes in solution at room temperature. At low temperatures in polymers, a transition from homogeneous to inhomogeneous broadening has been observed and studied as a function of temperature.
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.
An analysis and model calculations are presented to clarity how both the electronic and vibrational inhomogeneities with no correlation between them influence the most relevant resonant steady-state third-order nonlinear optical mixing processes (CARS, CSRS, polarization spectroscopy and Raman gain (loss)).It is shown that all these processes may be divided into three groups: 1) processes yielding almost homogeneous spectra: both inhomogeneities are greatly reduced; 2) processes yielding quasihomo- geneous spectra: inhomogeneities are present, but the electronic one is not manifest in the spectrum; 3) processes yielding completely inhomogeneous spectra.The suppression of inhomogeneous broadening allows to study the excited electronic states and the ultrafast relaxation processes in inhomogeneous media more effectively than in linear spectroscopy. * About another steady-state frequency domain technique byhot luminescence measurements for the study of ultrafast energy relaxation see.e. g. f l4 ].ЁЁЗТТ NSV TEADUSTE AKADEEMIA TOIMETISED.30.