Tensors Raman scattering

Fig. 2 Raman spectra of a single-crystal of orthorhombic Sg at three different polarizations in which the off-diagonal elements of the Raman scattering tensor are non-zero big, b2g, b g), after [105]. However, Raman intensities of other polarizations like flg components ( 54 cm ) penetrate in the spectra due to optical anisotropy in the crystal...

Accordingly, for a given Raman-active resonance r, the amplitudes of XijM can be expressed in terms of the isotropy and symmetric anisotropy invariants of the corresponding spontaneous Raman scattering tensor, a2 and 7S2, respectively. In the case of frequency-degenerate CRS considered here, the two relevant independent tensor components assume the following form [33, 34] ... 

For a purely isotropic Raman scattering tensor, the depolarization ratio will be zero since the scattered light from such a system must have a polarization parallel to the incident beam. This is evident when equation equation (5.29) is used in equation (5.30) so that [21],... 

Shegai TO, Haran G (2006) Probing the Raman scattering tensors of individual molecules. J Phys Chem B 110(6) 2459-2461... 

K. Jurkowska and R. Mierzecki. The influence of intermolecular interactions on the invariants of the Raman scattering tensors, II. The CDCI3 tensors in solutions with acetone, dioxane, benzene and mesythylene. Acta Phys. Polonica, A, 63 701-706 (1983). 

The HT coupling mechanism was first considered in the context of the Raman scattering tensor hy Albrecht (9) whose approach was briefly discussed in Section 2.4. 

It is readily shown that this is identically equal to the electronic Raman scattering tensor for the Raman transition /> <- 0>. Note that the first term in Eq. (5.15) dominates if there exists a state r> such that Ef xhco the second term dominates if there is a state such that ,o Such cases lead to resonance enhancement and will be discusse[Pg.57]

More recent interest has focused upon the interpretation of the relative intensities of the electronic Raman transitions. The theory of electronic Raman spectroscopy has been well-summarized elsewhere [63, 202], and the electronic Raman scattering amplitude from an initial i/rf) to a final jfj) vibronic state (where the phonon states are the same, and usually zero-phonon (i.e. electronic) states) is given by (i/ r czpCF In this expression, the cartesian polarizations of the incident photon (hcv) and the scattered photon (hcvs) are a and p, respectively. The Cartesian electronic Raman scattering tensor is written as... 

In the same approximation, the Raman scattering tensor for Stokes scattering given by... 

The nonvanishing resonance components of the Raman scattering tensor are then... 

The Raman scattering tensor for the fundamental of this mode under resonance with P o... 

The intensity of a vibrational band in the Raman spectrum of DNA is given by the absolute square of the Raman scattering tensor, ,... 

Zuber, G., 8c Hug, W. (2004). Rarefied basis sets for the calculation of optical tensors. 1. The importance of gradients on hydrogen atoms for the Raman scattering tensor. Journal of Physical Chemistry A, 108, 2108. 

Owing to the coherence, we need to consider the macroscopic evolution of the field in a medium that shows a macroscopic polarization induced by the field-matter interaction. This will be done in three steps. First, the polarization induced by an arbitrary field will be calculated and expanded in power series in the field, the coefficients of the expansion being the material susceptibilities (frequency domain) or response function (time domain) of wth-order. Nonlinear Raman effects appear at third order in this expansion. Second, the perturbation theory derivation of the third-order nonlinear susceptibility in terms of molecular eigenstates and transition moments will be outlined, leading to a connection with the spontaneous Raman scattering tensor components. Last, the interaction of the initial field distribution with the created polarization will be evaluated and the signal expression obtained for the relevant techniques of Table 1. 

If an optical frequency co is close to one-photon electronic resonance with an intermediate state /, the terms including the denominator -co — 0 will be dominant and we obtain a good approximation by retaining only these (resonant nonlinear Raman spectroscopy). In the absence of such additional electronic resonances, we can neglect the damping coefficient for all denominators whose absolute value is far from zero and write them in terms of real Raman scattering tensor components for the transition from... 

H) = component of with Cartesian index fia y, Rab component along fi of the transition dipole matrix element for transitions from a to b Tj = population relaxation characteristic time T2 = phase relaxation characteristic time V t) = interaction operator (a,((o))g= Raman scattering tensor for transitions from state g to state / ... 

M is the electric dipole transition moment vector T is the two-photon absorption tensor a is the Raman scattering tensor and is a unit vector in the direction of light polarization U. 

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