Resonance modes filtering in structured x-ray waveguides

We discuss the self-imaging effect that occurs in a multimode planar x-ray waveguide (WG) with a nanometer vacuum gap, where an additional longitudinal periodicity has been imposed by a periodical structure (a micron scale step-like grating) on the reflecting sidewalls. Taking into account the general Montgomery conditions and the particular case of Talbot effect, we show that this additional longitudinal periodicity, if suitably designed, can filter out the asymmetric and the high order resonance modes, providing a coherent beam at the exit, even if the WG is illuminated by an incoherent source.