We show theoretically that a one-dimensional photonic crystal containing a negative-index material has an omnidirectional gap, owing to the mechanism of zero (volume) averaged refractive index. In contrast to the Bragg gap, the edge of such a zero-n̄ gap is insensitive to incident angle and polarization. When an impurity is introduced, a defect mode appears inside the zero-n̄ gap with a very weak dependence on incident angle and invariant with scaling.

The transmission properties of a one-dimensional photonic crystal containing two kinds of single-negative (permittivity- or permeability-negative) media are studied theoretically. We show that this structure can possess a type of photonic gap with zero effective phase (phi(eff) ). The zero-phi(eff) gap distinguishes itself from a Bragg gap in that it is invariant with a change of scale length and is insensitive to thickness fluctuation. In contrast to a photonic gap corresponding to zero averaged refractive index, the zero-phi(eff) gap can be made very wide by varying the ratio of the thicknesses of two media. An equivalent transmission-line model is utilized to explain the properties. A photonic quantum-well structure based on zero-phi(eff) gaps is proposed as a multiple channeled filter that is compact and robust against disorder.

OUTLINE I. Introduction II. Basic physics of hyperbolic metamaterials A. Physical properties 1. Dispersion relation of the anisotropic materials 2. Enhanced spontaneous emission 3. Abnormal refraction, reflection, and scattering B. Realization ways 1. Effective medium theory 2. Hyperbolic metasurface 3. Natural hyperbolic media III. Topological transition of dispersion A. Dispersion transition from closed ellipsoids to open hyperboloids 1. Materials dispersion steered topological transition 2. Loss induced topological transition 3. Actively controlled topological transition B. Transition points at two kinds of topological transition 1. Anisotropic zero-index metamaterials 2. Linear crossing metamaterials IV. Dispersion control in Hypercrystals A. Controlling the dispersion of band structure B. Cavity modes and edge modes with special dispersion V. Applications A. Hyperlens B. Long-range energy transfer C. High sensitivity sensors