Effective-periodicity effects in Fibonacci slot arrays

Abstract

In this Letter, the transmission properties of a nonperiodic array of slots arranged in the form of a Fibonacci sequence are investigated. By arranging the slots in this manner, an additional periodicity can be utilized, resulting in corresponding resonance features in the transmitted signal. By investigating the transmission response of a perforated metallic sheet over a broad frequency range (6-40 GHz), it is shown that this simple one-dimensional chain supports two periodicities, one due to the regular periodic separation and one due to average spacing-which is related to the golden ratio. This response replicates the resonant behavior of a two-dimensional periodic array with a single nonperiodic array also creating new families of diffraction lobes in the far-field region.

Super band gaps and periodic approximants of generalised Fibonacci tilings

“…2, then it is likely to be in a super band gap. Other approximate approaches for predicting the locations of super band gaps also exist, such as considering an "effective lattice" that is the superposition of two periodic lattices, with periods differing by a ratio equal to the golden mean [14]. This work builds on these previous results by developing the first rigorous justification for the occurrence of super band gaps in materials generated by generalised Fibonacci tilings.…”

“…Given the challenges of characterising the spectra of quasicrystals, a common strategy is to consider periodic approximants of the material, sometimes known as supercells. This approach is commonplace in the physical literature (for example, in [5,9,14]) and has the significant advantage that the spectra of the periodic approximants can be computed efficiently using Floquet-Bloch analysis. This method characterises the spectrum as a countable collection of spectral bands with band gaps between each band.…”

Super band gaps and periodic approximants of generalised Fibonacci tilings

“…They succeed in predicting the approximate locations of these super band gaps using the function Hn:Rfalse→false[0,normal∞false) defined by Hnfalse(ωfalse)=|trfalse(Tnfalse(ωfalse)false)trfalse(Tn+1false(ωfalse)false)|.They observed numerically that if ω∈R is such that H2false(ωfalse)≫2, then it is likely to be in a super band gap. Other approximate approaches for predicting the locations of super band gaps also exist, such as considering an ‘effective lattice’ that is the superposition of two periodic lattices, with periods differing by a ratio equal to the golden mean [16]. This work builds on these previous results by developing the first rigorous justification for the occurrence of super band gaps in materials generated by generalised Fibonacci tilings.…”

“…Given these challenges concerning the spectra of quasicrystals, a common strategy is to consider periodic approximants of the material, sometimes known as supercells. This approach is commonplace in the physical literature (for example, in [14][15][16]) and has the significant advantage that the spectra of the periodic approximants can be computed efficiently using Floquet-Bloch analysis. This method characterises the spectrum as a countable collection of spectral bands with band gaps between each band.…”

Multi-resonant tessellated anchor-based metasurfaces

“…Much of the work has focused on adding additional resonances or broadening the bandwidth. These approaches included the use of multi-layer structures 13 , multi-resonant unit cells 14 – 16 , fractal geometries 17 – 19 , non-periodic patterns 20 – 23 , and magnetic materials 24 . The use of multi-layer structures offers an extremely effective method for broadening the absorption bandwidth.…”