Jason C. Kirkwood

Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes

Higher order time resolved nonlinear optical processes can often be obscured by sequential lower order processes that compete with the direct event and give similar time domain behavior though they probe different dynamics. This is true for a certain fifth order coherent anti-Stokes Raman scattering (CARS) spectroscopy designed to probe overtone vibrational dynamics. The homodyned intensity from the two competing processes is calculated and it is shown how only the direct fifth order polarization probes overtone dephasing.

Fifth-order nonlinear Raman processes in molecular liquids using quasi-cw noisy light. II. Experiment

Fifth-order analogs of coherent Raman scattering generated in a number of molecular liquids using broadband quasi-cw noisy light are presented. It is seen how the signal for the direct fifth-order process, which probes the dynamics of both a fundamental vibration and its overtone, is often contaminated by a sequential process, that is only capable of probing the vibrational dynamics of the fundamental. Although these two processes are virtually indistinguishable when a single Raman resonance is excited, we find that when a second Raman resonance is available within the experimental window governed by the bandwidth of the noisy light, new frequency components in the signal arise and the two competing fifth-order processes become distinguishable. These new frequency components, as well as their decay, are explained in terms of spectral filtering of the noisy light by the Raman resonances. This spectral filter analogy predicts which of the two competing processes dominates in an equimolar mixture of benzene-...

Fifth-order nonlinear Raman processes in molecular liquids using quasi-cw noisy light. I. Theory

Fifth-order nonlinear Raman processes using broadband, incoherent light are treated for a multiply resonant, multicomponent mixture. In particular, the theoretical development of the direct and the sequential fifth-order analogs of coherent Raman scattering is presented. Of the complete formalism, only the dominant doubly Raman resonant hyperpolarizability contributions to the signal intensity are discussed in this article. Furthermore, application is made to simulate fifth-order signals from a variety of hypothetical molecular liquids. It is seen how the direct and the sequential processes can distinguish themselves in a mixture, in a neat liquid with more than one Raman coherence, and also whenever the Raman active modes are taken to be anharmonic. This theoretical treatment anticipates experimental results presented in the following paper.

Theory of coherent Raman scattering with quasi-cw noisy light for a general line shape function

The theory of electronically nonresonant coherent Raman scattering (CRS) with quasi-cw noisy light (I(2) CRS) is developed for a general material response. The (Raman) resonant–resonant and resonant–nonresonant hyperpolarizability contributions to the I(2) CRS signal are interferometrically separable. It is found that, in general, the interferometric decay of each of these terms exposes the Raman line shape function in a different manner. Only for a Lorentzian line is their decay identical. Thus, in principle, I(2) CRS provides a new way to explore the line shape function that is analytically distinct from frequency domain and time domain methods. By way of illustration, the general theory is applied to three common line shapes: Lorentzian (as in the original I(2) CRS theory), Gaussian, and Voigt. The results are shown to be consistent with the principles of factorized time correlation diagram analysis.

Electronically nonresonant coherent Raman scattering using incoherent light: Two Brownian oscillator approaches

The theory for electronically nonresonant coherent Raman scattering using incoherent light (I(2)CRS) is presented for a Brownian oscillator material response. The exploration of Raman line shapes is based on two different approaches, both of which incorporate the Brownian oscillator model. The first takes the Raman transition as a two-level system that is indirectly coupled to the bath through “primary” Brownian oscillators. The I(2)CRS signal in the overdamped, high temperature regime is calculated analytically using this approach. The second approach is the standard one in which the Raman transition itself is represented by primary Brownian oscillators that are directly coupled to the bath. This method permits analytic calculation of the I(2)CRS signal for the entire parameter space and also for a distribution of oscillators to account for inhomogeneous linewidth broadening. These two methods allow for different interpretations of Raman line shapes using noisy light spectroscopy.

On the mechanism of vibrational dephasing in liquid benzene by coherent anti-Stokes Raman scattering using incoherent light

Abstract Coherent anti-Stokes Raman scattering using incoherent light (I (2) CARS) for the ring breathing mode of neat benzene is analyzed using a Brownian oscillator lineshaping model. Three low frequency modes of benzene are investigated for their possible role in the vibrational dephasing process. Unlike cw CARS, it is found that I (2) CARS can strongly discriminate between the dephasing activity of the three low frequency modes and suggests that rotation about the C 6 axis is responsible for dephasing in this case. This agrees with previous findings in femtosecond CARS experiments on the liquid.

Time-Frequency ResolvedCoherent Raman ScatteringFrom Molecular Liquidsand Their Mixtures With Quasi-CwNoisy Light: I(2) CRS Spectrograms

It is demonstrated how time-frequency resolved coherent Raman scattering (CRS) signals generated by broadband, non-transform limited, quasi-cw (noisy) light can be sensitive probes of molecular vibrational dynamics. The coherent Raman scattering signals from molecular liquids and their mixtures with noisy light are dispersed onto a CCD array and probed interferometrically to produce time-frequency domain spectrograms. These spectrograms offer an extensive oversampling of the data resulting in improved precision of measured parameters over previous noisy light methods. This technique has been very useful in measuring small changes in material parameters, such as Raman frequency shifts and linewidth changes, in dilution series with Raman inactive diluents. Very recently theory and experiment have extended to include mixtures with multiple Raman resonances. Several examples of experiments are presented and discussed.

RAMAN SCATTERING FROM A BROWNIAN OSCILLATOR WITH NONOHMIC DRUDE DISSIPATION : APPLICATIONS TO CONTINUOUS WAVE, IMPULSIVE, AND NOISY EXCITATION

An extension of the Brownian oscillator model in nonlinear optical spectroscopy to include frictional memory is treated. Although we have obtained analytic expressions for this model, their unwieldiness makes the understanding of the effect of nonzero frictional memory difficult. However, by focusing on the behavior of the analytically continued oscillator coordinate correlation function in the complex frequency plane, qualitative insight is obtained. Applications to spontaneous Raman scattering and two time-resolved coherent Raman scattering spectroscopies are briefly explored.

On librational broadening of vibrational transitions in liquids: a simple model

Abstract Sensitive absorption measurements can expose irregularly shaped vibrational overtone bands from the near-IR well into the visible region for stretching modes involving light atoms—particularly hydrogen. For the fifth overtone transition of the C-H stretching mode of liquid benzene, the asymmetric shape has been modelled as Franck–Condon structure in the separate rolibrational space of the molecule. The two rolibrational potentials, one for the ground state, the other for the fifth overtone state, were approximated as truncated anharmonic wells. In the present work the rolibrational potentials are treated as periodic cosinusoids and the associated Franck–Condon structure is derived in which one can smoothly pass from hindered rotation to free rotation, which is particularly relevant to potential barriers that are on the order of kT or less. Application to benzene provides a fit to the shape of the asymmetric fifth overtone band that is essentially within experimental error. The symbolic capabilities of Mathematica (ver. 3.0) have greatly facilitated the calculations by providing a quasi-analytic approach valid over a large range of parameters.