Abstract

In general, Liouville's theorem holds for any time-reversible Hamiltonian system including the geometrical optics (both imaging and nonimaging^1,2) model of monochromatic rays, where, in Hamiltonian formulation,² the z-coordinate is treated as a parameter equivalent to the time variable in statistical classical mechanics. Thus the so-called ideal nonimaging optical elements, well known in the IR/VIS/UV region,^1,3 can also be introduced to the collimation and concentration of XUV electromagnetic radiation (1–100 nm). Contrary to the IR/VIS/UV region, where the nonimagng elements are based on either metallic reflection or dielectric total internal reflection, the XUV concentrators/collimators are based on grazing incidence total external reflection, since the refractive index of all optical materials is smaller than 1 in the XUV region.

© 1987 Optical Society of America