Development of X-ray laser media. Measurement of gain and development of cavity resonators for wavelengths near 130 angstroms, volume 3

In this document the authors summarize our investigation of the reflecting properties of X-ray multilayers. The breadth of this investigation indicates the utility of the difference equation formalism in the analysis of such structure. The formalism is particularly useful in analyzing multilayers whose structure is not a simple periodic bilayer. The complexity in structure can be either intentional, as in multilayers made by in-situ reflectance monitoring, or it can be a consequence of a degradation mechanism, such as random thickness errors or interlayer diffusion. Both the analysis of thickness errors and the analysis of interlayer diffusion are conceptually simple, effectively one dimensional problems that are straightforwared to pose. In the authors analysis of in-situ reflectance monitoring, they provide a quantitative understanding of an experimentally successful process that has not previously been treated theoretically. As X-ray multilayers come into wider use, there will undoubtedly be an increasing need for a more precise understanding of their reflecting properties. Thus, it is expected that in the future more detailed modeling will be undertaken of less easily specified structures than those above. The authors believe that their formalism will continue to prove useful in the modeling of these more complex structures. One such structure that may be of interest is that of a multilayer degraded by interfacial roughness.