Low-frequency photonic band structures in graphene-like triangular metallic lattice

Abstract

We study the low frequency photonic band structures in triangular metallic lattice, displaying Dirac points in the frequency spectrum, and constructed upon the lowest order regular polygonal tiles. We show that, in spite of the unfavourable geometrical conditions intrinsic to the structure symmetry, the lowest frequency photonic bands are formed by resonance modes sustained by local structure patterns, with the corresponding electric fields following a triangular distribution at low structure filling rate and a honeycomb distribution at high filling rate. For both cases, the lowest photonic bands, and thus the plasma gap, can be described in the framework of a tight binding model, and analysed in terms of local resonance modes and their mutual correlations. At high filling rate, the Dirac points and their movement following the structure deformation are described in the same framework, in relation with local structure patterns and their variations, as well as the particularity of the metallic lattice that enhances the topological anisotropy.