The term “material world” refers in some contexts to the limitations of our will, the wall on which ideas crash to become just reality. And yet materials are – with all their imperfections – one of the ultimate fabrics for testing our thoughts. Fortunately, between the world of pure ideas and the actual material reality, there exists an exciting third region: the region of possibilities. This region is occupied by materials not forbidden by Nature that, however, do not actually occur (or occur very rarely). It contains everything we can soundly think of, but that is too odd as to have been inspected by Nature. A family of such entities is formed by what is termed “metamaterials.”

Optical metamaterials are man-made materials whose peculiar properties emerge from an artificial inner structure, carefully crafted at the nanoscale. It is possible (yet not easy) to produce materials whose fine structure tricks visible light to bend in unconventional (yet not impossible) ways. These severe alterations of the refraction properties of a material might produce supermagnifying lenses – with enough power to see directly a DNA chain – or even guide the trajectory of light around an object and render it invisible: light would illuminate the metamaterial covering the object and travel along it to emerge to our eyes in the same direction and carrying the same information it had prior to illumination. No reflection, no absorption: a true invisibility cloak.

Such response of light to structure is possible because light is an electromagnetic wave. Indeed light, as described by Maxwell's laws, consists of an electric field and a magnetic field whose spatiotemporal variations are related to each other, to their sources, and to the characteristics of the medium through which it propagates. If the “tricks” introduced in the structure of the material are smaller than the wavelength of light, then, although microscopically the passage of light through the material is extremely intricate, macroscopically it can be described in terms of the new characteristics of the effective medium, that turn out to be extraordinary. Invisibility cloaks and supermagnifying lenses, although amazing, are still in their infancy.