Analysis of tapered front-coupling X-ray waveguides

The coupling and propagation of electromagnetic waves through planar X-ray waveguides (WG) with vacuum gap and Si claddings are analyzed in detail, starting from the source and ending at the detector. The general case of linearly tapered WGs (i.e. with the entrance aperture different from the exit one) is considered. Different kinds of sources, i.e. synchrotron radiation and laboratory desk-top sources, have been considered, with the former providing a fully coherent incoming beam and the latter partially coherent beams. It is demonstrated that useful information about the parameters of the WG can be derived, comparing experimental results with computer simulation based on analytical solutions of the Helmholtz equation which take into account the amplitude and phase matching between the standing waves created in front of the WG, and the resonance modes propagating into the WG.