Non-reciprocal space-time gratings

Reciprocity is a desired property in many wave applications. Nevertheless, sometimes we would like to be able to violate reciprocity, and in the extreme case design devices such as isolators or circulators. This ability is rather mature at radio-frequencies, where one usually utilizes the gyrotropic property of rare-earth materials in order to break reciprocity. Unfortunately, an extension of such techniques into the optical regime is challenging if not impossible due to changes in the properties of gyrotropic materials at these frequencies. Therefore, a different methodology should be followed. According to Lorentz reciprocity theorem, a structure is reciprocal if it is linear, time-invariant structure and if it is made of symmetric materials (ε= ε^T, μ = μ^T). Thus, in order to break reciprocity, except for using gyrotropic materials, one may use either non-linear or time dependent materials.