Negative Luneburg lens based on the graded annular photonic crystals

Focusing by the designed negative Luneburg lens which is based on graded annular photonic crystals (GAPCs) are studied in this paper. The GAPCs are composed of ring-shaped silicon pillars in a hexagonal lattice. The gradient of refractive index is achieved by modifying the radii of inner holes. The effective negative refractive index is analyzed based on the photonic band structures and verified by the simulation of negative refraction in APCs flat lens. Numerical simulation results show that a 0.6λ focusing spot can be realized by our designed Luneburg lens and it has the potential to be utilized in photonic integrated circuits.