Studying Focusing Properties of Graded Index Photonic Crystals Made of Material with Different Refractive Index

In this paper we investigate focusing properties of graded index (GRIN) photonic crystal (PC) structures which are composed of different materials with different refractive indices. GRIN PC structure is constructed from air holes in dielectric background. The holes radii are varied in the normal direction to the propagation in such a way that a parabolic effective refractive index is produced. The focusing characteristic is studied relative to the refractive index variation of background material. While increasing refractive index of background material of the GRIN PC structure, the effective refractive index of the structure increases. With increasing effective refractive index, the focusing capability of the GRIN PC structure increase and outgoing wave at focal point will be more concentrated. The result shows that the designed GRIN PC structure work very well as a focusing lens. The finite-difference time-domain (FDTD) method was employed to compute field propagation through GRIN PC structure. Also, plane wave expansion (PWE) method has been carried out to extract the dispersion properties.