Fast processing of large amounts of data has become increasingly important in a technologically demanding world. Nanoscale optics may bring new solutions into this arena. In 2004, we have presented one such application: a new paradigm for performing mathematical operations, using wave evolution in specially designed metamaterials.
In our vision for wave-based “metamaterial analog computation,” an input wave with a given spatial profile propagates through an artificial material block designed to execute a specific mathematical operation, such as differentiation, and emerges at the output with its profile changed into the result of the desired operation. We have proposed two paths for this “photonic calculus”: 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. More recently, we have also explored time-varying platforms.
We have shown, theoretically and numerically, that light-matter interaction can be tailored to “do math with light.” These concepts have resonated in the research community, and have been validated experimentally. Such wave-based photonic calculus may open new avenues for handling and processing large data sets with unprecedented speed.