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The Journal of Chemical Physics

Resonant coherent hyper-Raman scattering (CHRS). II. A theory on the general relationship between CHRS and coherent Raman scattering (CRS) processes

Minhaeng Cho

Published Aug 8, 1998• 4 citations
Publisher

Abstract

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.

DOI
10.1063/1.476787

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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 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.
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.
Abstract The theory of differential scattering described in part I (preceding paper) is applied to the Raman process. Here, a distinction between inequivalent and equivalent chromophores is required. For systems with inequivalent chromophores, the leading contribution to the differential intensity of scattering involves the interference of second- and fourth-order probability amplitudes; in near- and far-zone limits, it depends on the inverse square of the group separation. For systems with equivalent chromophores, the spectrum should, in general, feature a doublet. The dominant contribution to the differential intensity comes from the second-order-second-order interference term and has a different sign for each doublet component. In many cases these contributions cancel and the leading term becomes the second-order-fourth-order interference term as in the case of inequivalent chromophores.
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.
Abstract The amplitudes and the excitation profiles of coherent resonant Raman scattering (coherent anti‐Stokes and Stokes Raman scattering (CARS and CSRS)) by impurity centers in crystals and/or molecules in solutions are studied, taking into account the coherence of the excited mode and the inhomogeneity of the environment. The CARS and CSRS excitation profiles can directly be related to one‐photon absorption when using the transform theory known from spontaneous resonant Raman scattering. The enlargement of the amplitude of the active mode reveals itself in an enhancement of the vibrational overtones. At large amplitudes, a splitting in the profiles caused by the contribution of two turning points of a strong coherent vibration is observed. The inhomogeneous broadening is different in the excitation profiles of CARS and CSRS. The overlapping contributions to spectrally narrow and broad transitions lead to Fano peculiarities. The effects are illustrated by model calculations. Copyright © 2011 John Wiley & Sons, Ltd.
A theory of resonant Raman scattering spectroscopy of one-dimensional electronic systems is developed on the assumptions that (i) the excitations of the one-dimensional electronic system are described by the Luttinger-liquid model, (ii) Raman processes involve virtual excitations from a filled valence band to an empty state of the one-dimensional electronic system, and (iii) excitonic interactions between the valence and conduction bands may be neglected. Closed form analytic expressions are obtained for the Raman scattering cross sections, and are evaluated analytically and numerically for scattering in the polarized channel, revealing a ``double-peak'' structure with the lower peak involving multispinon excitations with total spin S=0S=0S=0 and the higher peak being the conventional plasmon. A key feature of our results is a nontrivial power-law dependence, involving the Luttinger-liquid exponents, of the dependence of the Raman cross sections on the difference of the laser frequency from resonance. We find that near resonance the calculated ratio of intensity in the lower energy feature to the intensity in the higher energy feature saturates at a value of the order of unity (times a factor of the ratio of the velocities of the two modes). We explicate the differences between the ``Luttinger-liquid'' and ``Fermi-liquid'' calculations of resonant Raman spectroscopy (RRS) spectra and argue that excitonic effects, neglected in all treatments so far, are essential for explaining the intensity ratios observed in quantum wires. We also discuss other Luttinger-liquid features which may be observed in future RRS experiments.