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Merging the concept of metamaterials with the nanophotonics platform brings new functionalities to the science and technology of both fields. Since photons are usually controlled by materials, metamaterials have provided interesting platforms for engineering light-matter interaction. In recent years, a variety of features and exciting applications of meso-, micro-, and nanoscale metamaterials have been explored and developed. One of these applications is the development of material-based wave-based analog computing machines, which we are investigating in my group. We have designed material structures that can perform mathematical operations as waves propagate through them. Such materials have effectively become computing machines. For example, we have explored metastructures that can solve integral and differential equations and can invert matrices using waves as incoming waves interact with them. Moreover, we have also been investigating how collections of other photonic networks (such as the Mach-Zehnder interferometers), either by themselves or together with metamaterials, can provide another light-based method for solving equations and performing mathematical operations with light. In this talk, I will discuss the most recent results in some of our ongoing research programs on this topic, will present physical insights into these results, and will forecast future research directions in this area.
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