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The nonlinear refraction coefficient of silica aerogel was estimated to be ∼−1.5×10−15 m2/W (∼−3.67×10−9 esu) with a signal-beam z-scan spectroscopy. The third-order nonlinear refraction coefficient of nanostructure silica aerogel was almost five orders larger than the nonlinear refraction (χ3) of bulk material. The large nonlinear refraction with high nonlinear figure of merit is an ideal optical property for nonlinear optical applications.

Resonant third-order nonlinear optical susceptibility and hyperpolarizability of CdSe nanocrystal quantum dots were revealed to be ~2.6×10-20-2.7×10-19 m 2 /V 2 and ~2.2×10-40 m 5 /V 2 by using nanosecond degenerate four-wave mixing at 532 nm. The large nonlinearity of the CdSe nanocrystals is attributed to the resonant excitation and multiple nonlinear optical processes.

For a multipartite quantum state, the maximal violation of all Bell inequalities constitutes a measure of its nonlocality [Loubenets, \emph{J. Math. Phys}. 53, 022201 (2012)]. In the present article, for the maximal violation of Bell inequalities by a pure bipartite state, possibly infinite-dimensional, we derive \emph{a new upper bound} \emph{expressed in terms of the Schmidt coefficients of this state. } This new upper bound allows us also to specify \emph{general analytical relations }between the maximal violation of Bell inequalities by a bipartite quantum state, pure or mixed, and such entanglement measures for this state as "negativity" and "concurrence". To our knowledge, no any general analytical relations between measures for bipartite nonlocality and entanglement have been reported in the literature though, for a general bipartite state, specifically such relations are important for the entanglement certification and quantification scenarios. As an example, we apply our new results to finding upper bounds on nonlocality of bipartite coherent states intensively discussed last years in the literature in view of their experimental implementations.

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