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Abstract 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. 

Wave-based analog computing in the forms of inversedesigned metastructures and the meshes of Mach−Zehnder interferometers (MZI) have recently received considerable attention due to their capability in emulating linear operators, performing vector-matrix multiplication, inverting matrices, and solving integral and differential equations via electromagnetic wave interaction and manipulation in such structures. Here, we combine these two platforms to propose a wave-based metadevice that can compute scattered fields in electromagnetic forward scattering problems. The proposed device consists of two subsystems: a set of reconfigurable couplers with a proper feedback system and an inverse-designed inhomogeneous material block. The first subsystem computes the magnitude and phase of the dipole polarization induced in the scatterers when illuminated with a given incident wave (matrix inversion). The second subsystem computes the magnitude and phase of the scattered fields at given detection points (vector-matrix multiplication). We discuss the functionality of this metadevice, and through several examples, we theoretically evaluate its performance by comparing the simulation results of this device with fullwave numerical simulations and numerically evaluated matrix inversion. We also highlight that since the first section is reconfigurable, the proposed device can be used for different permittivity distributions of the scatterer and incident excitations without changing the inverse-designed section. Our proposed device may provide a versatile platform for rapid computation in various scattering scenarios.