Optical Properties of the Quasi-Periodic One-Dimensional Genarilized Multilayer Fibonacci Structures

Optical properties of generalized dielectric Fibonacci multilayer generated by the rule Sl+1 = Sn l S m l−1 with a pair of positive integers m and n were studied. The initial generations S1 and S2 are taken as S1 = H and S2 = L where H and L are two elementary layers with refractive indices nL = 1.45 and nH = 2.3, respectively. In the following numerical investigation, we chose SiO2 (L) and TiO2 (H) as two elementary layers. We use the so-called “antitrace” map to determine the transmission spectra of the structures. Based on the representation of the transmittance spectra in the visible range an analysis depending on the pair (n,m) is presented. We show that the whole structure Sn l S m l−1 has an interesting application for well selection pairs (m,n) values.