Department of Physics, National Tsing Hua University^{*} National Synchrotron Radiation Research Center^{**}

â—‹Mau-Sen Chiu^{*} Yu P Stetsko^{**} Shih-Lin Chang^{*}

The theoretical approach of using a Cartesian coordinate representation for polarization based on the dynamical theory is applied to the back diffraction of Si (12 4 0) in a two-plate cavity at 14.4388 keV. At this photon energy, simultaneous twenty-four beam diffraction consisting of nine coplanar reflections occurs. Also the interference due to Fabry-Perot type resonance produces intensity undulation in both transmitted and back-reflected beams. In order to understand the wavefield distribution and interaction of 24-beam diffraction with the resonant X-rays, the geometry of the dispersion surface, linear absorption coefficients, wavefield intensity, and excitation of mode are calculated. The calculated intensity distributions of the transmitted and back-reflected beams are in good agreement with the observed ones. Details about the interaction between the multiply diffraction X-rays and cavity resonant photons will be reported.