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.

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