Electrical susceptibility third order

For each EA spectrum, the transmission T was measured with the mechanical chopper in place and the electric field off. The differential transmission AT was subsequently measured without the chopper, with the electric field on, and with the lock-in amplifier set to detect signals at twice the electric-field modulation frequency. The 2/ dependency of the EA signal is due to the quadratic nature of EA in materials with definite parity. AT was then normalized to AT/T, which was free of the spectral response function. To a good approximation [18], the EA signal is related to the imaginary part of the optical third-order susceptibility ... 

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

The third term describes the polarization set up by ultrafast drift-diffusion currents, which can excite coherent phonons via TDFS (or via the buildup of electric Dember fields [9,10]). The first two terms represent the second- and the third-order nonlinear susceptibilities, respectively [31]. The fourth term describes the polarization associated with coherent electronic wavefunctions, which becomes important in semiconductor heterostructures. 

In the limit of the oriented gas model with a one-dimensional dipolar molecule and a two state model for the polarizability (30). the second order susceptibility X33(2) of a polymer film poled with field E is given by Equation 4 where N/V is the number density of dye molecules, the fs are the appropriate local field factors, i is the dipole moment, p is the molecular second order hyperpolarizability, and L3 is the third-order Langevin function describing the electric field induced polar order at poling temperature Tp - Tg. 

The interest in semiconductor QD s as NLO materials has resulted from the recent theoretical predictions of strong optical nonlinearities for materials having three dimensional quantum confinement (QC) of electrons (e) and holes (h) (2,29,20). QC whether in one, two or three dimensions increases the stability of the exciton compared to the bulk semiconductor and as a result, the exciton resonances remain well resolved at room temperature. The physics framework in which the optical nonlinearities of QD s are couched involves the third order term of the electrical susceptibility (called X )) for semiconductor nanocrystallites (these particles will be referred to as nanocrystallites because of the perfect uniformity in size and shape that distinguishes them from other clusters where these characteriestics may vary, but these crystallites are definitely of molecular size and character and a cluster description is the most appropriate) exhibiting QC in all three dimensions. (Second order nonlinearites are not considered here since they are generally small in the systems under consideration.)... 

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). 

In conclusion the contribution to the dielectric response given by the third order susceptibility has different sources with opposite signs. Molecular simulations on ions in solution show that both dielectric saturation and electrostriction effects are presumably present and that for ions with a high charge density electric saturation predominates. This suggestion is in agreement with the general consensus that dielectric saturation is the first element to consider in the description of nonlinearities. 

The external electric field is assumed to be parallel to the x-axis. In the case of an isotropic solution only the element Axl4x( 3co,co,co,co) of the third-order susceptibility creates a polarization at 3 , which is parallel to the incident electric field Ea ... 

The dimensions of the first-, second-, and third-order susceptibilities in both systems are simply derived from the polarizability power series equation.24 In the Gaussian system, polarization P and electric field strength E have equivalent dimensions [units statV cm 1 = statC cm 2 = (erg cm 3)112] and are related by... 

Here Pind is the induced dipole moment per unit volume, and X X and X are the first-, second-, and third-order electric susceptibilities of the sample, where the order refers to the power of electric field (not of X). Equation (1) represents the macroscopic (bulk) form for the polarization in terms of single molecule properties, the induced dipole moment per molecule is written as... 

Equations (18)-(21) were given for the case of real susceptibilities. However, they have to be treated as complex quantities if the frequency is close to or within the region of an optical transition in the medium. An example in the domain of linear optics was given in (12) where the imaginary part of the first-order susceptibility, ft) w), was related to the absorption coefficient, of the medium. An example from non-linear optics is the technique of electro-optical absorption measurements (EOAM, p. 167) where the UV-visible absorption is studied under the influence of a static electric field. In EOAM, the imaginary part of the third-order susceptibility, w,0,0), is... 

The chemical structure of the polyimide polymers (named PI-1 and PI-2) studied by Sekkat et al. is shown in Figure 12.12. They prepared the polymer samples by spin-casting onto glass substrates. PTl was cast from a cyclohexanone solution and PI-2 from 1,1,2,2- tetrachloroethane. The Tg values of PI-1 and PI-2 were determined to be 350°C and 252 C, respectively, by scanning calorimetry method. The thicknesses of the PI-1 and PI-2 films were, respectively, approximately 0.72 im and 0.14 im, and their respective optical densities were approximately 0.79 and 0.3 at 543.5 nm. Details of the preparation and characterization of the samples can be found in References 3 and 20. In their EFISH experiment, a typical corona poling technique was used to pole the samples, with a dc electric field about 2-3 MV/cm across a 1-2 lm thick polymer film. They used the SHG output from the EFISH experiment to in situ monitor the photochemical change in the third-order susceptibility of the PI-1 and PI-2 polymers. 

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 ... 

In a subsequent paper, Munn [98] showed that the frequency-dependent local-field tensors accounted for the shift of the poles of the linear and nonlinear susceptibilities from the isolated molecular excitation frequencies to the exciton frequencies. The treatment also described the Davydov splitting of the exciton frequencies for situations where there is more than one molecule per unit cell as weU as the band character or wave-vector dependence of these collective excitations. In particular, the direct and cascading contributions to x contained terms with poles at the molecular excitation energies, but they canceled exactly. Combining both terms is therefore a prerequisite to obtaining the correct pole structure of the macroscopic third-order susceptibility. Munn also demonstrated that this local field approach can be combined with the properties of the effective or dressed molecule and can be extended to electric quadrupole and magnetic dipole nonlinear responses [96]. 

The conceptually simplest NLO property is the electric first dipole hyperpolarizability 13. Nevertheless, it is a challenging property from both the theoretical and experimental side, which is related to the fact that, as third-rank tensor, it is a purely anisotropic property. Experimentally this means that (3 in isotropic media (gas or liquid phase) cannot be measured directly as such, but only extracted from the temperature dependence of the third-order susceptibilities In calculations anisotropic properties are often subject to subtle cancellations between different contributions and accurate final results are only obtained with a carefully balanced treatment of all important contributions. 

Hameka et al., has calculated polarizabilities up to third order for several organic systems [40, 76, 77, 78, 121, 122, 123, 124]. In his pioneering papers, the nonlinear polarizability was calculated by using sum over orbitals within the Hiickel approximation. This approach was later improved by using extended Hiickel method (EHM) [123, 124]. The quality of EHM third-order electric susceptibility was tested by... 

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