Non-linear susceptibility

With a non-linear susceptibility, the polarization is composed of non-linear terms such as eox E, eoX E as well as the linear term cqx E. It is clear that these elements in the polarization maybe oscillating at 2co and 3co respectively, giving rise to harmonics of the original frequency co. Because the higher order terms in the susceptibility are small compared with the first term, non-linear optical effects were not observed until after the invention of the laser in 1960. 

Non-linear second-order optical properties such as second harmonic generation (SHG) and the linear electrooptic effect are due to the non-linear susceptibility in the relation between the polarization and the applied electric field. SHG involves the... 

A colloid chemical approach to CdS/HgS/CdS spherical quantum wells was described [79]. Size-dependent third-order non-linear susceptibilities of CdS clusters were investigated [80]. Reviews appeared on size-quantized nanocrystalline semiconductor films [81] and on the quantum size effects and electronic properties of semiconductor microcrystallites [82]. 

In addition to photoconductivity, polysilanes have been found to exhibit marked nonlinear optical properties,95-97 suggesting that they may eventually be useful in laser and other optical technology. The third-order non-linear susceptibility, X3, is a measure of the strength of this effect. The non-linear properties of polysilanes, like the absorption spectra, seem to be dependent on chain conformation and are enhanced for polymers having an extended, near anti conformation (Table 5.5). The value of 11 x 10 12 esu observed for (n-Hex2Si) below its transition temperature is the largest ever observed for a polymer which is transparent in the visible region. 

Table 5.5 Third-Order Non-linear Susceptibilities for Polysilanes and Some Related Polymers...

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. 

As mentioned above, the intensity of the VSFS signal is dependent on the nonlinear polarization induced in the medium. The polarization that gives rise to sum-frequency generation, P f, is in mm dependent on the surface non-linear susceptibility... 

Since the non-linear susceptibility is generally complex, each resonant term in the summation is associated with a relative phase, y , which describes the interference between overlapping vibrational modes. The resonant macroscopic susceptibility associated with a particular vibrational mode v, Xr, is related to the microscopic susceptibility also called the molecular hyperpolarizability, fiy, in the following way... 

Equation (6) shows that the sum-frequency intensity is dependent on the second-order polarization However, that polarization is a vector quantity P f. Within the electric dipole approximation the local fields E and re coupled by the second-order non-linear susceptibility, [16], inducing the following non-linear polarization at... 

Figure 2.5 shows a few of the Lorentzian line shapes in the Gaussian distribution of the real part (top) and imaginary part (bottom) of the resonant non-linear susceptibility... 

From the results of MD simulations, the non-linear susceptibility, Xs p. can be calculated for each interfacial species of water molecule as a function of distance along the simulation cell (see Figure 2.13) to determine how each species contributes to the SF signal and to the depdi that SF intensity is generated. Although this representation is only a first approximation of the SF probe depth, it is the most relevant measure of interfacial thickness for SF experiments because it indicates the depth to which water molecules are affected by the presence of the interface. To make a direct comparison to experiment, the contribution from each OH oscillator to the total xisp is multiplied by a factor, linear in frequency, that accounts for the IR vibrational response dependency on frequency. For example, an OH vibration at 3400 cm is approximately 12 times stronger in SF intensity than the free OH. 

Non-linear optics non-linear susceptibilities ( " ) 128 Molecular polarizabilities 133... 

In this section, we investigate the relations between the macroscopic susceptibilities and the molecular polarizabilities. Consistent microscopic interpretations of many of the non-linear susceptibilities introduced in Section 2 will be given. Molar polarizabilities will be defined in analogy to the partial molar quantities (PMQ) known from chemical thermodynamics of multicomponent systems. The molar polarizabilities can be used as a consistent and general concept to describe virtually all linear and non-linear optical experiments on molecular media. First, these quantities will be explicitly derived for a number of NLO susceptibilities. Physical effects arising from will then be discussed very briefly, followed by a survey of experimental methods to determine second-order polarizabilities. 

During the measurement, phase conjugate waves (Figure 2) of fairly high intensities were observed in an ocilloscope. Unusually high values of optical 3rd order non-linear susceptibility were observed for 3a and The value for 3a amounts to more than thousand times higher than that of all-trans polyacetylene. 

The second-order non-linear susceptibility x is a third-rank tensor, which, in Cartesian coordinates, is defined by a set of 27 elements with i.J and k rep-... 

V.P. Sokhan, D.J. Tildesley, The Ftee Surface of Water Molecular Orientation, Surface Potential and Non-linear Susceptibility (Molecular Physics Lecture). MoL Phys. 92 (1997) 625. 

The susceptibility described above is also called the linear susceptibility because, in a Taylor expansion of M(H) about the applied field value, it is the coefficient of the term that is linear in H. In this way, higher order susceptibilities can be defined and measured. The higher order (non-linear) susceptibilities can provide information that is not contained in the linear term alone. This information has turned out to be vital in systems of interacting clusters or particles, such as ensembles of magnetic nanoparticles, canonical spin glasses and cluster spin glass systems (see below). 

Many substituted benzene derivatives show large microscopic second-order non-linear susceptibilities, which probably arise from highly asymmetric charge distribution83. Among these, nitroanilines deserve particular attention84, in view of the considerable number of... 

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