  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 dieletric 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 dieletric multilayer is composed of two building blocks,
silicon dioxide (building block A = SiO2) 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
bandgaps (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 this
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.
