Linear dispersion properties

The comparison of the SC spectra obtained using the realistic and artificial water susceptibilities is shown in Fig. 13.10. The original and artificial medium spectra agree quite well in the vicinity of the excitation wavelength. However, at high frequencies the two materials produce drastically different continua. The long-dashed line shows the SC spectrum transformed by the same transformation that produced the artificial medium susceptibility from the water susceptibility. This appears to be very close to the artificial medium spectrum. This indicates that the extent of the spectrum is actually determined mostly by the linear dispersion properties of the medium. 

The present study demonstrates that the analytic calculation of hyperpolarizability dispersion coefficients provides an efficient alternative to the pointwise calculation of dispersion curves. The dispersion coefficients provide additional insight into non-linear optical properties and are transferable between the various optical processes, also to processes not investigated here as for example the ac-Kerr effect or coherent anti-Stokes Raman scattering (CARS), which depend on two independent laser frequencies and would be expensive to study with calculations ex-plictly frequency-dependent calculations. 

One of the advantages of a monochromator with an echellette grating is that in contrast to a prism monochromator, the dispersion of radiation along the focal plane is, for all practical purposes, linear. Figure 25-9 demonstrates this property. The linear dispersion of a grating greatly simplifies the design of monochromators. 

Fig. 6. Dispersion of the electro-optic hyperpolarizabUity for chromophores with different linear absorption properties...

Gahleitner et al. (1994) describe the rheology of talc-filled PP. They note the effects of filler concentration, particle size and dispersion on linear viscoelastic properties. 

One of the hurdles in this field is the plethora of definitions and abbreviations in the next section I will attempt to tackle this problem. There then follows a review of calculations of non-linear-optical properties on small systems (He, H2, D2), where quantum chemistry has had a considerable success and to the degree that the results can be used to calibrate experimental equipment. The next section deals with the increasing number of papers on ab initio calculations of frequency-dependent first and second hyperpolarizabilities. This is followed by a sketch of the effect that electric fields have on the nuclear, as opposed to the electronic, motions in a molecule and which leads, in turn, to the vibrational hyperpolarizabilities (a detailed review of this subject has already been published [2]). Section 3.3. is a brief look at the dispersion formulas which aid in the comparison of hyperpolarizabilities obtained from different processes. 

The original Placzek theory of Raman scattering [30] was in terms of the linear, or first order microscopic polarizability, a (a second rank tensor), not the third order h3q)erpolarizability, y (a fourth rank tensor). The Dirac and Kramers-Heisenberg quantum theory for linear dispersion did account for Raman scattering. It turns out that this link of properties at third order to those at first order works well for the electronically nonresonant Raman processes, but it cannot hold rigorously for the fully (triply) resonant Raman spectroscopies. However, provided one discards the important line shaping phenomenon called pure dephasing , one can show how the third order susceptibility does reduce to the treatment based on the (linear) polarizability tensor [6, 27]. 

The linear optical properties of the isomers of 4-[ethyl(2-hydroxy-ethyl) aminoj-4-nitrobenzene (disperse red 1 or DRl) have attracted the attention of researchers for many years, and during the last decade, the nonlinear optical properties of DRl placed in a polymer environment also have been of interest. The trans- and as-isomers of DRl are illustrated in Figure 9.1. Tlie photoisomerization reaction begins by elevating molecules to excited electronic states, followed by nonradiative decay back to the ground slate in either the cis or trans forms, as illustrated in Figure 9.2. TTie ratio of dsUrans states is dependent on the quantum yield of the appropriate photoisomerization reaction (e.g., and for the direct trans= cis and reverse cis= trans photoisomerization reactions, respectively). As the trans-isomer is more stable than the c/s-isomer, molecules in the cis form convert to the trans form bv... 

The third order non-linear optical properties of pseudoisocyanine J-aggregates in thin solid films were studied using the Z-scan method as well for PIC iodide anion as for PIC with closo-hexahydrodecaborate anion (BioHio -) (Markov et al., 1998a, 1998b Plekhanov et al., 1998a, 1998b). The dispersions values of imaginary and real parts of cubic... 

The rheological characterisation of non-Newtonian fluids is widely acknowledged to be far from straightforward. In some non-Newtonian systems, such as concentrated suspensions, rheological measurements may be complicated by non-linear, dispersive, dissipative and thixotropic mechanical properties and the rheometrical challenges posed by these features may be compoimded by an apparent yield stress. 

In 1949 Harrison described the production of a grating intermediate between the Michelson echelon and the Wood echelette, which he called an echelle. The echelle grating possesses properties different from those of other gratings, particularly as to the method by which high resolution and linear dispersion are achieved. 

Non-linear mechanical properties were observed for rubber eomposites and referred to as the Payne effect. The Payne effeet was interpreted as due to filler agglomeration where the filler clusters formed eontained adsorbed rubber. The occluded rubber molecules within filler elusters eould not eontribute to overall elastic properties. The composites behaved similarly to rubber composites with higher filler loading. Uniform and stable filler dispersion is required for rubber composites to exhibit linear viscoelastic behaviour. Payne performed dielectric measurements on SBR vulcanizates containing silica or carbon black. The dielectric data were used to construct time-temperature superposition master curves. The reference temperature increased with crosslinking but not significantly with filler. Comparison of dynamic mechanical and dielectric results for the SBR blended with NR was made and interpreted. ... 

Thus, for all practical purposes, if the angle r is small, the linear dispersion of a grating monochromator is constant, a property that greatly simplifies monochro-malur design. 

F. Simoni, Non-linear optical properties of liquid crystals and polymers dispersed liquid crystals - series on liquid crystals, Vol. 2, pp. 217-250, World Scientific, Singapore. (1997). 

Water-soluble EMA resins and derivatives of these materials function very well as dispersants (Table A.3). For example, the amide-salt derivative exhibits excellent dispersant properties for pigments in waterborne synthetic latice systems. Dispersants for the coatings, rubber, leather, cosmetic, ceramics, photographic film, and agricultural field have been claimed for EMA resins. The linear derivatives are especially useful as dispersants and stabilizers for emulsion bead polymerizations. For example, EMA-type dispersants (emulsifiers) are very useful for PVC production. The resins also function well as macromolecular dispersants for the suspension copolymerization of a-olefins and aromatic vinyl compounds with MA. ... 

---