Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion

Abstract

The structure of one-dimensional photonic crystal (1DPC) containing indefinite metamaterials with a hyperbolic dispersion relation is proposed to realize the omnidirectional gap for the design of omnidirectional reflectors and filters. It is demonstrated that this 1DPC can result in a similar zero average index (zero-n¯) gap usually appearing in the 1DPC containing isotropic left-handed materials. The properties of zero-n¯ gap and defect modes of this photonic crystal are studied in detail. The edge of this zero-n¯ gap is insensitive to incident angle and polarization of light in contrast to the Bragg gap. When a defect layer is introduced into the 1DPC, a defect mode appears inside the omnidirectional gap. The spectral position of defect mode is found to be weakly dependent on the incident angle of light and nearly invariant to the scale length of photonic crystal.