Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials

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.