Tunable wave localization at the Dirac frequency in a metallic photonic crystal cavity

In this study, the two-dimensional (2D) triangular lattice metallic photonic crystals (PCs) in visible and infrared bands have been utilized to achieve light confinement at the Dirac frequency. Distinct from the traditional bandgap or total internal reflection cavity modes, the unique photonic localization mechanism leads to an unusual algebraic decay of state and a unique frequency located beyond any bandgaps. This investigation delves into the band structure analysis of 2D metallic PCs, specifically focusing on their distinctive features, such as photonic bandgaps and Dirac cones. The plane wave expansion (PWE) method, enhanced with a linearization technique, is employed for band structure calculations, considering both the frequency-dependent dielectric properties and the intrinsic lossy nature of metallic materials described by the Drude model. The study provides a comprehensive derivation of the PWE equations for metallic PCs and investigates their band characteristics under both TM and TE polarizations. Focusing on TM modes in triangular lattice metallic PCs, it reveals zero density of states (DOS) at K points of the Brillouin corner and the existence of Dirac cones with linearly dispersion and linearly vanishing DOS. The study extends to exploring localized modes at Dirac frequencies, employing a relativistic quantum mechanics approach analogous to graphene's charge carriers. Theoretical predictions are corroborated by numerical simulations, and the potential for tunable Dirac localized modes is highlighted. This research not only deepens the understanding of Dirac properties in graphene-like systems but also lays the groundwork for further exploration of the practical quasi-2D devices, which will provide assistance in the integration of micro- and nano- devices, especially in applications requiring long-range coupling, given the critical importance of optical cavities in contemporary optical technologies.