Effective index approximation method for Graded Photonic Crystals slabs: precise design of a Mikaelian lens

In this article, we propose an effective index approximation to precisely engineer the effective index of 2D Photonic Crystal slab with a subwavelength lattice period. This procedure is firstly tested on a standard Silicon-on-Insulator platform, and compared with the Bloch modes effective index calculated by 3D FDTD and the results are in good agreement. This method is further applied to design a perfect optical system: the Mikaelian lens. It is implemented via a Graded Photonic Crystal, that operates at 1.55 µm. The focal plane of the designed Mikaelian lens is correctly located and its focus spot is near-diffractionlimited (FWHM=0.383λ0), validating the approximation method. The latter can be widely applied to subwavelength 2D Photonic Crystals slab systems that require precise refractive index control, notably GRaded INdex photonic components and wave coupling components. These are particularly suitable for Photonic Integrated Circuits, especially in Silicon Photonics.