Devices based on metamaterial structures to guide and manipulate light, other electromagnetic radiation and acoustic waves. For example, a lens can include a metamaterial structure comprising nano structures of metallic and dielectric materials; and a plasmonic waveguide coupler formed over the metamaterial structure for coupling electromagnetic radiation to or from metamaterial structure. The metamaterial structure has an anisotropic structure and the plasmonic waveguide coupler is structured to include metal and non-metal parts to support surface plasmon polaritons and to cause different phase delays at different locations of an interface with the metamaterial structure in a way that the metamaterial structure and the plasmonic waveguide coupler effect a lens for performing a Fourier transform of the electromagnetic radiation coupled between the metamaterial structure and the plasmonic waveguide coupler.