Collimating lenses from non-Euclidean transformation optics

Based on the non-Euclidean transformation optics, we design a thin metamaterial lens that can achieve wide-beam radiation by embedding a simple source (a point source in three-dimensional case or a line current source in two-dimensional case). The scheme is performed on a layer-by-layer geometry to convert curved surfaces in virtual space to flat sheets, which pile up and form the entire lens in physical space. Compared to previous designs, the lens has no extreme material parameters. Simulation results confirm its functionality.