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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.

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