Advanced Optical Metamaterials

Optical metamaterials have the potential to control the flow of light at will, which, in the long term, may lead to spectacular applications as a 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 geometry. Here, we lift these limitations in a twofold way. Methodically, we suggest a procedure to design metamaterials with a predefined characteristic of light propagation. Optically, we show thatmetamaterials can be optimized such that they exhibit either an isotropic response or permit diffractionless propagation. Metamaterials are usually characterized deriving their optical properties from the geometry of the subwavelength unit cells rather than from the materials they consist of, attaining an effective permittivity eeff(v) or permeability meff(v) not accessible by naturally occurring materials. In particular, a sufficient condition for the existence of left-handed waves (the wave vector k is antiparallel to the Poynting vector S) as eigenmodes in this material is that the real part of both effective parameters is negative. Then, at normal incidence an effective refractive index may be introduced, which attains negative values, e.g., n1⁄4 1. Frequently, it is then concluded that such a metamaterial might be employed as a perfect lens. But this conclusion implicitly assumes that this effective index is invariant for all propagating and evanescent waves. However, for all current metamaterials designed to operate at optical frequencies this requirement is not fulfilled; thus, most metamaterials performworse than an ordinary lens, since even in the long wavelength limit their refraction, diffraction, and absorption properties are anisotropic. In this case, one appropriately has to resort to quantities to be derived from the isofrequency surface v 1⁄4 vðkx; ky; kzÞ 1⁄4 const: of the dispersion relation, such as refraction ( @kz=@kx;y) and diffraction coefficients ( @kz=@kx;y). [11] Indeed, characterizing the properties of artificial bulk materials in terms of their dispersion relation is a standard technique, i.e., for photonic crystals, but it is rather exotic when