Surface and bulk plasmon-polaritons in semiconductor photonic crystals with embedded graphene sheets

A theoretical study is made for the bulk and surface plasmon-polaritons in one-dimensional semi-infinite layered semiconductor photonic crystals with graphene interlayers. The retarded dispersion relations are calculated in a general way and applied to two cases, depending on whether a graphene sheet is present or absent at the first interface of the semi-infinite structure. We apply the result to doped GaAs as the constituent material, considering the layers to be arranged in a periodic fashion with alternating layer thicknesses. Both s- and p-polarized modes are evaluated with the effects of retardation on the polaritons being included in the general expressions. Simplifications, particularly for the surface modes, are studied for the case when retardation effects are small. Through numerical examples, we illustrate the important role of the graphene sheets in modifying the plasmon-polariton properties (focusing on the region near the bulk plasma frequency). A strong dependence on the mode polarization is found.