Second-order hyperpolarizability

Keywords First-order hyperpolarizability second-order hyperpolarizability sum-over-states method ... 

A crude experimental estimate for the A s coefficient is obtained from Sheltons fit of ESHG measurements for the hyperpolarizability ratio 7 /7i to the expression 3(1 +A a 22)- Using the dispersion expansions (79) and (89), we obtain for the ratio 7 /7x up to second order in the frequencies the expansion... 

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]. 

This calculation has shown the importance of the basis set and in particular the polarization functions necessary in such computations. We have studied this problem through the calculation of the static polarizability and even hyperpolarizability. The very good results of the hyperpolarizabilities obtained for various systems give proof of the ability of our approach based on suitable polarization functions derived from an hydrogenic model. Field—induced polarization functions have been constructed from the first- and second-order perturbed hydrogenic wavefunctions in which the exponent is determined by optimization with the maximum polarizability criterion. We have demonstrated the necessity of describing the wavefunction the best we can, so that the polarization functions participate solely in the calculation of polarizabilities or hyperpolarizabilities. 

A computer program for the theoretical determination of electric polarizabilities and hyperpolarizabilitieshas been implemented at the ab initio level using a computational scheme based on CHF perturbation theory [7-11]. Zero-order SCF, and first-and second-order CHF equations are solved to obtain the corresponding perturbed wavefunctions and density matrices, exploiting the entire molecular symmetry to reduce the number of matrix element which are to be stored in, and processed by, computer. Then a /j, and iap-iS tensors are evaluated. This method has been applied to evaluate the second hyperpolarizability of benzene using extended basis sets of Gaussian functions, see Sec. VI. 

Second Order Static Hyperpolarizabilities of Insaturated Polymers... 

In a previous work [1,2], we were interested in the calculation of second order hyperpolarizabilities of eonjugated systems including substituted benzenes, pyridine N-oxydes and vinyl oligomers, in relation with non linear optical activity [3]. We showed that MNDO ealeulations were in good agreement with SCF ab initio results obtained using a double zeta basis set plus polarization and diffuse orbitals. 

Trans-polyenes H-(-HC=CH-),, -H, trans-polyenynes H-(HC=CH-C=C) -H, cumulenes H2C=(C=C) =CH2 and polyynes H-(C=C) -H have been studied (M=N-1). For eentrosymmetrie molecules, the first order hyperpolarizability p is equal to zero so that non linear effects are of second order nature. Furthermore, (the x axis goes through the middle of the C-C bonds of the polyenes, or is the intemuclear axis in the case of linear molecules) is the most important component of the second order y hyperpolarizability tensor, the other components being negligible. Both y and the mean hyperpolarizability... 

These monodimensional compounds, rich in it electrons, have been the object of several experimental[35] and theoretical work[20,35,36]. Perry et al.[35], using a powder SHG technique, have studied diaryl polyynes and have shown that some of them exhibit second order hyperpolarizabilities of very high magnitude. On another hand, Jameson and Fowler[36] carried out ab initio calculations in order to study basis sets effects on the electrical properties of acetylene and diacetylene. Furthermore, Chopra et al [20], then Maroulis and Thakkar [37] have been interested in the influence of the lengthening of the... 

SECOND ORDER STATIC HYPERPOLARIZABILITIES OF INSATURATED POLYMERS... 

Second order static hyperpolarizabilities of insaturated polymers... 

The large molecular hyperpolarizability of the merocyanine chromophore (4,5) and the highly polar environment of the quasicrystals has prompted studies of the second order nonlinear optical properties of these materials (6). 

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). 

For obtaining the information on fabrication of noncentrosymmetric LB films with highly efficient second-order optical nonlinearity, six azobenzene-linked amphiphiles were synthesized as a model compound, and their molecular hyperpolarizabilities (3, monolayer-formation at the air-water interface, and molecular orientation and second-order susceptibilities of the azobenzene-linked amphiphiles LB films were evaluated. The molecular structures of the azobenzene-linked amphiphiles are shown in Fig.2. 

Stark effect measurements for determination of molecular orientation and second-order molecular hyperpolarizability... 

Evaluation of second-order molecular hyperpolarizability using the quadratic Stark effect... 

On the two level model [3], second-order molecular hyperpolarizability p is given by... 

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