Time Varying Metasurfaces: using rapidly varying components for arbitrary wave transformations.

Metamaterials and metasurfaces are specially structured matter, structured on a small enough scale to change its macroscopic properties.

Periodically patterning a surface, for instance with metal and dielectric yields a 'metasurface' that can behave as neither of its constituents: e.g. as an effective "artificial" magnetic conductor [1].

As is now well established, slowly grading this structuring can then give additional functionality, the material acting as e.g. a flat lens [2], or a component of an optical computer [3].

Grading a metamaterial in all three dimensions then allows almost arbitrary transformations of the electromagnetic field; from invisibility [3] to super-scattering.