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 (τ + 2)(Fµ + τ F µ+1 ) −1 p/(2q) or (τ + 2)(Lµ + τ L µ+1 ) −1 p/(2q) of the Talbot distance. Here, (p, q) are coprime integers, µ is an integer, τ is the golden mean, and Fµ and Lµ 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.

Optical Texture Super‐Lattices Produced by Talbot Effect at Superimposed Gratings

“…Usually, this effect is considered on one‐dimensional (1D) or 2D periodic structures, having a limited spectrum of obtained configurations of the light field distribution. A lot of attempts have been made to widen this spectrum by using such non‐trivial gratings, as radial, [ 21 ] fractal, [ 22 ] Fibonacci‐like, [ 23 ] Moiré, [ 24 ] and other complex structures [ 25 ] promising for a wide range of photonics applications.…”