We investigate the appearence of non-Bragg band gaps in 1D fractal photonic structures, specifically the Cantor-like lattices combining ordinary positive index materials and dispersive metamaterials. It is shown that these structures can exibit two new type of photonic band gaps with self-similarity properties around the frequencies where either the magnetic permeability or the electric permittivity of the metamaterial is zero. In constrast with the usual Bragg gaps, these band gaps are not based on any interference mechanisms. Accordingly, they remain invariant to scaling or disorder. Some other particular features of these polarization-selective gaps are outline and the impact on the light spectrum produced by the level of generation of the fractal structure is analyzed.
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