Zero-width band gap associated with the n[over] = 0 condition in photonic crystals containing left-handed materials

We demonstrate that the band structure of a photonic crystal consisting of alternating layers of right-handed material (RHM) and left-handed material (LHM) can exhibit two types of zero- n[over ] gaps of zero width. It is shown that each type has an associated null-gap condition which determines the scaling properties of the frequency nu(0) at which the corresponding null gap occurs. Specifically, while scaling in the layer thicknesses does not modify the value of the frequency nu(0) determined by one of these conditions, the frequency nu(0) associated with the other one does not exhibit such a scaling behavior. We have also shown that near the touching point nu(0) (for both types of null gaps) and around the center of the Brillouin zone, the dispersion curves exhibit a linear dependence on the Bloch wave vector k . As a consequence, the corresponding density of states and group velocity are practically flat as functions of k in the neighborhood of k=0 . Another interesting property of the considered structure is that an electromagnetic wave with frequency nu(0) can be transmitted through a finite RHM-LHM photonic crystal without any change in amplitude and phase.