Linear Sub-Diffraction Spatial Filtering with Plasmonic Materials

We optimise the transfer function of layered metal-dielectric metamaterials for imaging with sub-wavelength resolution, for high-pass spatial filtering, and for diffraction compensation. A variant of a genetic algorithm is used to optimise the metamaterial. The optimisation criteria include transmission, and reflection coefficients averaged over a range of spatial frequencies, and a measure of similarity between the optimised and desired transfer function. This measure is normalised using the Holder's inequality and is invariant to scaling by a multiplicative complex factor. The overall criterion is a linear combination of these three basic criteria.