A new method of design for multilayer structures with broadband spectral responses is presented. A stochastic design approach is utilized, based upon a simulated (SA) annealing algorithm, which optimizes the multilayer structure for a particular set of criteria. In particular, we consider a mirror for which the requirement is for high reflectivity, over a broad wavelength range, in the soft x-ray region, as might be compatible with the output from a laser plasma source. The design algorithm is used to maximize a merit function for the structure by manipulating the ordering, the thickness and the material types of each of the constituent layers. The merit function may also be configured to include a number of other desirable properties for the high reflectivity mirror including broad angular response, polarization response and uniformity of reflectivity over a prescribed wavelength range.
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