Hyperpolarizabilities p and

The susceptibility tensors give the correct relationship for the macroscopic material. For individual molecules, the polarizability a, hyperpolarizability P, and second hyperpolarizability y, can be defined they are also tensor quantities. The susceptibility tensors are weighted averages of the molecular values, where the weight accounts for molecular orientation. The obvious correspondence is correct, meaning that is a linear combination of a values, is a linear combination of P values, and so on. 

Two of the most important nonlinear optical (NLO) processess, electro-optic switching and second harmonic generation, are second order effects. As such, they occur in materials consisting of noncentrosymmetrically arranged molecular subunits whose polarizability contains a second order dependence on electric fields. Excluding the special cases of noncentrosymmetric but nonpolar crystals, which would be nearly impossible to design from first principles, the rational fabrication of an optimal material would result from the simultaneous maximization of the molecular second order coefficients (first hyperpolarizabilities, p) and the polar order parameters of the assembly of subunits. (1)... 

Nonlinear optical activity reflects the nonlinear response of /r, (f- ) to electromagnetic radiation, which Eq. (7) shows to be governed by the first and second hyperpolarizabilities, p and y. A high level of such activity can have important applications in a variety of electro-optical devices,82,86,87 such as frequency converters, modulators, switches, etc. 

Effective second harmonic generation is attained in materials which have both high second-order molecular hyperpolarizability, p, and high second-order bulk susceptability, x - Molecular polarization is described by the field dependent molecular dipole moment, p (eq 1), expanded as a function of the applied field strength, E, which may be electric or optical (that is, electromagnetic) in nature. The field strength E is a vector, and Pq is the intrinsic dipole... 

There are many terms in the total response of materials to electric and magnetic fields, but the polarizability (ot) and hyperpolarizabilities (P and y) defined above are the NLO properties that are the focus of this chapter. For more general treatments of other properties, see the reviews by Buckingham and Bishop. As illustrated in Eq. [4], the NLO molecular properties are second-, third-, and fourth-rank tensor quantities, respectively. In the most general case, a has 9 components, p has 27 components, and y has 81 components because of symmetry properties, however many of these components are often interrelated or equal to zero. 

Note that to generate a large SHG, the material has to have laige values of the hyperpolarizabilities p and y. The THG needs a large y. In both cases, a strong laser electric field is a must. The SHG and THG therefore require support from the theoretical side we are looking for high hyperpolarizability materials and quantum mechanical calculations before an expensive... 

Table L Dipole moments p, hyperpolarizability p, and charge transfer band maximum Xcr of donor-acceptor substituted calix[4]arenes. ...

The effective electro-optic coefficient, r, of a material is related to chromophore number density, N, chromophore molecular first hyperpolarizability, P, and acentric order parameter, , by... 

The most commonly used model for understanding the relationship between the hyperpolarizability P and molecular structure is the two-state model (Oudar and Chemla, 1977). This model provides only a rough description but it allows a qualitative understanding of the nonlinear optical properties of molecules. For push-pull compounds with electron donors and acceptors, the P value depends mainly on the intramolecular polarization, the oscillator strength, and the excited state of the material (Allis and Spencer, 2001). There are three different possibilities for a refinement of the two-state model semi-empirical, ab initio and density functional theory methods (Li et al., 1992 Kanis et al., 1994 Kurtz and Dudis, 1998). 

This is the generation of a second-harmonic signal from a centro-symmetric material (e.g. a solution) when an electric field is applied. The electric field will orient polar molecules and hence induce a non-centrosymmetric polar structure capable of SHG. At the molecular level, EFISH can be described in terms of the reorientation of molecules with finite first-order hyperpolarizability p and a contribution from y. Then... 

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