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Band structure and photonic band gap in comb-like structure asymmetric with left-handed materials

We investigate the dispersion relations through an infinite structure and the transmission coefficient of an asymmetric comb-like structure composed of periodic waveguides with right-handed material RHM, along a finite waveguide with two different resonators of different lengths. These resonators composed of left-handed material LHM, grafted onto N equidistant sites. We study special dispersion curves, which do not cover the whole first Brillouin area, although some values of wave vector k are without propagative modes. We study also the effect of the number and the lengths of the asymmetrical resonators on the behavior of the band gaps. This considered structure provides good information for the design of adjustable wide band gaps filters with high performance.