The properties of X-ray vacuum-gap waveguides (WGs) with additional periodic structure on one of the reflecting walls are studied. Theoretical considerations, numerical simulations and experimental results confirm that the periodic structure imposes additional conditions on efficient propagation of the electromagnetic field along the WGs. The transmission is maximum for guided modes that possess sufficient phase synchronism with the periodic structure (here called `super-resonances'). The field inside the WGs is essentially given at low incidence angle by the fundamental mode strongly coupled with the corresponding phased-matched mode. Both the simulated and the experimental diffraction patterns show in the far field that propagation takes place essentially only for low incidence angles, confirming the mode filtering properties of the structured X-ray waveguides.
Keywords: X-ray beams and X-ray optics; X-ray microscopes; interference; synchrotron radiation instrumentation; transmission and absorption; wave propagation.