Transverse coherence properties of X-ray beams in third-generation synchrotron radiation sources

This article describes a complete theory of spatial coherence for undulator radiation sources. Current estimations of coherence properties often assume that undulator sources are quasi-homogeneous, like thermal sources, and rely on the application of the van Cittert-Zernike theorem for calculating the degree of transverse coherence. Such assumption is not adequate when treating third generation light sources, because the vertical(geometrical) emittance of the electron beam is comparable or even much smaller than the radiation wavelength in a very wide spectral interval that spans over four orders of magnitude (from 0.1 Angstrom up to 10^3 Angstrom). Sometimes, the so-called Gaussian-Schell model, that is widely used in statistical optics in the description of partially-coherent sources, is applied as an alternative to the quasi-homogeneous model. However, as we will demonstrate, this model fails to properly describe coherent properties of X-ray beams from non-homogeneous undulator sources. As a result, a more rigorous analysis is required. We propose a technique, based on statistical optics and Fourier optics, to explicitly calculate the cross-spectral density of an undulator source in the most general case, at any position after the undulator. Our theory, that makes consistent use of dimensionless analysis, allows relatively easy treatment and physical understanding of many asymptotes of the parameter space, together with their region of applicability. Particular emphasis is given to the asymptotic situation when the horizontal emittance is much larger than the radiation wavelength, and the vertical emittance is arbitrary. This case is practically relevant for third generation synchrotron radiation sources.Comment: 71 pages, 20 figures - Version accepted for publication in Nuclear Inst. and Methods in Physics Research,

Search for Photon-Photon Elastic Scattering in the X-ray Region

We report the first results of a search for real photon-photon scattering using X rays. A novel system is developed to split and collide X-ray pulses by applying interferometric techniques. A total of $6.5\times10^{5}$ pulses (each containing about $10^{11}$ photons) from an X-ray Free-Electron Laser are injected into the system. No scattered events are observed, and an upper limit of $1.7\times 10^{-24}$ ${\rm m^{2}}$ (95% C.L.) is obtained on the photon-photon elastic scattering cross section at 6.5 keV

High efficiency and low absorption Fresnel compound zone plates for hard X-ray focusing

Circular and linear zone plates have been fabricated on the surface of silicon crystals for the energy of 8 keV by electron beam lithography and deep ion plasma etching methods. Various variants of compound zone plates with first, second, third diffraction orders have been made. The zone relief height is about 10 mkm, the outermost zone width of the zone plate is 0.4 mkm. The experimental testing of the zone plates has been conducted on SPring-8 and ESRF synchrotron radiation sources. A focused spot size and diffraction efficiency measured by knife-edge scanning are accordingly 0.5 mkm and 39% for the first order circular zone plate.Comment: 5 pages, 7 figure