Third-Order Electronic Polarizabilities

Using the same straightforward thongh cumbersome algebra, the third-order density matrix element p 2(0 and the corresponding nonlinear polarizability tensor component jyich can be obtained. It suffices to note that p (t) will involve a triple product of d . E and oscillate as where co, co, and co are the frequency compo- 

From this, the third-order polarizability tensor component y pf, [-( +co + ) co , cd, cd] can be identified from 

If we account for relaxation mechanisms, again, all the co s will be replaced by the corresponding Q=(a-iy. From Equation (10.44) we can see that besides one and 

From these expressions for the second- and third-order nonlinear polarizabilities, several observations can be made  

The magnitudes and signs of the nonlinear responses of a molecule are highly dependent on the state [e.g., p 2 it is in an excited-state molecule obviously has a nonlinear response very dilferent from a groimd-state molecule. 

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New THG Methods For Molecular Liquid Characterization. An area which is essential for understanding general third-order nonlinear polarizability is characterization of the purely electronic contributions (48). Several methods have been employed for this... 

Through this mechanism, the nonlinear response is produced by the changes on the electronic cloud around the atom or molecule through the optical field. It is related to the microscopic third-order molecular polarizability y. Typically, nonresonant electronic processes in non-absorbing media yield values of 10 esu. The... 

A detailed formalism for describing second and third order electronic molecular polarizabilities and macroscopic susceptibilities is given in... 

The structure/property relationships that govern third-order NLO polarization are not well understood. Like second-order effects, third-order effects seem to scale with the linear polarizability. As a result, most research to date has been on highly polarizable molecules and materials such as polyacetylene, polythiophene and various semiconductors. To optimize third- order NLO response, a quartic, anharmonic term must be introduced into the electronic potential of the material. However, an understanding of the relationship between chemical structure and quartic anharmonicity must also be developed. Tutorials by P. Prasad and D. Eaton discuss some of the issues relating to third-order NLO materials. 

The search of third-order materials should not just be limited to conjugated structures. But only with an improved microscopic understanding of optical nonlinearities, can the scope, in any useful way, be broadened to include other classes of molecular materials. Incorporation of polarizable heavy atoms may be a viable route to increase Y. A suitable example is iodoform (CHI ) which has no ir-electron but has a value (3J ) comparable to" that of bithiophene... 

The second-order molecular polarizability, /, and the third-order nonlinear susceptibility, have been measured for many compounds (see Table 5.7). Note that the f value of nitroaniline, where the centrosymmetric benzene ring carries an electron withdrawing nitro-group and an electron-donating amino-group, is larger than that of monosubstituted benzenes. 

The original Placzek theory of Raman scattering [30] was in terms of the linear, or first order microscopic polarizability, a (a second rank tensor), not the third order h3q)erpolarizability, y (a fourth rank tensor). The Dirac and Kramers-Heisenberg quantum theory for linear dispersion did account for Raman scattering. It turns out that this link of properties at third order to those at first order works well for the electronically nonresonant Raman processes, but it cannot hold rigorously for the fully (triply) resonant Raman spectroscopies. However, provided one discards the important line shaping phenomenon called pure dephasing , one can show how the third order susceptibility does reduce to the treatment based on the (linear) polarizability tensor [6, 27]. 

Luo237 has attempted to establish a power law for scaling the static y-hyperpolarizabilites of the fullerenes as a function of the number of carbon atoms. C6o does not fit into the relationship, a result attributed to its exceptional electron localization. An intermolecular potential model of with distributed dipole interactions has been used by Gamba238 to obtain the polarizability and multipole moments. Measurements of the third order response of fullerenes in CS2 have been reported by Huang et al.239 and correlated with chemical structure. 

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