Third-order susceptibility estimation

Third-order susceptibilities of the PAV cast films were evaluated with the third-harmonic generation (THG) measurement [31,32]. The THG measurement was carried out at fundamental wavelength of 1064 nm and between 1500 nm and 2100 nm using difference-frequency generation combined with a Q-switched Nd YAG laser and a tunable dye laser. From the ratio of third-harmonic intensities I3m from the PAV films and a fused quartz plate ( 1 thick) as a standard, the value of x(3) was estimated according to the following equation derived by Kajzar et al. [33] ... 

Fevine and Bethea have estimated the third-order susceptibilities for solutions in terms of the coherence lengths and second-harmonic signal intensities using quartz as a reference [33, 63] ... 

The most widely exploited effect in display applications is the influence of low frequency electric fields on the birefringence. Here, due to a distortion of the director, elements of the dielectric tensor change as a function of the applied field. From Eq. (6), the contribution of the third-order susceptibility -or,0,0,co) to the dielectric tensor is given by e=eo I+) U) Ea Eac]. Although the response is non-local, it is possible to obtain a crude estimate of the average susceptibility E. ), where... 

Three excitation pathways dominate the expression of the static third-order susceptibility two positive contributions from the lA- IB— m3A IB—> lA and lA—> lB->m2A- IB—> lA channels and a negative contribution from the lA —> IB —V lA — IB lA channel. The 7 value mainly results from the incomplete cancellation between these terms. The 2A state is involved in two types of pathways lA—> IB—>2A IB —> lA and lA lB 2A nlB— lA. As these two contributions have opposite signs, the resulting role played by the 2A state in the description of the third-order nonlinearity is strongly reduced. We note, however, that the cancellation is only partial (in contrast to what is assumed in the essential-state model of Mazumdar and co-workers [137-139]) and that a quantitative estimate of the static 7 values requires to include in the SOS expression the following states lA, IB, 2A, m2A, m3 A, nlB, n2B, and n3B. These states form our model for the NLO response of thiophene oligomers. 

Reis et al. report theoretical studies of the urea250 and benzene251 crystals. Their calculations start from MP2 ab initio data for the frequency-dependent molecular response functions and include crystal internal field effects via a rigorous local-field theory. The permanent dipolar fields of the interacting molecules are also taken into account using an SCF procedure. The experimental linear susceptibility of urea is accurately reproduced while differences between theory and experiment remain for /2). Hydrogen bonding effects, which prove to be small, have been estimated from a calculation of the response functions of a linear dimer of urea. Various optoelectronic response functions have been calculated. For benzene the experimental first order susceptibility is accurately reproduced and results for third order effects are predicted. Overall results and their comparison with studies of liquid benzene show that for compact nonpolar molecules environmental effects on the susceptibilities are small. 

The magnitude of the third-order nonlinear susceptibility, was estimated from a measurement of the intensity of the phase-conjugate beam relative to that of a reference sample of CS2 placed in a quartz cell of 2-mm path length. The value of was obtained from (22) ... 

The NLO properties in the above-mentioned Pis are attributed to the NLO chromophores which are molecularly dispersed in or covalently bonded to thermally stable PI chains. Aromatic polyisoimides (Pil), isomers of PI, have conjugated structure along their main chains, and hence are supposed to show intrinsic third-order NLO properties. The third-order non-linear susceptibility, of several Pil films was estimated to be in the order of esu by third harmonic generation measurements (Table 13) with... 

The contributions to the fifth-order nonlinear optical susceptibility of dense medium have been theoretically estimated by using both the local-field-corrected Maxwell-Bloch equations and Bloembergen s approach. In addition to the obvious fifth-order hyperpolarizability contribution, the fifth-order NLO susceptibility contains an extra term, which is proportional to the square of the third-order hyperpolarizability and which originates purely from local-field effects, as a cascaded contribution. Using as model the sodium 3s 3p transition system, it has been shown that the relative contribution of the cascaded term to the fifth-order NLO susceptibility grows with the increase of the atomic density and then saturates. 

The parameters b and (or their dimensionless counterparts b and ) are thus of major importance parameter 8 places a close third, followed in order by e and rj (e = 0 and rj = b are the most common assignments for these quantities). Significantly, b and are also susceptible to simple empirical interpretation, and hence to rough estimation. This is illustrated schematically in Figure 2, a plot of Z vs. Pr (for fixed Tr). 

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