Photonic band gap from a stack of single-negative materials

We investigate the transmission gap of the multilayer structure consisting of alternate permittivity-negative material layer and permeability-negative material layer. It is found that for both normal and oblique incidences, there exists a transmission gap which is invariant with a change of scale length. In view of the fact that the layers are electrically thin, the effective permittivity ɛeffɛeff and permeability μeffμeff are introduced to study the transmission property of electromagnetic waves. Numerical results show that the transmission gap can be well explained by the total reflection (ɛeffμeff-ɛairμairsin2θ<0, where θθ is the incident angle). To one's interest, the edges of the gap can be accurately determined by ɛeffμeff-ɛairμairsin2θ=0. In addition, we show that zero effective phase shift gap (zero-φeffφeff gap) and zero volume averaged refractive index gap (zero-n¯ gap) can also be understood in a similar way.