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An analytical approach describing properties of focused partially coherent X-ray beams is presented. The method is based on the results of statistical optics and gives both the beam size and transverse coherence length at any distance behind an optical element. In particular, here we consider Gaussian Schell-model beams and thin optical elements. Limiting cases of incoherent and fully coherent illumination of the focusing element are discussed. The effect of the beam defining aperture, typically used in combination with focusing elements at synchrotron sources to improve transverse coherence, is also analyzed in detail. As an example the coherence properties in the focal region of compound refractive lenses at the PETRA III synchrotron source are analyzed.
A general theoretical approach based on the results of statistical optics is used for the analysis of the transverse coherence properties of 3-rd generation synchrotron sources and x-ray free-electron lasers (XFEL). Correlation properties of the wave
We discuss the properties of pure multipole beams with well-defined handedness or helicity, with the beam field a simultaneous eigenvector of the squared total angular momentum and its projection along the propagation axis. Under the condition of hem
We demonstrate X-ray phase contrast microscopy performed at the European X-ray Free-Electron Laser sampled at 1.128 MHz rate. We have applied this method to image stochastic processes induced by an optical laser incident on water-filled capillaries w
We report on the generation of a narrow divergence ($thetaapprox 2.5$ mrad), multi-MeV ($E_text{MAX} = 18$ MeV) and ultra-high brilliance ($approx 2times10^{19}$ photons s$^{-1}$ mm$^{-2}$ mrad $^{-2}$ 0.1% BW) $gamma$-ray beam from the scattering of
Graphene plasmons are of remarkable features that make graphene plasmon elements promising for applications to integrated photonic devices. The fabrication of graphene plasmon components and control over plasmon propagating are of fundamental importa