Low-frequency photonic bands in square Mediterranean and hexagonal snowflake metallic structures

Abstract

We study the low frequency photonic band structures in square Mediterranean and hexagonal snowflake metallic structures, both constructed upon two sets of adjustable tiles. The band formation and evolution are comparatively investigated with respect to local resonances and their variations following the modulations of the tile sizes and shapes. We show that the lowest frequency bands are formed by s-like resonance modes sustained by the structure tiles, of which the contributions vary following local structure modulations, and, under certain conditions, the second bands (above the first photonic bandgaps) are formed by p-like modes sustained by the same tiles. The s and p bands can both be described in the framework of a tight-binding model, allowing band structure analyses in terms of relations between local resonance modes and their mutual correlations. In this schema, the plasma gaps and the first photonic bandgaps arise naturally from local structure patterns, which determine both the local resonance conditions and their correlation relations.