Polarizabilities optical, origins

In an organic molecule, the nonlinear optical effect originates from nonlinear polarization of the molecules. The polarizability of a molecule is the ability of a charge in the molecule to be displaced under the driving of the electric field. Under an intense optical field, induced polarizability p can be expressed as a polynomial function of local field strength e, [34] ... 

Four frequently used conventions exist for the definition of non-linear optical polarizabilities, leading to confusion in the realm of NLO. This has been largely clarified by Willets et al. (1992) and in their nomenclature we have used the Taylor series expansion (T convention), originally introduced by Buckingham (1967), where the factorials n are explicitly written in the expansion. Here the polarizabilities of one order all extrapolate to the same value for the static limit w— 0. /3 values in the second convention, the perturbation series (B), have to be multiplied by a factor of 2 to be converted into T values. This is the convention used most in computations following the sum-over-states method (see p. 136). The third convention (B ) is used by some authors in EFISHG experiments and is converted into the T convention by multiplication by a factor of 6. The fourth phenomenological convention (X) is converted to the T convention by multiplication by a factor of 4. 

In spite of the practical usefulness of such empirical sector mles, the physical origin of the optical activity in these molecules remains an open question. In fact, polarizability calculations (both by means of the Weigang amplified sector mle for allowed transitions and the DeVoe dynamic coupling model), taking full account of the interaction between the Ag — transition dipole and the polarizable matter around it, give the wrong sign. 

The extension of the bond polarizability theory to ROA is based on the origin-dependence of G p and AaPr Thus using (2.6) the optical activity tensors of the molecule, written as sums of corresponding bond tensors, are... 

Thus the polarizability tensor of the molecule is written as a sum of local atomic polarizabilities, each modified through dipolar interactions with the electric dipole moments on all the other atoms induced by the electric vector of the incident light wave. Similarly for the local atomic polarizabilities appearing in the origin-dependent parts of the optical activity tensors. But unlike the bond polarizability development, no allowance can be made for intrinsic local optical activity tensors Gj ap and Aj since these now pertain to spherical atoms. We refer to the original articles for the explicit Raman intensity and optical activity expressions generated by the atom dipole interaction theory. 

Exact static optical susceptibilities are conveniently calculated as successive derivatives on an applied electric field of the gs polarization, defined, in linear aggregates, as the dipole moment per unit length. The linear polarizability (a), the first and second hyperpolarizabilities (jS and y, respectively) obtained for 16-sites clusters are shown as full lines in Fig. 5. Left, middle and right panels refer to A, B and C clusters, respectively, for the parameters that, in Fig. 4 drive the system through the neutral-zwitterionic interface. Susceptibilities show a strong and non-trivial dependence on the intermolecular distance, and, to understand the physical origin of this complex and interesting behavior we shall discuss several approximated results. 

The vibrational contribution to the polarizability of poly acetylene amounts to 10% of its electronic counterpart and mainly originates from low-frequency transverse acoustic modes (TAMs) [73]. It tends towards zero in the optical regime. The nature of the frequency dispersion, therefore, constitutes a major difference between electronic and vibrational (hyper)polarizability contributions. The response time is also different the electronic processes are faster and their response time is of the order of 1 fs, whereas vibrational phenomena are slower and have response times ranging between 10 and 100 fs as a function of the associated vibrational normal mode frequency. 

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