We report ultrafast third-order nonlinear optical (NLO) properties of several chalcogenide glasses GeS_x (x=1.8, 2.0, 2.5) measured by femtosecond time-resolved optical Kerr gate technique at 820nm. The third-order nonlinear susceptibility of GeS _1.8 glass is determined to be as large as 1.41×10^-12 esu, which is the maximum value of the third order nonlinear susceptibility
χ⁽³⁾ for the three compositions investigated. The symmetric Gauss profiles of
optical Kerr signals reveal the nature of ultrafast nonlinear response of these samples, which are originated from the ultrafast polarization of the electron clouds. By detailed microstructural analysis of these glasses based on the chain-crossing model (CCM) and the random-covalent-network model (RCNM), it can be concluded that χ⁽³⁾ value of GeS_x glasses can be enhanced greatly by S--S covalent bonds or S₃Ge--GeS₃ ethane-like units.

We investigate the navigation process on a variant of the Watts--Strogatz small-world network model with local information. In the network construction, each vertex of an N×N square lattice sends out a long-range link with probability p. The other end of the link falls on a randomly chosen vertex with probability proportional to r-α, where r is the lattice distance
between the two vertices, and α≥0. The average actual path length, i.e. the expected number of steps for passing messages between randomly chosen vertex pairs, is found to scale as a power-law function of the network size N^β, except when α is close to a specific value α_min, which gives the highest efficiency of message navigation. For a finite network, the exponent β epends on both α and p, and α_min drops to zero at a critical value of p which depends on N. When the network size goes to infinity, β depends only on α, and α_min is equal to the network dimensionality.