# Spectral Properties of 1D Fibonacci Quasicrystals

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This Demonstration shows the spectral properties of the Fibonacci quasicrystal from both algebraic and graphical points of view; in the latter case in real and reciprocal space. The Fibonacci quasicrystal is the most studied one-dimensional (1D) quasiperiodic model structure, given its interesting applications in photonics and acoustics.

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Contributed by: Jessica Alfonsi (November 2018)

(Padova, Italy)

Open content licensed under CC BY-NC-SA

## Details

Snapshot 1: letter sequence for the single periodic approximant at the initial stage with , with a frequency ratio limit still far from the golden number

Snapshot 2: same as the Thumbnail image but with transmission plot (, ) enabled, instead of the Fourier power spectrum

Snapshot 3: Fourier spectrum similar to the Thumbnail image but with a higher value, therefore with more spectral components

References

[1] W. Steurer and D. Sutter-Widmer, "Photonic and Phononic Quasicrystals," *Journal of Physics D: Applied Physics*, 40(13), 2007 R229. doi:10.1088/0022-3727/40/13/R01.

[2] U. Grimm and M. Schreiber, "Energy Spectra and Eigenstates of Quasiperiodic Tight-Binding Hamiltonians," *Quasicrystals: Structure and Physical Properties* (H.-R. Trebin, ed.), Weinheim, Germany: Wiley-VCH, 2003 pp. 210–235. arxiv.org/abs/cond-mat/0212140.

## Snapshots

## Permanent Citation