Abstract
The transmission properties of hybrid quasi-periodic photonic systems (HQPS) made by the combination of one-dimensional periodic photonic crystals (PPCs) and quasi-periodic photonic crystals (QPCs) were theoretically studied. The hybrid quasi-periodic photonic lattice based on the hetero-structures was built from the Fibonacci and Thue-Morse sequences. We addressed the microwave properties of waves through the one-dimensional symmetric Fibonacci, and Thue-Morse system i.e., a quasi-periodic structure was made up of two different dielectric materials (Rogers and air), in the quarter wavelength condition. It shows that controlling the Fibonacci parameters permits to obtain selective optical filters with the narrow passband and polychromatic stop band filters with varied properties which can be controlled as desired. From the results, we presented the self-similar features of the spectra, and we also presented the fractal process through a return map of the transmission coefficients. We extracted powerfully the band gaps of hybrid quasi-periodic multilayered structures, called pseudo band gaps, often containing resonant states, which could be considered as a manifestation of numerous defects distributed along the structure. The results of transmittance spectra showed that the cutoff frequency could be manipulated through the thicknesses of the defects and the type of dielectric layers of the system. Taken together, the above two properties provide favorable conditions for the design of an all-microwave intermediate reflector.
Highlights
Photonic crystals (PCs) are artificial materials made from periodic arrays of dielectric or metallic building blocks
We showed that the corresponding transmission coefficients exhibited interesting properties, so it was found that the reflection bands of the Fibonacci sequence structures could cover all the spectral range by increasing the two parameters m=n
We found that the two sequences: Fibonacci or Thue-Morse, could exhibit multiple reflections of frequencies versus the multiplicity degree which joined the two parameters of the quasi-periodic system, m and n
Summary
Photonic crystals (PCs) are artificial materials made from periodic arrays of dielectric or metallic building blocks. The transmission of the wave through the quasi-periodic multilayer arranged by the Fibonacci or Thue-Morse sequences has been widely studied in different domains [11]. It can be applied for special applications such as the possibility of optical frequency-selective filters and memories. The transmission spectra through the photonic band gap material with the quasi-crystal order according to hybrid generalized quasi-periodic sequences are examined in the microwave domain. The important characteristics of the quasi-periodic order is a transmission spectrum varying according to the arrangement of layers This transmission spectrum is controlled by the parameters of the quasi-periodic sequences due to their peculiar fractal gaps explained by the different interface correlations. An association of the high reflector with multitude narrow band gaps can be designed, which can be used for photonic applications
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