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The XEUS X-ray mission is currently being studied by ESA. It will be based on a huge (10 m of aperture diameter) grazing-incidence mirror unit with 50 m focal length, realized by a two separate satellites system, one dedicated to host the mirror module and the other for the detector. The current baseline foresees a single reflecting layer of Gold for the full set of 562 mirror shells of the XEUS telescope (296 shells of the first stage of the project, named XEUS I, with a maximum diameter of ~ 4 m, plus 266 shells of the second phase, named XEUS II, that will be activated after about 5 years). However, the use of multilayer mirrors instead of Au for XEUS-I (i.e. where the incidence angles of the mirror shells series are smaller) is an interesting alternative, already recently proposed by other authors, to extend the XEUS operative range in the hard X-ray region (up to 80 keV). In this work we applied a global optimization approach based on an “Iteraded Simplex Procedure” to optimize the sequence of bi-layers of depth-graded multilayer films, in order to get the best achievable response by the XEUS-I mirrors in the hard X-ray region. In addition, we theoretically evaluated the performances of the XEUS-II mirrors after the introduction of constant d-spacing multilayers with a thin (100 Å) overcoating of Carbon instead of Au. In this case the main advantage is given by an enhancement of the telescope effective area in the soft X-ray region (0.1-10 keV). The role of the Carbon top layer is to reduce the photoelectric absorption effect in the total-reflection regime, with an important improvement of the reflection efficiency with respect the usual mirrors based on high density materials like, e.g., Au, W, Ir and Pt.
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