摘要： The light-matter interaction is a very active and attractive research field and it is the basis of the photonic devices based on the generation, processing and storage of photons. In this work, we theoretically study the propagation of electromagnetic waves in one-dimensional photonic crystals consisting of two different dielectric slabs (silicon dioxide and titanium dioxide) separated by graphene. The spatial arrangement of the slabs is periodic, but we introduce randomness by using a Gaussian distribution of thickness with a specific standard deviation σ. The well-known transfer-matrix method is used as the mathematical approach. Our main goals are to investigate how the presence of such randomness can change the light transmission spectra and the emergence of robust photonic band gaps. For a given angle of incidence, our numerical results show that the two lowest frequency bandgaps are insensitive to the influence of the Gaussian distribution. Those band gaps emerge from two different mechanisms: one is due to the presence of graphene, while the other is due to the Bragg’s scattering. A strong transmission dependence on the standard deviation σ is also observed in our numerical results. More interesting, for the transversal magnetic case (angle of incidence θ ? 60°) the system can be adjusted to present transmission coefficient near to 1 and work like a perfect transparent media, what is useful for technological applications.