Local field factors nonlinear optical properties

The oriented gas model was first employed by Chemla et al. [4] to extract molecular second-order nonlinear optical (NLO) properties from crystal data and was based on earlier work by Bloembergen [5]. In this model, molecular hyperpolarizabilities are assumed to be additive and the macroscopic crystal susceptibilities are obtained by performing a tensor sum of the microscopic hyperpolarizabilities of the molecules that constitute the unit cell. The effects of the surroundings are approximated by using simple local field factors. The second-order nonlinear response, for example, is given by... 

It is also important to realize that the nonlinear optical properties of a molecule in solution or in the solid state will differ from that of the isolated molecule due to polarization effects caused by the surrounding molecules. In theoretical calculations of molecules in die liquid phase, these effects may be modeled using for instance dielectric continuum models [33, 41, 42, 52, 56]. The use of such schemes for estimating the polarization of the solute by the solvent does not resolve the issue of local field factors. 

Whatever the degree of approximation used in evaluating the effective nonlinear susceptibility of a composite medium, it can be seen in Eqs. (22), (23) or (27) that the result depends on the product of two complex quantities One linked with the medium morphology and composition (the local field factor), the other linked with the nonlinear optical properties of the metal inclusions themselves (the intrinsic third-order susceptibility, Xm ) - inasmuch as the own contribution of the host matrix to the whole nonlinear response still remains negligible. We will focus here on the second factor. It is noteworthy that very few theoretical work has been accomplished regarding the value of Xm for noble metal nanoparticles after the pioneering smdies of Flytzanis and coworkers [79, 80, 89, 90]. Moreover, as will be underlined below, their results may not be used in every experimental situation as they are. 

As already stated for other experimental parameters, two factors may account for the nonlinear optical response dependence on excitation wavelength Local field factor, f, and intrinsic nonlinear properties of the particles, x2 - The interband contribution to x2 expected to vary only for photon energies at least equal to the IB transition threshold, provided the intraband contribution remains negligible. On the other hand, the hot electron contribution, which accounts for the Fermi smearing mechanism, presents spectral variations for photon energies close to the IB transition threshold, since the electron distribution is modified around the Fermi level by the temperature increase subsequent to light absorption (see 3.2.3). The wavelength dependence of x has been already discussed in Section 6. 

Several methods have been developed in order to determine the macroscopic optical properties [63], of which the simplest is the oriented gas model due to Chemla et al. [64, 65] In that method, the hnear and nonlinear susceptibilities (Eq. (8.2) are calculated from simple tensor sums of the (hyper)polarizabihties of the molecules constituting the elementary unit cell. Corrective factors can subsequently be added to account for the effects of local electric fields. The relevance of this method is ensured provided the intermolecular interactions are weak, while the macroscopic responses are strongly dependent on the values of local field factors. More sophisticated schemes take into account the intermolecular interactions. They include the supermolecule model [66-69], where an aggregate of... 

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