"It was during the 1980s that quasiperiodic structures in solid state physics amazed the scientific community  as it was not clear until then that structures holding short range but lacking long range order  can emerge in nature. As in many cases solid state physics can easily be transferred to photonic systems since their mathematical description of wave propagation have similar structures, only a short time after this discovery first optical experiments were implemented in order to analyze quasiperiodic media   . Such as in the latter publication, asking for quasiperiodic structures rapidly the nomenclature of a Fibonacci grating came up for this often is referred to as the embodyment of irregularity  . "
[Show abstract][Hide abstract] ABSTRACT: We report on the optical induction of Fibonacci lattices in photorefractive
strontium barium niobate by use of Bessel beam waveguide-wise writing
techniques. Fibonacci elements A and B are used as lattice periods. We further
use the induced structures to execute probing experiments with variously
focused Gaussian beams in order to observe light confinement owing to the
quasiperiodic character of Fibonacci word sequences. Essentially, we show that
Gaussian beam expansion is just slowed down in Fibonacci lattices, as compared
with appropriate periodic lattices.
"The trace-map technique  has proven to be a powerful tool to investigate the properties of various aperiodic systems. The transfer matrices A l used in the trace-map technique are written as : "
[Show abstract][Hide abstract] ABSTRACT: The transmission properties in microwave domains (10 GHz to 40 GHz) of generalized dielectric Fibonacci multilayer generated by the rule S<sub>l</sub> <sub>+1</sub> = S<sup>m</sup><sub>l</sub>S<sup>n</sup><sub>l</sub> <sub>–1</sub>: with a pair of positive integers m and n were studied. The initial generations of generalized Fibonacci sequence are taken as follows: S <sub>0</sub> = L and S <sub>1</sub> = H , where H and L are two elementary layers with refractive indices n<sub>L</sub> = 1 (air) and n<sub>H</sub> = 3 (ceramic). The so-called “trace map method” was used to simulate the transmission spectra of the multilayer structures at normal incidence. Based on the representation of the transmittance spectra in the microwave range an analysis depending on the pair ( n , m ) is presented. It has been shown that the reflection bands of the proposed quasi-periodic structure could cover the whole spectral range. By comparison, it is impossible to reach this result by using the periodical multilayer structure.
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