Transmission properties of left-handed band-gap structures
  We analyze transmission of electromagnetic waves through a periodic band-gap structure consisting of slabs of a left-handed metamaterial and air. Using the effective parameters of the metamaterial derived from its microscopic structure, we study, with the help of the transfer-matrix approach and by means of the finite-difference-time-domain numerical simulations, the transmission properties of such a left-handed photonic crystals in a novel type of band gap associated with the zero averaged refractive index. We demonstrate that the transmission can be made tunable by introducing defects, which allow to access selectively two different types of band gaps. 
Ilya V. Shadrivov, Nina A. Zharova, Alexander A. Zharov, Yuri S.   Kivshar