Study of Photonic Quasicrystals of Fibonacci, Octonacci and Dodecanacci with Graphenes
Quasicrystals, Photonic Crystals, Fibonacci, Octonacci, Dodecanacci
The richness of optical and electronic properties of graphene has attracted enormous interest. Graphene has high mobility and optical transparency, in addition to flexibility, robustness and stability. Until recently, the main focus has been on fundamental physics and the physics of electronic devices. However, we believe that the full potential of graphene is in photonics and optoelectronic, where the combination of their optical and electronic properties are unique and can be fully exploited even in the absence of an electronic "band gap". In this master thesis we studied the optical transmissivity spectra in periodic dielectric multilayer (photonic crystals) and multilayers who obey quasiperiodic sequences (photonic quasicrystals) composed of graphene and compare our results with the same structures without graphene. Thus, first we calculate the transmittance spectrum photonic crystal formed by alternating layers of dielectric permittivities with and B, for comparative purposes. In the second stage, we have introduced between the dielectric monolayers a monolayer of graphene. Then we study the photonic Fibonacci’s quasicrystals, with and without graphene entres the dielectric layers, which can be generated by a recurrence relation of the type: Sj + 1 = Sj Sj-1 where S0 = B and S1 = A. In both cases we use the transfer-matrix technique to obtain the transmittance spectra. We have also studied a generalization of the Fibonacci quasicrystal structure called “Octonacci”, where the n-th stage of these multilayer structure (Sn) is given by the recurrence rule: Sn = Sn-1 Sn-2Sn-1, with n>2 to S1=A and S2=B. Finally, for completeness, we study the further generalization of the Fibonacci sequence called Dodecanacci, which can be generated starting from the inflation rule: A-> AABAA and B-> AB. Our results show that all the optical spectra are affected and their "band gap", and slightly translated to high frequencies. We also show that the properties of fractality and self-similarity of the spectra are maintained to high frequencies. Our results show a good insight into new devices that use the quasiperiodic multilayer instead of the well known Bragg reflectors.