Theory for polaritons in graphene photonic crystals in an applied magnetic field

The dispersion relations for bulk and surface plasmon-polaritons in a semi-infinite 1D photonic crystal interlayered with graphene are calculated in the presence of an applied magnetic field. The results are applied to SiO2 as the constituent material in geometry where the layers are arranged in a periodic array with the same layer thickness. The static magnetic field is applied perpendicular to the plane of layers. Numerical results are presented for the modes in THz range, up to 10 THz, to illustrate the important role of the applied magnetic field on the graphene sheets in modifying the polariton dispersion curves, especially for magnetic fields of the order of 1 T. It is found that the polariton frequencies and band gaps have a sensitive dependence on the electron scattering rate parameter (and hence the applied magnetic field strength) in the graphene sheets. Electromagnetic retardation effects are fully taken into account for the bulk bands, while for the surface modes (which are shown to have a novel non-reciprocal propagation characteristics) it is convenient to focus on the regime where retardation is small