Noncentrosymmetric molecules

Answering this question involves an examination of Equation (12). The largest QEO nonlinearities are available when the QEO probe frequency, co, is close to resonance. This is the restriction that can potentially allow the two-level model to be applicable. Note that the two-level model depends on the competition between yc and yn, which have opposite sign. It is important to note that under centrosymmetry, yc should be the only contribution to yqeo> while the yqeo for noncentrosymmetric molecules consists of yc+yn. A first order correction to this model will require the additional term yfp. It is important to judge what effect this term may have on this speculation and the potential interpretation. In general, it should be to lower (However, note as in the case of frans-octatetraene,... 

I 7c+Ytp I > I Yc I) the expected yqeo I for centrosymmetric molecules, but increase the susceptibility magnitude expected in noncentrosymmetric molecules. 

Noncentrosymmetric molecules with strong donors and acceptors can also... 

Fig. 28. Structure of the noncentrosymmetric molecule that was theoretically analyzed for the optimization of the two-photon absorption cross-section 6...

In this equation, po is the permanent dipole moment of the molecule, a is the linear polarizability, 3 is the first hyperpolarizability, and 7 is the second hyperpolarizability. a, and 7 are tensors of rank 2, 3, and 4 respectively. Symmetry requires that all terms of even order in the electric field of the Equation 10.1 vanish when the molecule possesses an inversion center. This means that only noncentrosymmetric molecules will have second-order NLO properties. In a dielectric medium consisting of polarizable molecules, the local electric field at a given molecule differs from the externally applied field due to the sum of the dipole fields of the other molecules. Different models have been developed to express the local field as a function of the externally applied field but they will not be presented here. In disordered media,... 

Figure 5.7 The first two permanent electric moments of some noncentrosymmetric molecules...

Cascading. In most cases, the distinction between second- and third-order nonlinearities is evident from the different phenomena each produce. That distinction blurs, however, when one considers the cascading of second-order effects to produce third-order nonlinear phenomena (51). In a cascaded process, the nonlinear optical field generated as a second-order response at one place combines anew with the incident field in a subsequent second-order process. Figure 2 shows a schematic of this effect at the molecular level where second-order effects in noncentrosymmetric molecules combine to yield a third-order response that may be difficult to separate from a pure third-order process. This form of cascading is complicated by the near-field relationships that appear in the interaction between molecules, but analysis of cascaded phenomena is of interest, because it provides a way to explore local fields and the correlations between orientations of dipoles in a centros5nnmetric material (52). 

A major difference between jStwo-ievei and ytwo-ievei is the presence of two competing terms in equation 22. (Only the second term will contribute, however, with a centrosymmetric material, yielding a negative y if Z>i 11 and Du are positive, as they must be below resonance.) Competition between the two terms of the model results for noncentrosjmimetric molecules. Fundamental calculations by Kuzyk show that the maximum theoretical result for noncentrosymmetric molecules is positive and four times the value in the centrosymmetric case (127). 

Often, as in the foregoing examples, parts of Raman and IR spectra are complementary, each being associated with a different set of vibrational modes within a molecule. For noncentrosymmetric molecules, many vibrational modes may be both Raman and IR active. For example, all of the vibrational modes of sulfur dioxide yield both Raman and IR bands. The intensities of the bands differ, however, because the probabilities for the transitions are different for the two mechanisms. Raman spectra are often simpler than IR spectra because the occurrence of overtone and combination bands is rare in Raman spectra. 

Illustration of the flexoelectricity assuming polar noncentrosymmetric molecules. Upper row pear-shape molecules Bottom row banana-shape molecules. (After Meyer. 

This simplified model is illustrated by Fig. 5.4 in both cases of centrosymmetric and noncentrosymmetric molecules. In the first case, the dipolar term of Equation 5.10 cancels and only the 2Ppart must be taken into account Equation 5.10 becomes Equation 5.11 [21] ... 

The three-level model Equation 5.10 shows that the 2PA efficiency is strongly correlated to the molecular charge transfer. Several reviews describe different molecular engineering approaches for the optimisation of G2pa values [25,42,43]. Several classes of molecules were studied for their 2PA properties, as displayed in Fig. 5.5 noncentrosymmetric molecules such as dipoles and ocmpoles, and centrosymmetric systems such as quadm-poles. In the last case, the dipolar term D of Equation 5.10 cancels, but the possibility of a 2PA resonance with the lowest excited state Si (Fig. 5.4 and Equation 5.11) leads to enhanced 2PA properties [44]. 

Figure 5.4 Schematic representation of 2PA three-level model for centrosymmetric and noncentrosymmetric molecules...

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