Band structures of one-dimensional subwavelength photonic crystals containing metamaterials

We study the band structures of one-dimensional (1D) photonic crystals (PCs) in the subwavelength limit. A '' spatial-averaged single-negative '' (SASN) gap whose edges correspond to zero (volume) averaged permittivity $(epsilon) over bar and zero (volume) averaged permeability $(mu) over bar will appear when metamaterial is included in the PC. Unlike the Bragg gap, the frequency range of the SASN gap is invariant to the geometrical scaling and insensitive to the incident angle and disorder. In the subwavelength limit, both the zero-$(n) over bar gap in the left-handed 1D PC and the zero-effective-phase gap in the single-negative 1D PC can be understood as SASN gaps. When the subwavelength condition is not fulfilled, the zero-$(n) over bar gap and zero-effective-phase gap begin to act differently.