Local field factors

As was mentioned in Section 2, there exists a variety of different theoretical approaches to calculate the local field factor g q). Following Farid et al. [7], the behavior of g q) for large q is connected to the size z of the step in the occupation number function n(k) fork = kF, kF being the Fermi-momentum (see Figure 8). This... 

The tensorial product of local field tensors is not averaged, but replaced by an arithmetic product of the average magnitude of four local field factors. 

Frequently correlations of local field amplitude and molecular type are ignored and a single family of solution local field factors is adopted. 

Where is the bulk second order NLO property, N is the number of molecules and / the local field factors. Erom this equation it can be readily seen that the target must be for molecules with a high f] in order to achieve high bulk activity, although in practice the relationship is not quite so simple. 

The preceding discussion assumed a pure liquid was used for the measurement. Most molecules of interest, however, are not in the liquid state at room temperature. In this case it is common to dissolve the compound in an appropriate solvent and conduct the measurement. Contributions to the second harmonic signal are therefore obtained from both the solvent and solute. Since r and the local field factors that are related to e and n, (the dielectric constant and refractive index respectively) are concentration dependent, the determination of p for mixtures is not straightforward. Singer and Garito (15) have developed methods for obtaining r0, eQ, and nQ, the values of the above quantities at infinite dilution, from which accurate values for p can be obtained in most cases. 

While distinct local field factors should, in principle, be used for each species in solution, L is usually taken as a uniform factor (defined in terms of the indices for the solution) for the whole solution. Limitations of microscopic models for nonlinear susceptibilities and the shortcomings of local field descriptions such as that above have been discussed by Meredith et al 26). Eq. 23 can be rewritten in terms of concentrations as... 

The measured dipole moments for X and XI in different solvents are summarized in Table III. First, the experimental values of p vary from solvent-to-solvent with a trend to higher values for more polar solvents. This may be partly due to the approximations mentioned above. It is also important to note that no attempt was made to account for the nonspherical shape of the dye molecule. We believe that this approximation is justified, since the local field factor used to calculate the hyperpolarizabilities in the EFISH experiment for the product p/J involves similar approximations. Thus, the effective dipole moment determined in these experiments,... 

In the limit of the oriented gas model with a one-dimensional dipolar molecule and a two state model for the polarizability (30). the second order susceptibility X33(2) of a polymer film poled with field E is given by Equation 4 where N/V is the number density of dye molecules, the fs are the appropriate local field factors, i is the dipole moment, p is the molecular second order hyperpolarizability, and L3 is the third-order Langevin function describing the electric field induced polar order at poling temperature Tp - Tg. 

A final point worth mentioning is the effect of local fields on the optical nonlinearities of strongly QC nanostructures. These arise from embedding QD s in a medium of different dielectric constant (2). One requires to know how the field intensity inside the particle varies at saturation in excitonic absorption. This has been approached theoretically by defining a local field factor f such that Em = f Eout (2). The factor f depends on the shape of the QD and the dielectric constant of the QD e = + E2 relative to that of the surrounding medium. Here... 

Similarly to IR, classical theories have also been proposed in the literature for Raman intensities in solution [29,32-38], The starting point is again the definition of the local field Eso1 acting on the molecule. In all cases the local field factor is defined as / = S-i/S-c, with 5 sc being the scattering intensity. 

Solvent effects on the optical rotation are traditionally accounted for using the Lorentz effective field approximation [38], in which the optical rotation is multiplied by a local field factor... 

From the point of view of theory, the formulae of Table 2.6 are equally applicable to both gas and condensed phase samples, as they include the local field factors, which account for local modifications to the Maxwell fields due to bulk interactions within the Onsager-Lorentz model. 

Again specializing to linear birefringences, it is convenient to define effective constants m W (m, T) which are obtained from those given in Table 2.7 multiplied by the local field factors originally included in wl7 cf. Table 2.6... 

X2 [3X2-(9lmaX)2]r0/3[ i2-( imax)2] Zero frequency local field factor for poling field f0=er(n2+2)/[2er+n2] where 8r is the relative dielectric constant... 

Local field factor for light wave field fA=(n2+2)/3... 

Fourier components of the electric field strength two-photon cross-section molar extinction coefficient local field factor... 

In this section, a simple description of the dielectric polarization process is provided, and later to describe dielectric relaxation processes, the polarization mechanisms of materials produced by macroscopic static electric fields are analyzed. The relation between the macroscopic electric response and microscopic properties such as electronic, ionic, orientational, and hopping charge polarizabilities is very complex and is out of the scope of this book. This problem was successfully treated by Lorentz. He established that a remarkable improvement of the obtained results can be obtained at all frequencies by proposing the existence of a local field, which diverges from the macroscopic electric field by a correction factor, the Lorentz local-field factor [27],... 

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