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Physical Review A

Coherent Raman scattering with incoherent light for a multiply resonant mixture: Theory

Jason C. Kirkwood, Darin J. Ulness, Michael J. Stimson, A. C. Albrecht

Published Feb 1, 1998• 8 citations
Publisher

Abstract

The theory for coherent Raman scattering (CRS) with broadband incoherent light is presented for a multiply resonant, multicomponent mixture of molecules that exhibits simultaneous multiple resonances with the frequencies of the driving fields. All possible pairwise hyperpolarizability contributions to the signal intensity are included in the theoretical treatment---(resonant-resonant, resonant-nonresonant, and nonresonant-nonresonant correlations between chromophores) and it is shown how the different types of correlations manifest themselves as differently behaved components of the signal intensity. The Raman resonances are modeled as Lorentzians in the frequency domain, as is the spectral density of the incoherent light. The analytic results for this multiply resonant mixture are presented and applied to a specific binary mixture. These analytic results will be used to recover frequencies and dephasing times in a series of experiments on multiply resonant mixtures.

DOI
10.1103/physreva.57.1417

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The theory for coherent Raman scattering (CRS) with broadband incoherent light is presented for a multiply resonant, multicomponent mixture of molecules that exhibits simultaneous multiple resonances with the frequencies of the driving fields. All possible pairwise hyperpolarizability contributions to the signal intensity are included in the theoretical treatment---(resonant-resonant, resonant-nonresonant, and nonresonant-nonresonant correlations between chromophores) and it is shown how the different types of correlations manifest themselves as differently behaved components of the signal intensity. The Raman resonances are modeled as Lorentzians in the frequency domain, as is the spectral density of the incoherent light. The analytic results for this multiply resonant mixture are presented and applied to a specific binary mixture. These analytic results will be used to recover frequencies and dephasing times in a series of experiments on multiply resonant mixtures.
Coherent Raman scattering using broadband, incoherent (noisy) light (termed I(2)CRS{\mathrm{I}}^{(2)}\mathrm{CRS}I(2)CRS---the I for interferometric and the superscript 2 for twice acting noisy fields) is treated for a multiply resonant, multicomponent mixture of molecules. Both the resonant-resonant and resonant-nonresonant hyperpolarizability contributions to the signal intensity are included in this formalism. The emphasis is on the physical understanding of this spectroscopy. To this end, factorized time correlator (FTC) diagram analysis is used to characterize the I(2)CRS{\mathrm{I}}^{(2)}\mathrm{CRS}I(2)CRS signal. The FTC diagram technique also serves to organize the terms that arise through the stochastic averaging of the noise at the intensity level. In addition to the FTC diagram analysis, a spectral filter analogy is employed to provide further insight into the physics behind I(2)CRS.{\mathrm{I}}^{(2)}\mathrm{CRS}.I(2)CRS.
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.
A new method to measure picosecond or subpicosecond vibrational-dephasing dynamics with the use of incoherent or broadband light is presented theoretically and experimentally. It is based on a transient coherent Raman process with three beams. In our experimental scheme, two of them are incoherent light from a single source, and a delay time between the two is variable. A third beam has a higher frequency than the incoherent light by a vibrational energy in a molecule of interest, and is coherent in the delay-time range of the measurement. The delay-time dependence of coherent Stokes Raman scattering (CSRS) intensity offers the information about the coherence dynamics of the vibrational transition with a resolution time determined only by the correlation time of the incoherent light. For the theoretical calculation, a three-level model of the molecular system with homogeneous broadening is used, and delay-time dependences of the CSRS signal are calculated for off-resonance and resonance cases. Dephasing dynamics of the 2915-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ mode in dimethylsulfoxide was observed experimentally by the new method with the use of nanosecond laser pulses, and the result agrees well with that obtained with picosecond pulses.
A theoretical description of the resonant coherent hyper-Raman scattering for an arbitrary system–bath interaction is presented. Particularly the relationship between the coherent hyper-Raman scattering (CHRS) and coherent Raman scattering (CRS) signals is established without alluding to any specific model of optical broadening. The permanent dipole moment difference between the excited and ground states of a given chromophore is shown to be proportional to the ratio of the CHRS to CRS signals, and it is proved that this result is valid regardless of the model for the chromophore–bath interaction.
The theoretical basis for new signal transients and spectral features generated in field-correlated four-wave mixing spectroscopies is developed. Special attention is given to those signal responses that are sensitive to phase or amplitude correlation among the input driving fields, and not simply their intensity correlation. Thus the cases of incoherent broadband excitation and of coherent short-pulsed excitation will be discussed and compared. Applications to the coherent Raman spectroscopies, both electronically nonresonant and full resonant, are analyzed. Novel interferometric oscillatory behavior is exposed in terms of radiation-matter detuning beats and matter-matter bilevel and trilevel quantum beats. In addition, new resonances are found that have submaterial linewidths and detuning parameters that lock onto the mode frequency of the driven chromophore. These spectral features are members of a class of bichromophore resonant line shapes arising from nonlinear mixing with correlated driving fields. Analytic results are presented and modeled to anticipate experimental results presented in the following paper [Phys. Rev. A 43, 3922 (1991)].
A theory for the resonance light scattering in a molecular system interacting with the heat bath is developed, taking into account the multilevel structure of the molecular system. An expression for the cross section of the resonance light scattering process is derived by using the Liouville operator method in the Markoff approximation; the cross section consists of three terms: resonance Raman scattering, resonance fluorescence, and their mixing. The mixing term vanishes in the limit of the zero vibrational dephasing constant. Analytical expressions for the resonance Raman scattering and resonance fluorescence cross sections are derived in the displaced harmonic oscillator model. Model calculations of the vibrational band structure in the resonance light scattering cross section are performed by using the expressions derived. Differences of the band intensity distribution in the resonance fluorescence from that in the resonance Raman scattering are illustrated.