Bulk second-order susceptibility

The odd order susceptibilities are nonzero in all materials. However, owing to the fact that x is a third rank tensor, the second order susceptibility is nonzero only in noncentrosym-metric materials, that is, materials possessing no center of symmetry. The focus of this paper is on second order processes, and the relationships between the bulk susceptibility, second harmonic generation, and the linear electro-optic effect. For second harmonic generation, Xijl is symmetric in ij, leading to the relationship between the second harmonic coefficient dijk and the bulk second order susceptibility x 2)[i2l... 

Materials that have a nonzero second-order susceptibility will produce light at twice the incident frequency. The magnitude of this effect is small, and has been a practical consideration only since the advent of lasers. If the symmetry of a crystal or other medium is such that it has a center of inversion, no SHG effect will be observed. However, surfaces by their very nature break this inversion symmetry. Hence, an SHG signal may arise at the electrode-solution interface even though both bulk phases may be considered centrosymmetric [66], The magnitude of the SHG signal is sensitive to surface conditions (e.g., electrode potential, ionic or molecular adsorption, etc.). Surface spectroscopy is also feasible since the SHG signal will be enhanced if either the incident frequency (to) or SHG (2co) corresponds to an electronic absorption of a surface species [66]. 

The requirement of non-centrosymmetry is not restricted to the molecular level, but also applies to the macroscopic nonlinear susceptibility, which means that the NLO molecules have to be organized in a non-centrosymmetric alignment. The first measurements of the macroscopic second-order susceptibility, have been performed on crystals without centrosymmetry [5]. However, many organic molecules crystallize in a centrosymmetric way. Other condensed oriented phases such as Langmuir-Blodgett (LB) films and poled polymers therefore seem to be the most promising bulk systems for NLO applications. 

From Equation (3), it is clear that even for molecular systems with nonzero/3, the bulk second-order nonlinearity, determined by the second-order nonlinear susceptibility will be absent if the bulk structure is centrosymmetric or... 

In the case of bulk materials or films the second-order susceptibility values, can be obtained by means of the investigation of the SHG [1-3]. The Kurtz-Perry technique [33] is often used to compare the intensity of the SHG of a powder sample with that of a reference sample of known such as quartz or urea. Although this technique is limited (the magnitude of the response is also dependent on particle size), it is a simple and rapid method for screening a large number of powder materials. 

One important use of SFG vibrational spectroscopy is the orientational analysis of ionic liquids at gas-liquid interfaces. For example, the study of the structural orientation ofionic liquids using common cation types, that is, [BMIM], combined with different anions, gives information on the effects of both cation and anion types [3, 22, 26-28]. Additional surface analytical work includes SFG studies under vacuum conditions for probing the second-order susceptibility tensor that depends on the polar orientation of the molecule and can be correlated to the measured SFG signal intensities. Supporting information is frequently obtained by complementary bulk spectroscopic techniques, such as Raman and Fourier transform infrared (FTIR) analysis, for the analysis of the pure ionic liquids. 

In centrosymmetric media, every element of the second-order susceptibility tensor is zero. To impart bulk... 

As in the case of molecular orientation at the interface of neat liquids, solute molecular orientation can provide insight into the local intermolecular interactions at the interface, which, in turn, is useful for interpreting dynamics, spectroscopy, and reactivity. The simple picture that the hydrophilic part of an asymmetric solute molecule tends to point toward the bulk aqueous phase, while the hydrophobic part points toward the opposite direction, has been confirmed in both simulations and experiments. Polarization-dependent SHG and SFG nonlinear spectroscopy can be used to determine relative as well as absolute orientations of solute molecules with significant nonlinear hyperpolarizability. The technique is based on the fact that the SFG and the SHG signals coming from an interface depend on the polarization of the two input and one output lasers. Because an interface with a cylindrical symmetry has only four elements of the 27-element second-order susceptibility tensor being nonzero, these elements (which depend on the molecular orientation) can be measured. This enables the determination of different moments of the orientational distribution ... 

Given the interest and importance of chiral molecules, there has been considerable activity in investigating die corresponding chiral surfaces [, and 70]. From the point of view of perfomiing surface and interface spectroscopy with nonlinear optics, we must first examhie the nonlinear response of tlie bulk liquid. Clearly, a chiral liquid lacks inversion synnnetry. As such, it may be expected to have a strong (dipole-allowed) second-order nonlinear response. This is indeed true in the general case of SFG [71]. For SHG, however, the pemiutation synnnetry for the last two indices of the nonlinear susceptibility tensor combined with the... 

Second order NLO properties including SHG arise from the second order NLO susceptibility x tensor in the relationship for the bulk polarization, P, such that (2-3)... 

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.)... 

The discontinuity of the interface leads to two contributions to the second order nonlinear polarizability, the electric dipole effect due to the structural discontinuity and the quadrupole type contribution arising from the large electric field gradient at the surface. Under the electric dipole approximation, the nonlinear susceptibility of the centrosymmetric bulk medium 2 is zero. If the higher order magnetic dipole... 

The fact that the susceptibility is proportional to the second order of the number of unpaired electrons explains the steep slope of the NO curves in Figure 8. This shows again that the surface has quite a different electron structure from that of the bulk. The NO is sorbed only on the surface, since there is no evidence that it is able to enter the crystal lattice of palladium. As we have indicated, the... 

Effective second harmonic generation is attained in materials which have both high second-order molecular hyperpolarizability, p, and high second-order bulk susceptability, x - Molecular polarization is described by the field dependent molecular dipole moment, p (eq 1), expanded as a function of the applied field strength, E, which may be electric or optical (that is, electromagnetic) in nature. The field strength E is a vector, and Pq is the intrinsic dipole... 

Since the electro-optic coefficient rij is defined by the electric field dependence of the optical indicatrix, is related to the second order bulk susceptibility through i... 

The SHG intensity from interfaces is determined by the second-order nonlinear susceptibility and the Fresnel coefficients. The SHG spectra of the probe pulses change depending on the transient electronic population and the orientation of the chromophores through these physical quantities. Hohlfeld and coworkers have studied hot electron dynamics in thin metal films by this technique [21]. From the transient response of the SHG intensity, electronic temperature decay due to the electron-phonon coupling in the metal substrate is extracted. Eisenthal and coworkers have studied ultrafast excited state dynamics of dye molecules at liquid interfaces [22]. Particularly, the isomerization dynamics of an organic dye at the interfaces was found to become significantly slower than in the bulk. 

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