Effective Plasma Frequency in Graphene-Based Photonic Crystals

Photonic crystals, based on graphene-dielectric multilayers, have been shown to exhibit tunable Bragg gap opening due to Fermi level tunability at each graphene layer. At low Frequencies (THz regime), a metallic-like gap is also observed with a doping dependent cutoff frequency which marks the beginning of the first transmission region. In this work, we numerically analyze this cutoff frequency as a function of Fermi level, interlayer distance and immersing dielectric constant for an equally doped graphene stack immersed in homogeneous dielectric. We give an analytical approach to deduce a Drude-like effective index for a graphene-dielectric unit cell which in turn, allows to obtain an analytical formula for this cutoff frequency. We determine parameter ranges where our analytical model fits better with the data obtained by numerical computation.