Optimized focusing properties of photonic crystal slabs

We propose an optimization procedure for focusing operation in finite two dimensional photonic crystal slabs. The device consists of a triangular lattice air holes etched in a semiconductor matrix at a nanometer scale to operate at 1.55 μm. To reach simultaneously an effective refractive index equal to −1 along with a very high transmission coefficient whatever optical wave incidence, the parameters as the lattice period and/or filling factor are precisely adjusted depending on the slab thickness. The method relies on Fabry-Perot resonances engineering in the air/crystal/air cavity constituting the lens.