Quadratic nonlinearities

In figure A3.3.9 the early-time results of the interface fonnation are shown for = 0.48. The classical spinodal corresponds to 0.58. Interface motion can be simply monitored by defining the domain boundary as the location where i = 0. Surface tension smooths the domain boundaries as time increases. Large interconnected clusters begin to break apart into small circular droplets around t = 160. This is because the quadratic nonlinearity eventually outpaces the cubic one when off-criticality is large, as is the case here. 

Another interesting comparison is between the coefficients for the functions representing the best-fitting models for the data and the coefficients for the functions that result from performing the linearity test as described in the previous chapter [4], We have not looked at these before since they are not directly involved in the linearity test. Now, however, we consider them for their pedagogic interest. These coefficients, for the case of testing a quadratic nonlinearity of the data from Figure 67-1, are listed in Table 67-2. 

The carbonyl complexes listed in Table V are of two types tricarbonyl-chromium rj6-arene 77-complexes, and pentacarbonyltungsten <7-pyridine complexes, with both complex types having relatively low y. Nonlinearities increase on arene or pyridine 77-system lengthening, and on proceeding from acceptor to donor substituent on the tricarbonylchromium-coordinated arene ring. Relative magnitudes and trends thus mirror those observed with quadratic nonlinearities of these complexes (see Ref. 1)... 

Coe, B. J., Molecular materials possessing switchable quadratic nonlinear optical properties. Chem. Eur. J. 1999, 5, 2464-2471. 

Coe, B. J., Jones, L. A., Harris, J. A., et al., Syntheses and spectroscopic and quadratic nonlinear optical properties of extended dipolar complexes with ruthenium(II) ammine electron donor and N-methylpyridinium acceptor groups. J. Am. 

Keywords. Electro-optic chromophores, Polymers, Waveguides, Quadratic nonlinearities, Phase-matching... 

Reviewed in Zyss J, Chemla DS (1987) Quadratic nonlinear optics and optimization of the second-order nonlinear optical response of molecular crystals. In Chemla DS, Zyss J (eds) Nonlinear and optical properties of organic molecules and crystals. Academic Press, Orlando, p 23... 

J. Zyss and D.S. Chemla, Quadratic Nonlinear Optics and Optimization of Second-Order Nonlinear Optical Response of Molecular Crystals, Eds. D.S. Chemla and J. Zyss, Academic Press, Orlando, FL, 1987, Vol. 1, pp. 23-191. 

Boltzmann s name is best reserved for the form that this equation takes when only binary collisions contribute to dfi/Sr, an explicit, quadratically nonlinear, integrodifferential equation. 

In Fig. 23, we show the time evolution of the variance (V2(t)) for various combinations of Levy index a and magnitude y2 of the quadratic nonlinearity (y0 = 1.0 and y4 = 0.0). For all cases with finite y2 (y2 = 0.1), we find convergence of the variance to a stationary value. For the two smaller a values (1.2 and 1.5), we observe some fluctuations however, these are comparatively small with respect to the stationary value they oscillate around. For a = 1.8, the fluctuations are hardly visible, and in fact the stationary value is practically the same as in the Gaussian case a = 2.0. In contrast, the case with vanishing... 

Noel C, Kajzar F (1998) Highly orientable liquid crystalline polymers for quadratic nonlinear optics. In Prasad PN, Mark JE, Kandil SH, Kafafi Z (eds) Proceedings of the fourth international conference on frontiers of polymers and advanced materials, Plenum Press, New York, p 275... 

Photonics is playing an ever-increasing role in our modern information society. Photon is gradually replacing the electron, the elementary particle in electronics. Several hooks and reviews have appeared dealing with the theory of nonlinear optics and the structural characteristics and applications of nonlinear optical molecules and materials [1—18]. Tlie earliest nonlinear optical (NLO) effect discovered was the electro-optic (EO) effect. The linear EO coefficient defines the Pockel effect, discovered in 1906, while the quadratic (nonlinear) EO coefficient s,i relates to the Kerr effect, discovered 31 years later (1875). Truly, all-optical NLO effects were not discovered until the discovery of lasers. Second harmonic generation (SHG) was first observed in a single crystal of quartz by Franken et al. [1] in 1961. They frequency doubled the output of a ruby laser (694.3 nm) into the 383... 

Coe, B.J., Harris, J.A., Brunschwig, B.S. Electroabsorption spectroscopic studies of dipolar ruthe-nium(II) complexes possessing large quadratic nonlinear optical responses. J. Phys. Chem. A 106, 897-905 (2002)... 

Sakaguchi, H., Nagamura, T., Penner, T.L., Whitten, D.G. Ultrafast optical modulation of quadratic nonlinearity from an Ru(II)-bipyridine complex in Langmuir-Blodgett assemblies. Thin Sohd Films 244, 947-950 (1994)... 

Zyss, J.. Dhenaut. C.. Chauvan, T., Ledoux, I. Quadratic nonlinear susceptibihty of octupolar chiral ions. Chem. Phys. Lett. 206, 409-414 (1993)... 

Maury, O., Viau, L., Senechal, K., Corre, B., Guegan, J.-P., Renouard. T.. Ledoux. I., Zyss, J., Le Bozec, H. Synthesis, linear, and quadratic-nonlinear optical properties of octupolar Dj and bipyridyl metal complexes. Chem. Eur. J. 10, 4454 466 (2004)... 

In theculinary spirit ofthe pastry map and the baker s map, Otto Rossler (1976) found inspiration in a taffy-pulling machine. By pondering its action, he was led to a system of three differential equations with a simpler strange attractor than Lorenz s. The Rossler system has only one quadratic nonlinearity xz ... 

Metal-Based Quadratic Nonlinear Optical Materials... 

METAL-BASED QUADRATIC NONLINEAR OPTICAL MATERIALS... 

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