Band structure of a periodic waveguide that include a dispersive metamaterial

In this work we consider an electromagnetic waveguide composed of two periodic and rippled periodic surfaces. An integral numerical method was applied to determined the bandgap structure of the system and the intensity field of its electromagnetic modes. We found that the variation of the ripples amplitudes allow to control at a certain degree the photonic band structure of the system. Although initially considered the medium inside the waveguide is vacuum, we also discuss the case of a dispersive metamaterial medium. We found interesting band structures that contains regions of nearly zero-dispersion and bandgaps for TM polarization. Moreover, for some parameters surface modes were obtained.