Vahid Nikkhah

In recent years, wave‐based analog computing has been at the center of attention for providing ultra‐fast and power‐efficient signal processing enabled by wave propagation through artificially engineered structures. Building on these structures, various proposals have been put forward for performing computations with waves. Most of these proposals have been aimed at linear operations, such as vector‐matrix multiplications. The weak and hardly controllable nonlinear response of electromagnetic materials imposes challenges in the design of wave‐based structures for performing nonlinear operations. In the present work, first, by using the method of inverse design we propose a three‐port device, which consists of a combination of linear and Kerr nonlinear materials, exhibiting the desired power‐dependent transmission properties. Then, combining a proper arrangement of such devices with a collection of Mach–Zehnder interferometers (MZIs), we propose a reconfigurable nonlinear optical architecture capable of implementing a variety of nonlinear functions of the input signal. The proposed device may pave the way for wave‐based reconfigurable nonlinear signal processing that can be combined with linear networks for full‐fledged wave‐based analog computing.

As standard microelectronic technology approaches fundamental limitations in speed and power consumption, novel computing strategies are strongly needed. Analog optical computing enables processing large amounts of data at a negligible energy cost and high speeds. Based on these principles, ultrathin optical metasurfaces have been recently explored to process large images in real-time, in particular for edge detection. By incorporating feedback, it has also been recently shown that metamaterials can be tailored to solve complex mathematical problems in the analog domain, although these efforts have so far been limited to guided-wave systems and bulky setups. Here, we present an ultrathin Si metasurface-based platform for analog computing that is able to solve Fredholm integral equations of the second kind using free-space visible radiation. A Si-based metagrating was inverse-designed to implement the scattering matrix synthesizing a prescribed Kernel corresponding to the mathematical problem of interest. Next, a semi-transparent mirror was incorporated into the sample to provide adequate feedback and thus perform the required Neumann series, solving the corresponding equation in the analog domain at the speed of light. Visible wavelength operation enables a highly compact, ultrathin device that can be interrogated from free-space, implying high processing speeds and the possibility of on-chip integration.

We present a metasurface-based platform that solves Fredholm integral equations of the second kind for free-space radiation. An inverse-designed metagrating is coupled to a semitransparent mirror providing feedback in order to perform an analog version of the Neumann series.