Numerical Investigation on the Spectral Properties of One-Dimensional Triadic-Cantor Quasi-Periodic Structure

Abstract

Abstract-We numerically investigate the optical spectra of a photonic band gap material realized by one-dimensional Triadic-Cantor quasi-periodic structure. The studied system is composed of two elementary layers H and L with refractive indices n L = 1.45 (SiO 2 ) and n H = 2.3 (T iO 2 ), respectively. Analytical calculations using a trace and antitrace maps approach have been used to find the reflection and transmission theoretical expressions in visible range under quarter wavelength condition. In our results we present the effect of iteration order of Triadic-Cantor sequence on the optical properties of these multilayer systems, namely the photonic band gap behavior and the optical windows presence, which makes this type of structures good candidates for interesting applications in the field of the nano-optical Engineering.

Omnidirectional high-reflectivity mirror in the 4–20μm spectral range

“…In the visible range, Deopura et al [4] described a highly efficient reflector formed by a stack of 19 alternating layers of tin (IV) sulfide and silica, while Lin et al [5] studied a highly efficient reflector with a 12-layer-pair stack of TiO SiO 2 2 . Onedimensional aperiodic multilayers can also behave as efficient mirrors in the visible, as recently reported by Barriuso et al [6] (generalized Fibonacci quasicrystals) or Bouazzi et al [7] (Triadic-Cantor structures). All these reflectors (periodic or aperiodic) combine high-and low-refractive-index layers where, to attain maximum reflectivity, the high refractive index should be larger than 2.26 and the corresponding low index similar to 1.5 [8].…”

“…A QW triadic Cantor structure of 3rd generation with 27 layers is depicted in figure 2 ) where its total length corresponded to 75.5 μm. Similarly to the Fibonacci structure, a number of reflection and transmission bands appear leading to a good reflector at specific spectra domain [7]. In addition, a QW periodic multilayer was numerically studied in figure 2(d with a total length of 80 μm.…”

“…As a result, when the rate of the thickness decrease of CsBr layers equals −59.5 nm/layer, an optimized average reflectance for p polarization á ñ = -´-R 1 6 10 p 6 can be obtained in the 4-20 μm spectral range for all angles of incidence. For s incident states, the average reflectance is even greater á ñ = -´-R 1 3 10 s 7 . Moreover, a near-zero transmittance region  -T 10 12 occurs in the 12-20 μm wavelength interval constituting (to our knowledge) the widest spectrum for a single omnidirectional mirror where such remarkable reflectance values can be achieved.…”

Metamaterial Control of Hybrid Multifunctional High-Tc Superconducting Photonic Crystals for 1D Quasi-periodic Structure Potential Applications

“…One of the quasi-periodic structures called the Fibonacci sequence (FS) has been investigated 22,23 . Recently, (FS) structure containing metamaterial has been studied, for which the zero n-gap 24,25 , the omnidirectional gap 26 and other unique phenomena were found, compared to the normal periodic PCs consisting of MTMs 27 . Based on the use of DNG material, the purpose of this paper is to study the transmission properties of Fibonacci photonic crystal consisting of metamaterial (DNG) and high Tc superconductor material theoretically.…”

Fractal Plasmons on Cantor Set Thin Film

“…It is important to note that realistic, fractal-like physical systems cannot contain infinitely small parts; if the construction is iterative, only a finite number of iterations is used. Examples of such structure are triadic-Cantor photonic crystals [18] and plasmonic superlattices [19] which can be analyzed using standard transfer matrix approach. Similarly, the finite number of Cantor set iterations in plasmonic structure allows one to approach the problem with classical optics and to use the standard form of Fourier transform.…”