A study of the brightest peaks in the diffraction pattern of Fibonacci gratings

Abstract

The diffraction patterns of 1D aperiodic Fibonacci gratings (FGs) are investigated here. We derive a set of simple formulae which allow the finding of the positions and the intensities of the strongest diffraction peaks amongst the infinite ones present inside a given reciprocal space interval , chosen according to a user-defined threshold. In this way the diffraction spectrum of FGs and of their generalizations, generalised Fibonacci gratings (GFGs), can be approximated to a good level as a set of discrete, properly indexed peaks with varying intensity, similarly to what is done for periodic structures. This approach is applied to real cases of GFGs fabricated and tested by two dedicated setups on a substrate of photorefractive Fe: LiNbO3. The experimental results are in excellent agreement with the proposed description and confirm the applicability of our approach.

Emergence of anomalous dynamics from the underlying singular continuous spectrum in interacting many-body systems

“…It is interesting to compare these features with those of the on-site Fibonacci model (OFM), showing a purely SC energy spectrum [36] induced by its quasiperiodic geometry [37,38] and displaying no phase transition. The OFM is obtained by setting n = λ( (n + 1)/τ − n/τ ) in Eq.…”

Optical computing of quantum revivals

“…2 do not reveal diffraction peaks at distance scales corresponding to the zeroth order periodicity T 0 , summarised in the first row of Table I. Most commonly, this periodicity is not observable through the far-field intensity pattern, as it appears in the argument of a global phase factor in (16). In order to observe diffraction peaks at distance scales of T 0 , we may interfere the diffracting fields represented in Fig.…”

“…Interference from aperiodic structures has also been studied in the context of photonic and plasmonic quasi-crystals [7][8][9]. Besides, studies on the focusing and deflection properties of aperiodic gratings have been carried out [10][11][12][13], with attention to structures ruled by Fibonacci sequences [14][15][16].…”

Localized Modes and Photonic Band Gap Sensitivities with 1D Fibonacci Quasi-Crystals Filled with Sinusoidal Modulated Plasma

“…The most common quasi-periodic sequence is the Fibonacci [21] one due to its incommensurable periods in the spatial spectrum of the structure-the so-called pure point spectrum. It shows Bragg-like peaks in its spatial spectrum [22]. The well-known symmetry of the Fibonacci sequence is generated by the inflation rule, F k+1 = {F k , F k−1 }.…”