Isotropic and non-diffracting optical metamaterials

Optical metamaterials have the potential to control the flow of light at will which may lead to spectacular applications as the perfect lens or the cloaking device. Both of these optical elements require invariant effective material properties (permittivity, permeability) for all spatial frequencies involved in the imaging process. However, it turned out that due to the mesoscopic nature of current metamaterials spatial dispersion prevents to meet this requirement; rendering them far away from being applicable for the purpose of imaging. A solution to this problem is not straightforwardly at hand since metamaterials are usually designed in forward direction; implying that the optical properties are only evaluated for a specific metamaterial. Here we lift these limitations. Methodically, we suggest a procedure to design metamaterials with a predefined characteristic of light propagation. Optically, we show that metamaterials can be optimized such that they exhibit either an isotropic response or permit diffractionless propagation.