Focussing light through a stack of toroidal channels in PMMA

We propose a transformational design of an axi-symmetric gradient lens for electromagnetic waves. We show that a metamaterial consisting of toroidal air channels of diameters ranging from 23 nm to 190 nm in a matrix of Polymethylmethacrylate (PMMA) allows for a focussing effect of light over a large bandwidth i.e. [600-1000] nm. We finally propose a simplified design of lens allowing for a two-photon lithography implementation.