Design of flat graded index lenses using dielectric Graded Photonic Crystals

• We report on the design of a graded index photonic lens.
• The effective index is extracted from the dispersion relation of Photonic Crystals.
• The filling factor of a Graded Photonic Crystal is engineered.
• Our method of extraction of the effective index is valid for any photonic band.

We designed graded index lenses using Graded Photonic Crystals which behave as Linear Homogeneous Isotropic medium at the scale of the elementary cell. In that aim, we extracted the effective index of Photonic Crystals from their relation of dispersion which is in the form of a band structure. Thereby, we shaped the profile of the effective index of the Graded Photonic Crystals so that they operate as graded index lenses. These lenses focus an incident plane wave and collimate the wave issued from a point source. Their thickness is about a wavelength, which demonstrates the efficiency of Graded Photonic Crystals for photonic devices, from microwave range to the optical domain.