X-ray guided modes produced by Bragg reflections of multilayers: an analytical treatment

It is analytically shown that X-ray Bragg reflections from periodical multilayer structures can be used for the excitation of guided modes. The X-ray guided modes in (i) a guiding film embedded in a periodical multilayer and (ii) an air gap between two space-separated multilayers have been considered. In the former case, analytical expressions have been obtained which describe a resonant X-ray intensity enhancement taking place inside the guiding film under the guided mode excitation. Optimal parameters of the waveguide have been found, which are needed to achieve a maximum intensity gain. In the latter case, eigen guided modes arising in the air gap have been determined. Properties of the eigen modes have been studied.