Abstract
AbstractThis dissertation aims at developing a theoretical approach to treat the 24-wave diffraction occurred in a Fabry-Perot type of resonant cavity of silicon by solving an eigenvalue-eigenvector equation, derived by Stetsko and Chang, deduced from the X-ray multiple-wave dynamical diffraction equation. We anticipate the calculations can offer a crystal clear physical picture for the experimental resonance pattern of the 24-wave diffraction in the X-ray Fabry-Perot cavity, and aid us design an appropriate resonant cavity to fulfill the experimental purposes.The resonance pattern accompanied by nine coplanar diffractions occurred in an X-ray Fabry-Perot cavity of silicon at photon energy of 14.4388 keV at which 24 beams are simultaneously excited has been realized by employing the back diffraction of (12 4 0) by Chang et al.. The calculation is in a good agreement with the observed one. The interference fringes of the concentric rings accompanied by nine diffraction lines passing through the center of rings distinctly show up in the calculated pattern. Meanwhile, the dispersion surface and the linear absorption coefficient have been mapped out from the solved eigenvalues. The excitation of mode and the phases of the diffracted waves have also been calculated from the solved eigenvalues and eigenvectors and from boundary conditions. According to the calculated dispersion surface and linear absorption coefficient, we find that in the total reflection region, most of energy is reflected off the crystal, and the absorption reaches the maximum value, and the phase of the diffracted waves changes drastically. In the exact 24-wave region, the phase of the diffracted wave changes further by doubling the values.The effect of the crystal thickness and the gap width on the reflectivity and transmissivity are also surveyed. The larger the reflectivity and the lower the transmissivity, the thicker is the crystal plate. The more the number of the resonance peaks, the wider is the gap width between the two plates. The time response curves of the cavity show a periodic structure of time due to the interference among the resonance peaks.In brief, we have established a theoretical approach to treat the multiple-wave diffraction in the Fabry-Perot type of resonant cavity. The calculation is in a good agreement with the observed one. The procedures for the dynamical calculations are also offered in this dissertation.