Sub-diffraction linear spatial filtering with layered metamaterials

We describe layered metal-insulator metamaterials using the model of a linear-shift-invariant system. We present the modelling and optimisation strategy for engineering such metamaterials. A variety of point spread functions may be reached, either for superresolution, or for far-field image processing. The first group includes layered superlenses and effective media for directed refraction. As an example of the latter, we demonstrate a metamaterial consisting of highly reflecting cavities coupled to form a high-pass spatial filter. The proposed filter can be applied for phase visualisation.