REFLECTING PROPERTIES OF X-RAY MULTILAYER DEVICES

In recent years much progress has been reported in the fabrication of multilayer reflectors for x-ray and XUV radiation (1(ANGSTROM) - 600(ANGSTROM)).; The characteristic optical properties of materials at these wavelengths (dielectric constants are complex and approach unity), allow one to obtain solutions to Maxwell's equations for a quasi-periodic reflector whose layers contain arbitrary index gradients.; This solution can be formulated as a difference equation that propagates the amplitude reflectance across each layer pair. The difference equation resembles the Airy summation for single layers, but has a simpler Ricatti form.; From the difference equation one can derive design criteria for maximization of multilayer reflectivity. These criteria provide guidance in the selection of appropriate multilayer materials, and have been used to derive approximate scaling laws for multilayer reflecting properties.; The difference equation forms the basis for a non-perturbative analysis of multilayer reflectivity in the presence of random thickness errors (including the residual loss in reflectivity that remains when reflectance monitoring is used to compensate for thickness errors during multilayer fabrication). Under certain circumstances, the difference equation can be used to analyze the effect of interfacial roughness on multilayer reflectivity. Accurate closed-form solutions to such stochastic problems can be found by neglecting higher order powers in the incoherent component of multilayer reflectivity.; The reflecting properties of x-ray multilayers may contain qualitative signatures that correspond to these different kinds of structural defects.; Our theoretical results indicate that significant constraints on efficiency and field of view are involved in using multilayers to extend optical technology to the x-ray regime. Examples discussed include microscopes operating at short x-ray wavelengths (1(ANGSTROM) - 2(ANGSTROM)), where multilayers can provide a useful level of spectral selectivity, and resonant cavities for projected x-ray lasers (50(ANGSTROM)- 200(ANGSTROM)), where the coupling of the intracavity field to the amplifier can be strongly increased if the cavity uses two multilayers tuned to reflect at normal incidence.