Analog signal processing with nonlinear nonlocal flat optics

Digital signal processing has significantly impacted a variety of scientific and engineering domains, yet faces constraints such as complexity and power consumption, primarily attributed to analog-to-digital converters. To address these challenges, optical analog computing has recently emerged as a promising solution. Recent advancements in flat optics devices unveil the potential for real time data processing with minimal power consumption and spatial footprint. To date, most achievements in analog signal processing have been realized through linear optics. Extending these capabilities to nonlinear optics offers even greater potential. Here, we demonstrate the synthesis of Volterra kernels with flat optics devices that leverage the inherent nonlocality of the nonlinear response. We delve into the potential applications of nonlinear nonlocal flat-optics, including nonlinear edge detection for image processing and vector-vortex beam generation, pivotal in the fields of optical communications and optical sensing. We demonstrate the feasibility of nonlinear signal processing, as well as nonlinear spin-orbit coupling, in a very simple setup, made of a single thin film with second-order nonlinear susceptibility. Our findings contribute to the advancement of active, nonlinear, and quantum photonic devices, offering new avenues for signal processing and beam generation technologies.