Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes

Supercritical Xe at 293 K offers a Kerr nonlinearity that can exceed that of fused silica while being free of Raman scattering. It also has a much higher optical damage threshold and a transparency window that extends from the UV to the infrared. We report the observation of nonlinear phenomena, such as self-phase modulation, in hollow-core photonic crystal fiber filled with supercritical Xe. In the subcritical regime, intermodal four-wave-mixing resulted in the generation of UV light in the HE12 mode. The normal dispersion of the fiber at high pressures means that spectral broadening can clearly obtained without influence from soliton effects or material damage

Manual of Quaternions

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Derivation of the Zakharov equations

This paper continues the study of the validity of the Zakharov model describing Langmuir turbulence. We give an existence theorem for a class of singular quasilinear equations. This theorem is valid for well-prepared initial data. We apply this result to the Euler-Maxwell equations describing laser-plasma interactions, to obtain, in a high-frequency limit, an asymptotic estimate that describes solutions of the Euler-Maxwell equations in terms of WKB approximate solutions which leading terms are solutions of the Zakharov equations. Because of transparency properties of the Euler-Maxwell equations, this study is led in a supercritical (highly nonlinear) regime. In such a regime, resonances between plasma waves, electromagnetric waves and acoustic waves could create instabilities in small time. The key of this work is the control of these resonances. The proof involves the techniques of geometric optics of Joly, M\'etivier and Rauch, recent results of Lannes on norms of pseudodifferential operators, and a semiclassical, paradifferential calculus

Inelastic X-ray scattering from valence electrons near absorption edges of FeTe and TiSe2_2

We study resonant inelastic x-ray scattering (RIXS) peaks corresponding to low energy particle-hole excited states of metallic FeTe and semi-metallic TiSe$_2$ for photon incident energy tuned near the $L_{3}$ absorption edge of Fe and Ti respectively. We show that the cross section amplitudes are well described within a renormalization group theory where the effect of the core electrons is captured by effective dielectric functions expressed in terms of the the atomic scattering parameters $f_1$ of Fe and Ti. This method can be used to extract the dynamical structure factor from experimental RIXS spectra in metallic systems.Comment: 6 pages, 4 figure

Exponential decay for the damped wave equation in unbounded domains

We study the decay of the semigroup generated by the damped wave equation in an unbounded domain. We first prove under the natural geometric control condition the exponential decay of the semigroup. Then we prove under a weaker condition the logarithmic decay of the solutions (assuming that the initial data are smoother). As corollaries, we obtain several extensions of previous results of stabilisation and control

Resonant X-ray diffraction studies on the charge ordering in magnetite

Here we show that the low temperature phase of magnetite is associated with an effective, although fractional, ordering of the charge. Evidence and a quantitative evaluation of the atomic charges are achieved by using resonant x-ray diffraction (RXD) experiments whose results are further analyzed with the help of ab initio calculations of the scattering factors involved. By confirming the results obtained from X-ray crystallography we have shown that RXD is able to probe quantitatively the electronic structure in very complex oxides, whose importance covers a wide domain of applications.Comment: 4 pages 4 figures, accepted for publication in PR

Diffusion in pores and its dependence on boundary conditions

We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes. Partial slip is shown to significantly influence the diffusion coefficient near a wall. Analytical expressions are derived in the low and high confinement limits, and are in good agreement with numerical results. These calculations indicate that diffusion of tagged particles could be used as a sensitive probe of the solid-liquid boundary conditions.Comment: soumis \`a J.Phys. Cond. Matt. special issue on "Diffusion in Liquids, Polymers, Biophysics and Chemical Dynamics

Geometric optics and instability for semi-classical Schrodinger equations

We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the problem cannot be reduced to the study of an o.d.e.Comment: 22 pages. Corollary 1.7 adde