A metamaterial having a negative refractive index is presented, which has a dielectric carrier material (12; 48), first electrically conductive sections (14.1, 14.2, 14.3, 14.4) and second electrically conductive sections (16.1, 16.2). The metamaterial is distinguished by the fact that the dielectric carrier material (12; 48) is realized as a volume which consists of one piece and which has at least one inner area which is prestructured by positive or negative rib or mesa structures (52.1, 52.2) in the dielectric carrier material (48) and is covered with first sections (14.1, 14.2, 14.3, 14.4) and second sections (16.1, 16.2) in such a way that the first sections form capacitive series impedances upon illumination with an electromagnetic wave having a specific propagation direction and polarization, while the second sections are arranged in such a way that they form inductive shunt impedances upon the illumination. An optical element, a preferred use of a metamaterial and also a method for producing a metamaterial are furthermore presented. The structuring of partial regions of the metamaterial can be effected with the aid of negative/positive mesa structures.