Nonlinear susceptibilities first order

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... 

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. 

Many of the different susceptibilities in Equations (2.165)-(2.167) correspond to important experiments in linear and nonlinear optics. x<(>> describes a possible zero-order (permanent) polarization of the medium j(1)(0 0) is the first-order static susceptibility which is related to the permittivity at zero frequency, e(0), while ft> o>) is the linear optical susceptibility related to the refractive index n" at frequency to. Turning to nonlinear effects, the Pockels susceptibility j(2)(- to, 0) and the Kerr susceptibility X(3 —to to, 0,0) describe the change of the refractive index induced by an externally applied static field. The susceptibility j(2)(—2to to, to) describes frequency doubling usually called second harmonic generation (SHG) and j(3)(-2 to, to, 0) describes the influence of an external field on the SHG process which is of great importance for the characterization of second-order NLO properties in solution in electric field second harmonic generation (EFISHG). 

Since the first nonlinear susceptibility is a third-rank tensor, it is only non-zero in non-centrosymmetric media. To break the centrosymmetry of the macroscopic media, poling techniques using optical and electric fields have been developed, or use was made of the inherent polar ordering in Langmuir-Blodgett films and crystals with non-centrosymmetric point groups. 

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. 

In the first part, emphasis will be put on the linear optical properties of dielectric media doped with noble metal nanoparticles. Indeed, the study of the linear response is definitely needed to further explore the nonlinear one. We will then introduce the fundamentals of the theoretical tools required to understand why and how people inquire into the third-order nonlinear properties of nanocomposite materials. In the second part, experimental results will be presented by first examining the different nonlinear optical phenomena which have been observed in these media. We will then focus on the nanoparticle intrinsic nonlinear susceptibility before analysing the influence of the main morphological factors on the nonlinear optical response. The dependence of the latter on laser characteristics will finally be investigated, as well as the crucial role played by different thermal effects. 

The polymers having delocalized r-electron in the main chain have been expected to possess extremely large third-order optical susceptibility.However, such an extended jr-electron conjugation generally rendered the polymers insoluble and infusible as well, which has seriously limited the fabrication of practical NLO devices. Recently, it was reported that the third-order nonlinear optical properties of poly(l,6-heptadiyne)s which were environmentally stable, soluble, and processable. The third-order optical nonlinearities of poly(l,6-heptadiyne)s bearing NLO active chomophores were evaluated for the first time. The third-order nonlinear susceptibility... 

Let us first give a sketch of the underlying theory. We consider an interface formed by two bulk media with centrosymmetry. Because of the broken symmetry at the interface, the second-order nonlinearity of the interface layer becomes nonvanishing (under the electric-dipole approximation). We can use a surface nonlinear susceptibility tensor to... 

The coefficients in the various terms in Eqs. (2a) and (2b) are termed the nth-order susceptibilities. The first-order susceptibilities describe the linear optical effects, while the remaining terms describe the nth order nonlinear optical effects. The coefficients are the nth-order electric dipole susceptibilities, the coefficients G " are the nth-order quadrupole susceptibilities, and so on. Similar terminology is used for the various magnetic susceptibilities. For most nonlinear optical interactions, the electric dipole susceptibilities are the dominant terms because the wavelength of the radiation is usually much longer than the scattering centers. These will be the ones considered primarily from now on. 

Linear optical phenomena involve the first-order susceptibility x and in that case only the first term in the equation above is important. Higher order susceptibilitites are involved in nonlinear optical phenomena. Susceptibilities are a fimction of wavelength. 

The coefficients x are applied for the description of the macroscopic susceptibilities instead of the molecular coefficients a, p, and y. The first-order susceptibility x describes linear processes such as refraction and absorption. Nonlinearities are characterized by the susceptibilities of higher order (x , x - ) The even- and odd-order terms lead to different nonlinear responses, is contributed to the polarization only in noncentrosymmetric media, and x contributing in any media irrespective of the symmetry (Prasad and Wilhams, 1991). 

Owing to the coherence, we need to consider the macroscopic evolution of the field in a medium that shows a macroscopic polarization induced by the field-matter interaction. This will be done in three steps. First, the polarization induced by an arbitrary field will be calculated and expanded in power series in the field, the coefficients of the expansion being the material susceptibilities (frequency domain) or response function (time domain) of wth-order. Nonlinear Raman effects appear at third order in this expansion. Second, the perturbation theory derivation of the third-order nonlinear susceptibility in terms of molecular eigenstates and transition moments will be outlined, leading to a connection with the spontaneous Raman scattering tensor components. Last, the interaction of the initial field distribution with the created polarization will be evaluated and the signal expression obtained for the relevant techniques of Table 1. 

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