Perfect cylindrical lenses

A slab of negatively refracting material is known to focus light and if 1 n = the focussing will be perfect, producing an image which is an exact replica of the object. Magnifying the image requires a new design concept in which the surface of the negatively refracting lens is curved. Here we show how a hollow cylinder of material can be designed to magnify an image but otherwise with the same perfection as the original lens. Curvature requires that epsilon and mu are now a function of position.