Graphene based 1D photonic crystals bands via the Fourier Modal Method

A theoretical approach for computing the photonic band structure of 1D graphene based photonic crystal (1DGPC) using the Fourier Modal method (FMM) is presented. It is based on the resolution of the Maxwell's equations and the Bloch theorem. In the model, the graphene sheet is considered as layer with atomic thickness characterized by a dielectric function, which is frequency dependent and has a non-zero imaginary part. This frequency dependency is given by the Drude dielectric function. Under these conditions, we show that within the framework of the FMM, it is possible to obtain a polynomial eigenvalue problem allowing the calculation of the band structure which reveals photonic band structures with photonic bandgaps. It is concluded that the existing photonic bandgaps are highly tunable by varying the graphene chemical potential. Furthermore, we explore the spatial field-structure of certain modes and show that the modes associated with the lower edges of the bandgaps can be considered as quasi-modes generated by a cavity formed by the graphene and the dielectric medium.