Hyperpolarizability generation, EFISH

TDDFT methods have also been applied successfully to the description of the linear and nonlinear optical properties of heteroleptic sandwich complexes. The optical spectrum and the hyperpolarizability of Zr(OEP)(OEPz,) for which large first hyperpolarizabilities, /JSHG (SHG=second-harmonic generation) were measured in an electric field induced second-harmonic generation (EFISH) experiment [182], have been investigated by TDDFT methods [134]. The excitation energies and oscillator strengths calculated... 

The first common method for molecular first hyperpolarizability determination is the electric field-induced second harmonic generation (EFISH) technique in solution [6-10]. This technique can be applied only to dipolar molecules. Under an applied external electric field, molecules in solution orient approximately in the direction of the field giving rise to second harmonic generation. The measured third-order nonlinear optical susceptibility is given by the following expression ... 

Suslick et al. measured the first hyperpolarizabilities ()S) of porphyrins having electron-donor (amino) and -acceptor (nitro) groups in the para-position of 5,10,15,20-substituted tetraphenylporphyrins (Figure 25) using electric field induced second harmonic generation (EFISH) technique at 1.19 pm with chloroform solutions. The dipole moment (p) and P values were affected by the position of donor and acceptor groups. A P value of 30 x 10 esu and dipole moment of 7 x 10 esu were measured for the porphyrin having R = R = NO2, R = R = NH2 and the porphyrin... 

Experimentally, mainly two techniques - the electric field induced second harmonic generation (EFISH) and hyper-Rayleigh scattering (HRS, also termed harmonic light scattering method) - are used in order to determine in solution the experimental value of the quadratic hyperpolarizability of molecular NLO chromophores. 

First, let us turn our attention to the issue of optimizing chromophore hyperpolarizability. An obviously important and necessary aspect of the process is the characterization of hyperpolarizabilities. The two most popular methods for characterizing chromophore second-order molecular optical nonlinearity are electric field-induced second harmonic generation (EFISH) [3,10,21-24] and hyper-... 

Assuming that arises from the third-order hyperpolarizability, elements of give information about the degree of orientational order. Measurements of electric-field-induced second-harmonic generation (EFISH) have been carried out [88] on 5CB, showing the expected temperature dependence. In liquid crystals, may originate from order or flexoelectric effects, or other mechanisms resulting in electric polarization. 

While the above discussion clearly highlights the importance of including solvent effects in the calculations, the calculated properties cannot be compared directly with experimental results. This is mainly caused by the many different conventions used for representing hyperpolarizabilities and susceptibilities. However, the calculated properties can be combined with appropriate, calculated Lorentz/Onsager local field factors to obtain macroscopic susceptibilities that can be compared with experimental results. For water, we used this to calculate the refractive index and the third harmonic generation (THG) and the electric field-induced second harmonic (EFISH) non-linear susceptibilities. The results are collected in Table 3-11. 

The HRS technique [25-27] involves the detection of the incoherently scattered second harmonic generated by the molecule in solution under irradiation with a laser of wavelength 2, leading to the mean value of the x tensor product. By analysis of the polarization dependence of the second harmonic signal, which can be evaluated selecting the polarization of the incident and scattered radiation, it is possible to obtain information about the single components of the quadratic hyperpolarizability tensor jS. Unlike EFISH, HRS can also be used for ionic molecular species and for nondipolar molecules such as ocmpolar molecules. In this chapter, the quadratic hyperpolarizability measured with an incident wavelength 2 by the EFISH and HRS techniques will be indicated as /l i(EFISH) and / (HRS), respectively. 

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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