Metal-dielectric layered metamaterials for sub-diffraction spatial filtering of the optical wavefront

Propagation of light through layered metamaterials consisting of a stack of optically linear metal and dielectric slabs may be described as linear spatial filtering. Depending on the point spread function, the metamaterial can be applied for sub-diffraction spatial filtering or for classical filtering operations on the wavefront. We optimize the metamaterial with respect to the shape of the complex amplitude transfer function, the average transmission coefficient and to average reflections. A measure of similarity obtained using the Hölder´s inequality is adapted to construct a criterion function. Optimization is conducted using a variant of genetic algorithm. In particular, the metamaterial´s transfer function is optimized for high-pass filtering. The metamaterial can be then applied to modify the contrast of the object or to introduce a phase-contrast.