Omnidirectional band gap in Fibonacci photonic crystals with metamaterials using a band-edge formalism

Omnidirectional zero-n gaps in one-dimensional photonic crystals with a Fibonacci basis containing frequency dependent metamaterials are examined. In this study, the band structure and band gaps are determined by an explicit band-edge equation rather than by a traditional dispersion equation. We find that the present method has better numerical stability than traditional methods, especially for calculating the zero-(n) over bar gap in the photonic crystals with metamaterials. We observe that the change in the width and location of the omnidirectional zero-(n) over bar gap is limited for the Fibonacci photonic crystals with different generation orders. However, the width of the omnidirectional gap in the Fibonacci photonic crystals is significantly affected by the filling factor of the metamaterials. We also find that the width of the gap will be maximum at an optimum filling factor. The gap will vanish if the filling factor is greater than a critical value. Moreover, for a given filling factor and a metamaterial, it is interesting that the gap will be enlarged as the refractive index of the traditional layer increases.