Negative refraction in a two-dimensional hexagonal lattice annular photonic crystal

Negative refraction has been the subject of considerable interest and it may provide the possibility of a variety of novel applications. Recently, it has been shown that photonic crystals (PhCs) composed of synthetic periodic dielectric materials can exhibit an extraordinarily high nonlinear dispersion which causes effects such as negative refraction and self-focusing properties that are determined by the characteristics of their photonic band structures and equal frequency contours (EFCs). In this paper we have theoretically studied the negative refraction in two-dimensional (2D) hexagonal lattices annular photonic crystal (APC) which composed of a dielectric-rod and a circular-air-hole array in a hexagonal lattice. By using Plane Wave Expansion (PWE) method and Finite-Difference Time-Domain (FDTD) method we have studied the photonic band structure, equal frequency contours and the electric field distribution of such photonic crystal. Numerical simulations show that negative refraction and superlense imaging can be realized in the designed annular photonic crystal.