Photonic crystals composed of virtual pillars with magnetic walls: Photonic band gaps and double Dirac cones

Abstract

Photonic crystals composed of virtual pillars with magnetic walls are proposed. A virtual pillar with a magnetic wall can be created inside a parallel perfect electric conductor plate waveguide by introducing a circular perfect magnetic conductor patch in the upper perfect electric conductor plate of the waveguide. The virtual pillar mimics a perfect magnetic conductor pillar with a radius less than that of the circular patch because electromagnetic waves can slightly penetrate the wall. Furthermore, the photonic band structures of a triangular photonic crystal composed of virtual pillars for the transverse electromagnetic modes of the waveguide are investigated. They are very similar to those of a triangular photonic crystal composed of infinitely long perfect electric conductor cylinders for transverse magnetic modes. The similarity between the two different photonic crystals is well understood by the boundary conditions of perfect electric and magnetic conductor surfaces. A double Dirac cone at the center of the Brillouin zone is observed and thus the virtual pillar triangular photonic crystal can act a zero-refractive-index material at the Dirac point frequency.