Maxwell Fish-Eye and Half-Maxwell Fish-Eye Based on Graded Photonic Crystals

We report on the design of the Maxwell fish-eye based on graded photonic crystals. It is a radially graded refractive index structure, whose remarkable property is to form perfect images in the sense of geometrical optics. The half-Maxwell fish-eye, which takes advantage of the symmetry of the previous, provides directive emission, which applies, amongst others, to wireless communications. The continuous gradient index is nevertheless difficult to practically realize. We show that graded photonic crystals make it possible to get the radially graded index of the Maxwell fish-eye and that the designed graded photonic crystals exhibit the expected properties. Graded photonic crystals fit the requirements of graded index optics. Moreover, they can be scaled with the wavelength.