Nanosecond nonlinear absorption in Au and Ag nanoparticles precipitated glasses induced by a femtosecond laser

We obtain Au and Ag nanoparticles precipitated in glasses by irradiation of focused femtosecond pulses, and investigate the nonlinear absorptions of the glasses by using Z-scan technique with ns pulses at 532 nm. We observe the saturable absorption behavior for An nanoparticles precipitated glasses and the reverse saturable ones for Ag ones. We also obtain, by fitting to the experimental results in the light of the local field effect near and away from the surface plasmon resonance, chi(m)((3)) = 4.5 x 10(-7) and 5.9 x 10(-8) esu for m the imaginary parts of the third-order susceptibilities for Au and Ag nanoparticles, respectively. The nonlinear response of Au nanoparticles in the glass samples arises mainly from the hot-electron contribution and the saturation of the interband transitions near the surface plasmon resonance, whereas that of Ag nanoparticles in the glass samples from the interband transitions. These show that the obtained glasses can be used as optoelectronic devices suiting for different demands. (c) 2005 Elsevier B.V. All rights reserved.

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.