X-Ray Reflectivity of Fibonacci Multilayers

TL;DR

This study numerically analyzes the X-ray reflectivity of Fibonacci multilayers, revealing unique self-similar and multifractal patterns that differ from periodic multilayers, with potential applications in X-ray device design.

Contribution

It introduces a numerical approach to analyze Fibonacci multilayer reflectivity and characterizes their complex patterns using multifractal analysis, highlighting their distinct behavior from periodic systems.

Findings

Fibonacci multilayers exhibit highly-fragmented, self-similar reflectivity patterns.

Reflectivity patterns become more complex with increasing layers.

Multifractal analysis effectively describes the fragmentation behavior.

Abstract

We have numerically computed the reflectivity of X-ray incident normally onto Fibonacci multilayers, and compared the results with those obtained in periodic approximant multilayers. The constituent layers are of low and high refractive indices with the same thickness. Whereas reflectivity of periodic approximant multilayers changes only slightly with increasing the number of layers, Fibonacci multilayers present a completely different behaviour. In particular, we have found a highly-fragmented and self-similar reflectivity pattern in Fibonacci systems. The behaviour of the fragmentation pattern on increasing the number of layers is quantitatively described using multifractal techniques. The paper ends with a brief discussion on possible practical applications of our results in the design of new X-ray devices.