Antireflection structure for an effective refractive index near-zero medium in a two-dimensional photonic crystal

Two-dimensional dielectric photonic crystals (PCs) having periodic air hole cylinders, when designed properly, exhibit near-zero effective refractive index and the wave impedance is dependent on local observation points. The incident wave is mostly reflected at the PC-air interface due to large impedance mismatch. We show, analytically and numerically, that even in the near-zero effective refractive index case the reflection can be suppressed by utilizing an antireflection structure consisting of a PC with the same lattice constant but a different radius for the periodic air hole cylinders. The antireflection PC must be truncated at properly selected cross sections in order to possess the same impedance at cross sections with the host PC and with the air structure. An analytical model combined with the plane-wave expansion method captures the antireflection behavior obtained by the full wave simulations.