Third-harmonic generation electric field induced second

Table 1 Coefficients for 7[ (a ) for third harmonic generation (THG), degenerate four wave mixing (DFWM), electric field induced second harmonic generation (ESHG), and Kerr effect in methane at the experimental geometry rcH = 2.052 a.u. A CCSD wavefunction and the t-aug-cc-pVDZ basis were used. (Results given in atomic units, the number in parentheses indicate powers of ten.)...

Third-Order NLO Techniques. There is a wider range of third-order techniques commonly used to characterize materials, including electric field induced second harmonic generation (EFISH) (15, 16), third harmonic generation (THG) (17) and degenerate four wave mixing (DFWM) (18). EFISH and DFWM will be discussed briefly then... 

Both theoretical analysis and dipole moment measurements indicated that sulfonyl-substituted compounds may have ft coefficients similar in magnitude to their nitro analogues. Therefore, we have measured p for several sulfonyl- and nitro-substituted compounds using electric-field-induced second-harmonic generation method (EFISH) (11,25). In this experiment, one measures an effective third-order nonlinearity rEFISH for a solution containing the compound of interest, given by... 

Poly(3-alkyl-a-thiophene) systems show significant third-order nonlinear susceptibilities ( ) Though, oligothiophenes have been studied for their third-order susceptibilities, accurate third-order optical nonlinearity data obtained by degenerate four-wave mixing or electric-field-induced second harmonic generation (EFISH) are difficult to attain reliably on samples with poor solubility characteristics (92MM1901). 

From TEEs unsubstituted, mono-, di-, tri-, and tetrasubstituted compounds were synthesized and investigated with third-harmonic generation [56] as well as electric field induced second-harmonic generation [67]. We here concentrate on the discussion of monomers of the most intriguing tetrasubstituted molecules and the symmetry dependence of their third-order nonlinearities [72]. Taking two donors and two acceptors three possible geometries can be realized (Fig. 23). The DDAA(cross)-TEE molecule has a mirror plane perpendicular to the y-axis, DDAA(ds)-TEE a mirror plane perpendicular to the x-axis, and DDAA(fra s)-TEE a two-fold rotation axis along z. 

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. 

Here Xo (2w), x (wiiw2) and Xo (O) are the non-resonant values of the hyperpolarisabilities. Thus second harmonic generation is resonantly enhanced at both the fundamental and the harmonic of the optical transition, sum and difference frequency generation at the fundamentals and the sum and difference frequencies, and the rarely observed optical rectification only at the fundamental frequency. The term 3 in the expansion gives rise to effects such as third harmonic generation, x(3) -3oj oj, oj,u>), electric field induced second harmonic generation, x(3) (- 2w 0,w, oj), the optical Kerr effect, x(3) (-oj oj, oj, -cj), etc. that will display resonances at oj, 2oj and 3u>. 

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 ... 

Electric field-induced second harmonic generation, f Third-harmonic generation. 

In order to select a particular experimental technique to measure x , it is very important to keep in mind which parameter of the third-order nonlinear response has to be characterized. For example, if one wants to determine the time-response due to molecular reorientation, one cannot choose Third-Harmonic Generation or Electric-Field-Induced Second-Harmonic Generation, since none of these techniques provide time-response information. Depending on the parameter of interest, a specific technique must be chosen. The following physical mechanisms can contribute to the third-order nonlinear response [54] ... 

Puccetti, G. Electric field induced second harmonic generation/third harmonic generation measurements on molecules with extended charge transfer Absorption domain and strong resonance effects, J. Chem. Phys. 102, 6463-6475 (1995)... 

Most of the studies on push-pull phthalocyanines have been carried out by means of Electric Field Induced Second Harmonic (EFISH) Generation experiments in solution. Since only one experimental condition is favorable for EFISH, namely, parallel polarizations for all optical and static fields, these experiments lead to only one observable the vector component along the charge transfer axis assuming that the dipole moment vector and the vector part of the third-rank tensor along tlie molecular z-axis are collinear). 

Under the influence of an optical pump, the molecular angular distribution described by Equation 12.4 can be considerably modified. In turn, this results in modification of the X/ kl tensor components. Further, we discuss the influence of a polarized pump beam on third-order nonlinear phenomena such as third harmonic generation (TFIG) [(described by XyfCL (-3a ,o ,w, u) coefficient], electric field induced second harmonic generation (EFISH) i 2co, (o, (o, 0)] and degenerate four-wave mixing (DFWM) X/yx/ -... 

The tensors and 7 constitute the molecular origin of the second-and third-order nonlinear optical phenomena such as electro-optic Pock-els effect (EOPE), optical rectification (OR), third harmonic generation (THG), electric field induced second harmonic generation (EFI-SHG), intensity dependent refractive index (IDRI), optical Kerr effect (OKE), electric field induced optical rectification (EFI-OR). To save space we do not indicate the full expressions for and 7 related to the different second and third order processes but we introduce the notations —(Ajy,ui,cj2) and 7(—a , o i,W2,W3), where the frequency relations to be used for the various non-linear optical processes which can be obtained in the case of both static and oscillating monochromatic fields are reported in Table 1.7. 

Furthermore, they examined the performance of different density functionals, including a local-density approximation and a generalized-gradient approximation as well as the functional of van Leeuwen and Baerends that has been constructed to have the correct asymptotic behaviour. Moreover, they considered different frequency-dependent processes, including third-harmonic generation [THG, corresponding to y( 3electric-field-induced second harmonic generation (EFISH, y( 2electro-optic Kerr effect [EOKO, y(—ft> optical rectification [OR, /S(0 [Pg.161]

Combination with Static Fieids. A common technique, useful for optoelectronic devices, is to combine a monochromatic optical field with a DC or quasistatic field. This combination can lead to refractive index and absorption changes (linear or quadratic electrooptic effects and electroabsorption), or to electric-field induced second-harmonic generation (EFISH or DC-SHG, 2 > = > - - third-order process. In EFISH, the DC field orients the molecular dipole moments to enable or enhance the second-harmonic response of the material to the applied laser frequency. The combination of a DC field component with a single optical field is referred to as the linear electrooptic (Pockels) effect co = co + 0), or the quadratic electrooptic (Kerr) effect ( > = > - - 0 -I- 0). These electrooptic effects are discussed extensively in the article Electrooptical Applications (qv). EFISH is... 

The static and dynamic linear responses, a(0 0) and a( co co), correspond to the so-called static and dynamic polarizabilities, respectively. At second order in the fields, the responses are named first hyperpolarizabilities whereas second hyperpolarizabilities correspond to the third-order responses. Different phenomena can be distinguished as a function of the combination of optical frequencies. So, p(0 0,0), p(—co co,0), p(0 o), — ea), and p(— 2co co,co) are associated with the static, dc-Pockels (dc-P), optical rectification (OR), and second harmonic generation (SHG) processes whereas y(0 0,0,0), y(- ( ( ,0,0), y( 2co co,( ,0), y( co co, — ca, ), and y(— 3 , , ) describe the static, dc-Kerr, electric-field-induced second harmonic generation (EFISHG), degenerate four-wave mixing (DFWM),... 

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. 

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