Engineering the point spread function of layered metamaterials

Layered metal-dielectric metamaterials have filtering properties both in the frequency domain and in the spatial frequency domain. Engineering their spatial filtering response is a way of designing structures with specific diffraction properties for such applications as sub-diffraction imaging, supercollimation, or optical signal processing at the nanoscale. In this paper we review the recent progress in this field. We also present a numerical optimization framework for layered metamaterials, based on the use of evolutionary algorithms. A measure of similarity obtained using Hölder's inequality is adapted to construct the overall criterion function. We analyze the influence of surface roughness on the quality of imaging.