X-ray propagation through a quasi-ordered multilayered structure

Abstract

We investigate the propagation of short wavelength transverse electric x-rays through a quasiordered  (Fibonacci) atomically commensurate multilayered structure using a transfer matrix model which treats each atomic plane as a diffraction unit. The reflectance spectrum has a rich structure being dominated by peaks associated with certain critical points of the system. Peaks around these special points exhibit self-similarity with a scaling factor approximately equal to the cube of the golden mean. At a critical point itself, the  electromagnetic energy distribution is neither localised nor extended. The Landauer resistance at the reflection  peaks exhibits a power law behaviour at low Fibonacci generation numbers but eventually increases exponentially; in the presence of absorption, the Landauer resistance reaches a plateau after its initial power law behaviour. The persistence, in the presence of absorption, of some reflectivity peaks at small angles of incidence is in line with current interest in the use of quasi-ordered multilayered structures as short wavelength near-normal incidence x-ray mirrors.

Keywords : X-rays, Fibonacci multilayered structures