Nonlinear first hyperpolarizability

Acentricity greatly enhances the y-value (see 92 vs 91 and 90 or 101 vs 99 and 100, Fig. 8). Such a trend had been predicted for certain ranges of compounds by theory [137] however when the first hyperpolarizability, which determines second-order nonlinear optical properties, is maximized, y is predicted to be zero [138]. 

These structure-function relationships provide extremely useful guidance for the future rational design of molecules and polymers with even higher optical nonlinearities. For non-centrosymmetric molecules such as 95, very high first hyperpolarizabilities /3 that determine the second-order nonfinear optical properties were also measured [140]. 

The proportionality constants a and (> are the linear polarizability and the second-order polarizability (or first hyperpolarizability), and x(1) and x<2) are the first- and second-order susceptibility. The quadratic terms (> and x<2) are related by x(2) = (V/(P) and are responsible for second-order nonlinear optical (NLO) effects such as frequency doubling (or second-harmonic generation), frequency mixing, and the electro-optic effect (or Pockels effect). These effects are schematically illustrated in Figure 9.3. In the remainder of this chapter, we will primarily focus on the process of second-harmonic generation (SHG). 

The ethynyl-linked complexes 105 were prepared and explored as potential building blocks for nonlinear optical (NLO) materials.129 Spectroscopic and cyclic voltammetry data indicate a small but real interaction between the ferrocenyl donor group and the borabenzene unit, increasing in the order RuHyper-Rayleigh scattering revealed small values for the first hyperpolarizability / , which increases in the same order. 

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)... 

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... 

Ever since HRS has been developed as an experimental technique to determine the first hyperpolarizability p of molecules in solution, it has been realized that multiphoton fluorescence is a competing nonlinear process, contributing to the HRS signal [26]. For the classical dipolar and neutral molecules that may exhibit multiphoton fluorescence, electric-field-induced second-harmonic generation (EFISHG) experiments are possible. However, for ionic and non-dipolar compounds, no electric field can be applied over the solution. Hence, no EFISHG measurements are possible. Then it is very tempting to rely on the HRS measurement only. When there is, however, a multi-photon fluorescence (MPF) contribution, an overestimation of the first hyperpolarizability value results [27]. 

The general quantum chemical description of the nonlinear susceptibilities and hyperpolarizabilities in the density matrix formalism was developed by Bloembergen and Shen [36]. A simplification of this model for dipolar organic molecules, by only considering the transition between the ground state and the first excited state, led to the well-known two-state expression for the first hyperpolarizability [37] (Eq. (23)). 

The first hyperpolarizabilities (/3) of the donor-acceptor (D-A) systems containing several 1,3-heteroatom 7t-bridging units (oxazole, imidazole, and thiazole) have been studied by the ab initio method (HF/6-31G) <2004JMT(677)173>. The static first and second hyperpolarizabilities of amino- and nitro-substituted chromophores containing thiazole rings have been calculated by the ab initio TDHF method. The computed nonlinear polarizabilities correlate well with frontier orbital energies and hardness parameter (77) <2003CPL(376)116>. 

The coeflScients a, P, and y are the second, third, and fourth rank tensors and are referred to as the polarizability, first hyperpolarizability, and second hyperpolarizability, respectively. The hyperpolarizability terms are responsible for the nonlinear response of the molecule to impinging radiation. These coefiBcients are not very large, and the associated nonlinear optical effects are usually studied by taking advantage of the high optical field obtainable with laser beams. 

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 ... 

Similar conclusions concerning the relation between the relative molecular orientation and the first hyperpolarizability have been drawn by Hamada [13] in the case of the MNA dimer as well as by Okuno et al. [53] in a study on linear and parallel dimers of 4-dimethylamino-4 -carboxyazobenzene and 4-dimethyl-amino-2 -nitro-4 -carboxyazobenzene. The impetus was the desire for an explanation for the large second-order nonlinear optical responses of cone-shaped azobenzene dendrimers. Okono et al. also assessed the adequacy of three classical electrostatic models (Section IV). 

Crystal violet, a trigonal conjugated cationic dye with electronic CT from peripheral dimethylamino donor groups to an electron deficient sp hybridized central carbon atom. A resonantly enhanced (3 value of 580 x 10 ° esu has been reported at 1.064 nm, in acetone solution = 590 nm) by Zyss et al. [16] The 1st hyperpolarizability, p, of crystal violet dye was measured at 1450 and 1500 nm by Rao et al. [91]. The resonance-free P value, p(°) for this octupole is comparable with that of the dipolar dye Disperse Red 1 but with the nonlinearity-transparency trade-off worse for the octupole. Symmetric cyanine dyes of the kind Me2N+ CH-(CH CH)n-NMe2 normally exhibit no first hyperpolarizabilities but have relatively long absorption... 

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