In collaboration with the Groups led by Nader Engheta (University of Pennsylvania) and Andrea Alù (University of Texas at Austin), we have put forward a general paradigm of “metamaterial analog computing” [1], in which properly designed metamaterial blocks may perform ubiquitous mathematical operations, such as spatial differentiation, integration or convolution, on the profile of the impinging light as it propagates through them (see the conceptual schematic in the figure top panel).

Our idea is inspired by the earlier “calculating machines” in the form of mechanical, electronic, and hybrid analog computers, which have been designed in the past to perform prescribed mathematical computations. These solutions suffered from substantial limitations, including relatively large size and slow response, and were quickly dropped with the advances on digital computers.

The figure bottom panel illustrates a possible application of our proposed “computational metamaterials” as a Laplace filter for edge detection, an increasingly common image processing technique that helps software find faces and identify objects in pictures.

These structures may be of subwavelength size, and several orders of magnitude smaller than conventional lens-based optical signal processing systems. In particular, we have proposed two possible architectures: specially designed subwavelength metasurfaces that operate in the spatial Fourier domain, combined with graded-index (GRIN) slabs or fibers; and layered metamaterials that engineer the desired operator’s Green’s function directly in the space domain.

These results (included as one of the Highlights in Optics in 2014 in “Optics & Photonics News”) may pave the way to a re-birth of optical analog computers, but at the nanoscale, entirely wave-based, integrable with nanophotonics and electronic, with potentially disruptive applications to several fields of science and engineering.

A particularly intriguing follow-up would be the design of metadevices capable of solving differential and/or integral equations.

## Relevant papers

- Silva, A., Monticone, F., Castaldi, G., Galdi, V., Alù, A., & Engheta, N. (2014). Performing mathematical operations with metamaterials.
*Science**343*(6167), 160–163.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.

@article{IJ109_Science_343_160_2014, author = {Silva, Alexandre and Monticone, Francesco and Castaldi, Giuseppe and Galdi, Vincenzo and Al{\`u}, Andrea and Engheta, Nader}, title = {{Performing mathematical operations with metamaterials}}, journal = {Science}, doi = {10.1126/science.1242818}, year = {2014}, volume = {343}, number = {6167}, pages = {160--163}, month = jan, note = {/assets/papers/IJ109_Science_343_160_2014_SM.pdf} }