Susceptibilities second-order

Electrooptic tensor General optical properties Refractive index Nonlinear dielectric susceptibility Second order Third order... 

TABLE 3 Third-Order Nonlinear Susceptibility Second-Order... 

Following the derivation of the linear susceptibility, we may now readily deduce the second-order... 

Figure Bl.5.3 Magnitude of the second-order nonlinear susceptibility x versus frequency co, obtained from the anliannonic oscillator model, in the vicinity of the single- and two-photon resonances at frequencies cOq and coq 2> respectively.

The second-order nonlinear susceptibility tensor ( 3> 2, fOj) introduced earlier will, in general, consist of 27 distinct elements, each displaying its own dependence on the frequencies oip cci2 and = oi 012). There are, however, constraints associated with spatial and time-reversal symmetry that may reduce the complexity of for a given material [32, 33 and Ml- Flere we examine the role of spatial synnnetry. 

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 contribution of the electron to the diamagnetic susceptibility of the system can be calculated by the methods of quantum-mechanical perturbation theory, a second-order perturbation treatment being needed for the term in 3C and a first-order treatment for that in 3C". In case that the potential function in 3C° is cylindrical symmetrical about the s axis, the effect of 3C vanishes, and the contribution of the electron to the susceptibility (per mole) is given... 

The reaction that normally occurs on treatment of a ketoxime with a Lewis or proton acid is the Beckmann rearrangement (18-17) fragmentations are considered side reactions, often called abnormal or second-order Beckmann rearrangements. Obviously, the substrates mentioned are much more susceptible to fragmentation than are ordinary ketoximes, since in each case an unshared pair is available to assist in removal of the group cleaving from the carbon. However, fragmentation is a side reaction even with ordinary ketoximes and, in cases where a particularly stable carbocation can be cleaved, may be the main reaction. ... 

G2, to G3, and to G4, the effective enhancement was 10%, 36%, and 35% larger than the value estimated by the simple addition of monomeric values. The enhancement included the local field effect due to the screening electric field generated by neighboring molecules. Assuming the chromophore-solvent effect on the second-order susceptibility is independent of the number of chro-mophore units in the dendrimers, p enhancement can be attributed to the inter-molecular dipole-dipole interaction of the chromophore units. Hence, such an intermolecular coupling for the p enhancement should be more effective with the dendrimers composed of the NLO chromophore, whose dipole moment and the charge transfer are unidirectional parallel to the molecular axis. 

Amidation is particularly well adapted to use as a polymer-forming condensation reaction. The reaction is rapid above 180° to 200°C, it is remarkably free from side reactions, no catalysts are required (indeed, none are known), and the process is of the second order so that the molecular weight increases directly as the time of reaction. Molecular weights of 20,000 to 30,000 are attainable with no great difficulty under favorable conditions. This is not true of particular polyamide reactants susceptible to side reactions, as, for example, in the reaction of a diamine with glutaric acid wherein the inherent instability of the glutaric amide unit leads to decomposition. 

If we introduce A = N/s ( a ), the description of macroscopic resonant second-order susceptibility,, is given by... 

Sum-frequency (SF) spectroscopy [1] has been used to achive vertical resolutions much better than the wavelength. Sum-frequency light is generated at an interface irradiated with infrared (IR) and visible light. The probability of sum-frequency generation is governed by a second-order susceptibility to be zero in any medium... 

For adsorbates on a metal surface, an SFG spectmm is a combination of resonant molecular transitions plus a nonresonant background from the metal. (There may also be a contribution from the water-CaF2 interface that can be factored out by following electrode potential effects see below.) The SFG signal intensities are proportional to the square of the second-order nonlinear susceptibility [Shen, 1984] ... 

The SHG signal intensity, 1(2 ), arising at the liquid-liquid interface is known to be proportional to the square of the second-order nonlinear electric susceptibility, c , at the surface [18,28,29],... 

A hysteresis cycle in the molar susceptibility measurements has been observed for [Ni2(Medpt)2(N3)2(/r-N3)2] (883). This has been ascribed to a phase transition caused by an asymmetrization process of the rhombus-like centrosymmetric [Ni-(N3)2-Ni] core that occurs with falling temperature. The asymmetrization transition can be explained in terms of a second-order Jahn-Teller distortion, taking into account the local symmetry of the dinuclear [Ni-(N3)2-Ni] entity (D2h, rhombic symmetry) before the arrangement.2128... 

For the latter two ions, the presence of low-lying excited states makes the inclusion of both the first-order contribution of the excited states and the second-order effects due to coupling of the ground / state with the excited states crucial in a correct estimation of the room-temperature values of xT. Indeed, second-order contribution in Van Vleck [9] expansion of the susceptibility is inversely proportional to the energy difference between the ground and the excited states ... 

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