X-UV synthetic interference mirrors : theoretical approach

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Abstract
The purpose of the paper is to give the theoretical basis for the design and optimization of X-UV interference mirrors. To achieve this original results are presented and the « state of the art » methods are reviewed. A new formulation of the Bragg conditions is obtained on the basis of the « Hill method » to solve the wave propagation equation in a periodically stratified medium. A large part of the paper is devoted to matricial formalism. The major role played by invariant quantities is emphasized. Recursive procedures to compute the reflectance are summarized. The problems of imperfections are also considered. Concerning the thickness errors, statistical universes are defined to give a coherent treatment of their effects. The matricial formalism is adopted to treat the influence of the interfacial roughness using the homogeneous transition layer model. Finally the perspective of a distributed X-UV amplifier in a periodic multilayered structure is proposed as an alternative to the Fabry-Perot resonator