Broad band focusing of photonic crystals with graded negative index

In this paper, we designed a hexagonal lattice photonic crystal (PC) which presents negative refraction behavior in the visible region. By varying the PC parameters, a graded index PC was obtained and used to focus a plane wave. Numerical calculation was adopted to demonstrate the negative refraction and focusing effect. Our calculation results demonstrated that the PC can realize focusing by negative refraction in visible region. Moreover, a broad band focusing ranging from 425 nm to 700 nm was observed with less chromatic aberration in the PC structure. The proposed structures provide an approach for designing the negative index imaging systems