Multiscale Talbot effects in Fibonacci geometry

Abstract

This article investigates the Talbot effects in Fibonacci geometry by introducing the cut-and-project construction, which allows for capturing the entire infinite Fibonacci structure into a single computational cell. Theoretical and numerical calculations demonstrate the Talbot foci of Fibonacci geometry at distances that are multiples $(\tau +2)(F_{\mu }+\tau F_{\mu +1}{)}^{-1}p/(2q)$ or $(\tau +2)(L_{\mu }+\tau L_{\mu +1}{)}^{-1}p/(2q)$ of the Talbot distance. Here, ($p$, $q$) are coprime integers, $\mu$ is an integer, $\tau$ is the golden mean, and $F_{\mu }$ and $L_{\mu }$ are Fibonacci and Lucas numbers, respectively. The image of a single Talbot focus exhibits a multiscale pattern due to the self-similarity of the scaling Fourier spectrum.

4 pages, 5 figures

References in corpus (2)

• An electron Talbot interferometer
• Scaling analyses based on wavelet transforms for the Talbot effect