Transmission properties of a double-periodic quasi-crystal containing single-negative materials

The transmission properties of a double-periodic quasi-crystal containing single-negative materials are investigated with the transfer matrix method and effective medium theory. It is shown that the double-periodic quasi-crystal has a single-negative band gap between the zeros of average permittivity and average permeability of the effective medium. These zeros are affected only by the filling factor of the structure, and are independent from the order of the double-periodic quasi-crystal. Moreover, we show that the periodic structure created by repeating the double-periodic quasi-crystal has some omnidirectional band gaps at the single-negative frequency region. The number of such omnidirectional band gap increases by increasing the order of double-periodic quasi-crystal. Then, the structure can be used as a multichannel filter.