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We present several time-dependent analytical solutions for the incompressible Euler system with a free surface. These analytical solutions give quantitative descriptions of some physical phenomena, such as water motion or waves on a space variable topography, and can be used as reference solutions when validating numerical simulation codes. They concern fluid flows governed by Euler equations with or without the hydrostatic hypothesis including a wet/dry interface, variable density and a wide variety of boundary conditions. [ABSTRACT FROM AUTHOR]

Parametric frequency conversion via four-wave mixing (FWM) in silicon nanocrystal (Si NC) waveguides is observed at 1550 nm. To investigate the role of Si NC, different types of waveguides containing Si NC in a SiO2 matrix were fabricated. Owing to the increase of the dipole oscillator strength mediated by the quantum confinement effect, the non-linear refractive index () of Si NCs is found to be more than one order of magnitude larger than the one of bulk Si. Coupled differential equations for the degenerate FWM process taking into account the role of Si NC were numerically solved to model the experimental data. The modeling yields an effective for Si NCs in SiO2 waveguides which is similar to the one of Si waveguides. We also measured a large signal to idler conversion bandwidth of ∼22 nm. The large non-linear refractive index is joined with a large two photon absorption coefficient which makes the use of Si NC in non-linear optical devices mostly suitable for mid-infrared applications. [ABSTRACT FROM AUTHOR]