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The Journal of Chemical Physics

Optical dephasing on femtosecond time scales: Direct measurement and calculation from solvent spectral densities

Peter Vöhringer, David C. Arnett, R. A. Westervelt, Mark J. Feldstein, Norbert F. Scherer

Published Mar 8, 1995• 138 citations
Publisher

Abstract

The connection between dephasing of optical coherence and the measured spectral density of the pure solvent is made through measurements and calculations of photon echo signals. 2-pulse photon echo measurements of a cyanine dye in polar solvents are presented. Signals are recorded for both phase matched directions enabling accurate determination of the echo signal time shift. Echo signals are calculated by two approaches that employ the response function description of nonlinear spectroscopy; (i) a single Brownian oscillator line shape model, and (ii) the line shape obtained using the solvent spectral density. The strongly overdamped Brownian oscillator model incorporates only a single adjustable parameter while the experimental data present two fitting constraints. The second model incorporates the measured solvent spectral density. Both give very good agreement with the experimental results. The significance of the second method lies in this being a new approach to calculate nonlinear spectroscopic signals, for comparison with experimental data, that uses directly the measured spectrum of equilibrium fluctuations of the solvent. This approach also provides a better conceptual perspective for deriving insight into the nature of the solute–solvent coupling mechanism. Comparing the parameters for the strength of interaction in a variety of polar solvents it is found that the coupling involves the solvent polarizability and not the solvent polarity. The interaction mechanism cannot be deduced from the Brownian oscillator calculations.

DOI
10.1063/1.468531

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The connection between dephasing of optical coherence and the measured spectral density of the pure solvent is made through measurements and calculations of photon echo signals. 2-pulse photon echo measurements of a cyanine dye in polar solvents are presented. Signals are recorded for both phase matched directions enabling accurate determination of the echo signal time shift. Echo signals are calculated by two approaches that employ the response function description of nonlinear spectroscopy; (i) a single Brownian oscillator line shape model, and (ii) the line shape obtained using the solvent spectral density. The strongly overdamped Brownian oscillator model incorporates only a single adjustable parameter while the experimental data present two fitting constraints. The second model incorporates the measured solvent spectral density. Both give very good agreement with the experimental results. The significance of the second method lies in this being a new approach to calculate nonlinear spectroscopic signals, for comparison with experimental data, that uses directly the measured spectrum of equilibrium fluctuations of the solvent. This approach also provides a better conceptual perspective for deriving insight into the nature of the solute–solvent coupling mechanism. Comparing the parameters for the strength of interaction in a variety of polar solvents it is found that the coupling involves the solvent polarizability and not the solvent polarity. The interaction mechanism cannot be deduced from the Brownian oscillator calculations.
A rigorous theoretical connection between the polarizability spectral density obtained from optical Kerr effect (OKE) measurement with the correlation function describing solvent-induced optical dephasing detected in photon echo measurements is given. The experimentally obtained spectral density has a more reasonable physical basis than model correlation function descriptions of solvent fluctuations. The experimental OKE spectrum is demonstrated to provide a natural description of solvent motions that modulate the chromophore electronic states in the case of weak induced-dipolar interactions. The chromophore optically active vibrational modes are obtained from pump-probe spectra and are employed in the calculation of echo signals. It is found that the fast decays of the two-pulse echo signals result from both solvent and solute intramolecular motions while the echo peak shifts are dominated by the solvent intermolecular modes.
Optical dephasing of a cyanine dye chromophore in solution is investigated by time-gated photon echo spectroscopy in a three-pulse scattering geometry. The third-order polarization response is gated by up-conversion with a reference pulse in a nonlinear optical crystal. Time gating establishes two controllable periods of system evolution in an optical coherence. The measurements are compared with numerical simulations employing the measured OKE spectrum of solvent (butanol, DMSO) fluctuations. The time-shift of the time-gated echo signals for several gating forming pulse time delays agrees with simulation while the narrower simulated widths suggest a frequency-dependent solute-solvent interaction and the consideration of chromophore vibronic transitions.
Two- and three-pulse photon echo signals are calculated for various model systems. The use of an experimental solvation correlation function as the solvent fluctuation correlation function leads to two conclusions. First, inertial solvent motion plays a major role in the electronic dephasing process. Second, simple models such as Markovian or exponential models for the solvent fluctuation correlation function may not provide an adequate description of the echo signal. The real and imaginary parts of the echo response, which may be measured via heterodyne detected stimulated photon echoes, are compared with conventional photon echo signals.
A theoretical analysis is carried out for the recently developed three-pulse photon echo spectroscopy employing dual frequency combs (DFC) as the light sources. In this method, the molecular sample interacts with three pulse trains derived from the DFC, and the generated third-order signal is displayed as a two-dimensional (2D) spectrum that depends on the waiting time introduced by employing the asynchronous optical sampling method. Through the analysis of the heterodyne-detected signal interferogram using a local oscillator derived from one of the optical frequency combs, we show that the 2D spectrum closely matches the spectrum expected from a conventional approach with four pulses derived from a single femtosecond laser pulse, and the waiting time between the second and third field-matter interactions is given by the down-converted detection time of the interferogram. The theoretical result is applied to a two-level model system with solvation effect described by solvatochromic spectral density. The model 2D spectrum reproduces spectral features such as the loss of frequency correlation, dephasing, and spectral shift as a function of the population time. We anticipate that the present theory will be the general framework for quantitative descriptions of DFC-based nonlinear optical spectroscopy.
A theory of optical echo spectroscopies of large polyatomic molecules in condensed phases is developed. Using phase space correlation functions, we examine the interrelationships among the following optical measurements: ordinary photon echo, stimulated photon echo, accumulated photon echo, incoherent accumulated photon echo, and pump–probe absorption. Conditions for the elimination of inhomogeneous broadening in these experiments are specified. A multimode Brownian oscillator model is used to account for high frequency molecular vibrations, as well as solvent modes, and electronic dephasing processes. The effects of quantum beats, spectral diffusion, and homogeneous dephasing on the echo signals are studied and compared in detail with pump–probe and hole burning spectroscopy.
We calculate the signal in a time-resolved, coherent light scattering experiment on a dilute solution of a nonpolar solute dissolved in a nonpolar solvent. We model the solute and solvent molecules as electronic two level systems, and assume that only the solute interacts with radiation. The electronic degree of freedom is treated perturbatively within the Born–Oppenheimer approximation. The nuclear degrees of freedom are treated classically, and their effects are modeled by a molecular dynamics simulation. We assume the electronic absorption spectrum is dominated by inhomogeneous broadening. The validity of this assumption for our model is verified through the calculation of the absorption line shape with and without the inhomogeneous broadening assumption. A quantitative measure of the homogeneous dephasing time is obtained from a calculation of the photon echo signal for our model. The time dependence of the light scattering signal is shown to reflect both dynamics of the fluid in its electronic ground state and in its electronic excited state. We analyze the relative importance of contributions to the signal from these two types of dynamics as a function of experimental time scale and laser frequency.