We present a short review of our activities carried out in Tongji University (Shanghai, China) in the field of theory and technology of soft X-ray multilayer diffraction gratings. Diffraction gratings are widely used to study the structure and dynamics of a matter in laboratory and space by spectral analysis techniques. Combining multilayer and grating structures into a single unit allows to increase essentially both the spectral resolution and the efficiency of the diffraction optics. The unified analytical theory of soft X-ray diffraction from multilayer gratings operating in the single-order regime is briefly discussed. The single-order regime occurs when incident wave excites the only diffraction order and it is characterized by ultimately high diffraction efficiency tending to the reflectivity of conventional multilayer mirror. Our first experiments in fabrication of the blazed multilayer gratings by anisotropic etching of a silicon crystal with small roughness of the facet surfaces are described.
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