Hyperpolarizability vector part

The important question in EFISHG, especially in the light of the complementarity with hyper-Rayleigh scattering (HRS), is What is actually experimentally determined The expression for the rotational contribution is determined by the scalar product of the dipole moment vector with the vector part of the third-rank hyperpolarizability tensor (Eq. (13)). 

As will be explained in Section 8.3.3, the reduction spectrum of rank-three tensors contains, in the general case, one (pseudo)scalar, three vectors, two (pseudo)devia-tors, and one septor [13]. Here, we only have to deal with the vectorial parts. They transform as a vector. Hence, the scalar product of the dipole moment vector with a vector part of the first hyperpolarizability tensor can be written as the simple product of two scalars, when we designate 9 as the angle between the molecular axis (z-axis) and the dipole moment axis (Eq. (14)). 

It is important to make the distinction, and state the exact relation, between the measured observable and the actual hyperpolarizability tensor component(s), even if, for specific experimental conditions and molecular symmetries, their values turn out to be identical. What is also important is the fact that only one experimental condition is favorable for EFISHG, namely parallel polarizations for all optical and static fields. This leads to only one observable, resulting in only a single value to be deduced. It is not possible with EFISHG to determine more than one tensor component hence, one often contends either with the approximation that P. was determined, or with the statement that / , was obtained, in any of the above-mentioned relations to the individual tensor components. Even then, the assumption that the dipole moment vector and the vector part of the third-rank tensor along the molec-... 

Following standard procedure [99], the vector part of the hyperpolarizability of molecule a is... 

In Figure 9 we plotted the ratio of the magnitude (square root of the sum of the squares of all components) of the vector part and the septor part y 3 / )93 vs. P xxIPzzz for molecules with only two independent hyperpolarizability components... 

Two major experimental techniques exist to probe the molecular first hyperpolarizability of solutions the EFISHG [41, 42] and the HRS [43]. The EFISHG technique consists in measuring the coherent light intensity at a frequency equal to twice the fundamental frequency of an incident laser pulse, generated by a solution submitted to a static electric field. This method is applicable only to polar and neutral molecules, and gives information on the projection of the vector part of on the dipole moment vector, so that only a combination of tensorial components of P can be obtained ... 

A similar reasoning can be applied to linear polarizabilities, a, and second-order hyperpolarizabilities, y, for the donor-acceptor Tr-conjugated molecules. The two-state models for a and y are given in Appendix A. Similarly as in the case of jS, the lowest CT excited state gives also a significant contribution to the values of a and y for the analyzed molecules [11, 14, 17-19, 38, 40], Also, the behaviour of a and y as a function of the solvent polarity seems to reflect the tendencies for jS. However, the a values appear to be less sensitive to the solvent effects than jS and y [14, 19, 26, 31, 36, 38], Recently, for the case of static vector components of jS and scalar part of y, it has been shown that the calculated ratio of is approximately equal to the ratio for a variety of the donor-acceptor... 

It is most important to note that in many cases of harmonic emission, a more completely index-symmetric form of the polarizability tensor is implicated. Consider once again the prototypical example of optical nonlinearity afforded by harmonic generation. When any harmonic is generated from a plane-polarized beam, in an isotropic medium, it produces photons with the same polarization vector as the incident light. In such a case the radiation tensor pyk becomes fully index-symmetric, and arguments similar to those given above show that only the fully index-symmetric part of the hyperpolarizability tensor, 3p(—2m co, co), can be involved. This does not mean that the tensor itself is inherently fully index-symmetric, but it does mean that experiments of the kind described cannot determine the extent of any index antisymmetry. 

---