Photonic band gap materials comprising positive-phase-velocity and negative-phase-velocity layers in waveguides

We have analyzed electromagnetic wave propagation in photonic bandgap (PBG) structures comprising alternating layers of isotropic dielectric-magnetic materials with positive phase velocity and negative phase velocity, implemented in different waveguides of uniform cross-section (parallel-plate, rectangular, circular, and coaxial) and perfectly conducting walls. The structures could be either ideal (i.e. of infinite extent along the waveguide axis) or real (i.e. terminated at both ends with homogeneously filled waveguide sections). The spectral locations of the band gaps do not directly depend on the cross-sectional shape and dimensions, but on the cut-off parameter instead, for ideal structures. The band gaps of an ideal structure are located in spectral regions where the reflectance of the corresponding real structure is large. The real structures show four types of band gaps, only one type of which is due to the periodically repetitive constitution of the PBG structure; the remaining three types are not of the Bragg type.