| Resumo: | The study of photonic crystals, artificial materials whose dielectric properties can be tailored according to the stacking of its constituents, remains an attractive research area. In this article we have employed a transfer matrix treatment to study the propagation of light waves in Fibonacci quasiperiodic dielectric multilayers with graphene embedded. We calculated their dispersion and transmission spectra in order to investigate the effects of the graphene monolayers and quasiperiodic disorder on the system physical behavior. The quasiperiodic dielectric multilayer is composed of two building blocks, silicon dioxide (building block A=SiO 2) and titanium dioxide (building block B=TiO2). Our numerical results show that the presence of graphene monolayers reduces the transmissivity on the whole range of frequency and induces a transmission gap in the low frequency region. Regarding the polarization of the light wave, we found that the transmission coefficient is higher for the transverse magnetic (TM) case than for the transverse electric (TE) one. We also conclude from our numerical results that the graphene induced photonic band gaps (GIPBGs) do not depend on the polarization (TE or TM) of the light wave nor on the Fibonacci generation index n. Moreover, the GIPBGs are omnidirectional photonic band gaps, therefore light cannot propagate in these structures for frequencies lower than a certain value, whatever the incidence angle. Finally, a plot of the transmission spectra versus chemical potential shows that one can, in principle, adjust the width of the photonic band gap by tuning the chemical potential via a gate voltage
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