The features of soft X-ray fluorescence spectra of radiation propagating inside micro-channel plates have been studied in the framework of wave approximation. X-ray and fluorescence yield due to the grazing incidence reflection phenomenon have been investigated with respect to the geometry of channel walls. We researched experimental spectra collected at the exit of micro-capillaries under total X-ray reflection condition and supported them with theoretical calculations taking into account a surface transition layer at waveguide surface. It was shown that the wave penetrating through cladding material substantially modifies the wave field near the waveguide surface. It results in a significant increase of total energy flux inside guiding layer and leads to additional spatial modulation of the electromagnetic field. Diffraction phenomena at the exit of a hollow X-ray waveguide (with real and imaginary parts of permittivity) were investigated using the model of Fraunhofer diffraction of waves at far zone.
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