%0 Journal Article
%A Silva, Alexandre
%A Monticone, Francesco
%A Castaldi, Giuseppe
%A Galdi, Vincenzo
%A Alù, Andrea
%A Engheta, Nader
%T Performing Mathematical Operations with Metamaterials
%D 2014
%R 10.1126/science.1242818
%J Science
%P 160-163
%V 343
%N 6167
%X Optical signal processing of light waves can represent certain mathematical functions and perform computational tasks on signals or images in an analog fashion. However, the complex systems of lenses and filters required are bulky. Metamaterials can perform similar optical processing operations but with materials that need only be a wavelength thick. Silva et al. (p. 160; see the Perspective by Sihvola) present a simulation study that shows how an architecture based on such metamaterials can be designed to perform a suite of mathematical functions to create ultrathin optical signal and data processors. We introduce the concept of metamaterial analog computing, based on suitably designed metamaterial blocks that can perform mathematical operations (such as spatial differentiation, integration, or convolution) on the profile of an impinging wave as it propagates through these blocks. Two approaches are presented to achieve such functionality: (i) subwavelength structured metascreens combined with graded-index waveguides and (ii) multilayered slabs designed to achieve a desired spatial Green’s function. Both techniques offer the possibility of miniaturized, potentially integrable, wave-based computing systems that are thinner than conventional lens-based optical signal and data processors by several orders of magnitude.
%U https://science.sciencemag.org/content/sci/343/6167/160.full.pdf