 Metamaterial models appear to be useful for non-trivial models such as 3D de Sitter space with one compactified dimension, 2D de Sitter space with two compactified dimensions, 4D de Sitter dS4, and anti-de Sitter AdS4 spaces.Transformation optics is employed to increase capabilities of gradient index lenses.Optical elements (lenses) perform a variety of functions, ranging from image formation, to light projection or light collection.