Polar-field susceptibility parameters

Table 3.1. Composition of the parameters, a, b, and c in terms of the surface and bulk susceptibility elements. P-polarized ( ) or s-polarized ( O) fundamental field, i = (x,y)...

The derivation of formulae for the frequency-dependent nonlinear susceptibilities of nonlinear optics from the time-dependent response functions can be found in a number of sources, (Bloembergen, Ward and New, Butcher and Cotter, Flytzanis ). Here it is assumed that the susceptibilities can be expressed in terms of frequency-dependent quantities that connect individual (complex) Fourier components of the polarization with simple products of the Fourier components of the field. What then has to be shown is how the quantities measured in various experiments can be reduced to these simpler parameters. 

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. 

L and dependence on temperature and film thickness in Fig. 3.24. It follows from Fig. 3.24a, c, that at fixed temperature the average polarization L decreases for the film thinning (compare curves 1-5). Built-in field smears the temperature of phase transition and susceptibility maximum its influence increases with the films thinning (see Fig. 3.24b, d). Moreover, the order parameter behavior for the thinnest possible films resembles that for thin films of ordered ferroelectrics with the thickness less than critical one (compare the curves 5 in Fig. 3.24c, d with Fig. in the paper [54]). Built-in field induces order parameter in the film with maximal disorder, see dotted curves 5 in Fig. 3.24a, b. However hysteresis loops is absent on these curves so that the behavior resembles that of electret state. 

Let us now look at the dielectric susceptibility in the high temperature phase (T> T c). Both the order parameters q and P are zero in the field-free state, but when an electric field is applied it will induce a polarization and, by virtue of the coupling between P and q, also a nonzero value of q. In the high temperature phase we will thus have a kind of reverse effect brought about by the same coupling mechanism whereas in the low temperature phase a non-zero q induces a finite P, here a non-zero P induces a finite q. 

Here, P is the bulk polarization, E is the electromagnetic field vector, and the fill in are, respectively, the 1st, 2nd, and 3rd order bulk susceptibilities of the material. These bulk polarizabilities are correlated to the molecular-level polarizability, hyperpolarizability and second hyperpolarizability, a, p and y respectively. However, exact relationships between the bulk and corresponding molecular parameters are still not firmly established. 

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