Plasmonic band structures in doped graphene tubes

We present theoretically the transport of plasmonic waves in doped graphene tube, which is made by rolling planar graphene sheet into a cylinder and periodic doping is applied on it. It is shown that periodic modulation of the Fermi level along the tube can open gaps in the dispersion relations of graphene plasmons and eventually create plasmonic band structures. The propagation of graphene plasmons is forbidden within the bandgaps; while within the band, the plasmonic waves present axially-extended field distributions and propagate along the tubes, yet well confined around the curved graphene surface. Furthermore, the bandgaps, propagation constants and propagation lengths of the modes in plasmonic band structures are significantly tuned by varying the Fermi level of graphene, which provides active controls over the plasmonic waves. Our proposed structures here may provide an approach to dynamically control the plasmonic waves in graphene-based subwavelength waveguides.