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 -bar eff and permeability μeff 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 (-bar effμeff--bar airμairsin2θ<0, where θ is the incident angle). To one's interest, the edges of the gap can be accurately determined by -bar effμeff--bar airμairsin2θ=0. In addition, we show that zero effective phase shift gap (zero-φeff gap) and zero volume averaged refractive index gap (zero-n-bar gap) can also be understood in a similar way