Passive harmonic mode locking of soliton crystals

We report experimental observation of passive harmonic mode locking (HML) in which the basic pattern is a soliton crystal. Several crystal states were generated from an initial large bound state by increasing the pump power. The soliton crystals are identical and progressively span along the cavity to finally take a regular spacing leading to HML of solitons crystal.     

Determination of the third- and fifth-order optical nonlinearities: the general case

We compute the evolution of the intensity (I) and the phase (φ) of a beam propagating in a nonlinear (NL) isotropic medium exhibiting third- and fifth-order NL optical characteristics. All formulas are analytic, but the general case requires a numerical inversion by means of Newton’s method. The solutions may differ if some coefficients vanish, so they are given in all cases up to the fifth-order nonlinearities. The analytical relations allow us to fit the experimental data using the recently introduced D4σ-Z-scan method. Carbon disulfide is tested at 532 and 1,064 nm in the picosecond regime deducing NL coefficients related to third- and fifth-order optical susceptibilities.     

Asymptotic Estimates for Interpolation and Constrained Approximation in H^{2} by Diagonalization of Toeplitz Operators

Sharp convergence rates are provided for interpolation and approximation schemes in the Hardy space that use band-limited data. By means of new explicit formulae for the spectral decomposition of certain Toeplitz operators, sharp estimates for Carleman and Krein-Nudel'man approximation schemes are derived. In addition, pointwise convergence results are obtained. An illustrative example based on experimental data from a hyperfrequency filter is provided. Submitted: August 17, 2001? Revised: November 5, 2001.     

PFG NMR measurements of flow through porous media: effects of spatial correlations of the magnetic field and the velocity field

Used for a long time for diffusion studies, PFG NMR techniques are now widely used to study flow through porous media. We discuss here the effects of the magnetic field inhomogeneities and the finite gradient pulse duration in this case. We propose a statistical model based on spatial correlations of the magnetic field and velocity field and as far as we can, we draw practical conclusions on the PFG NMR measurements conditions.