Analog log-polar transformation with nonlinear flat optics

Image processing is crucial for extracting quantitative information and enhancing image quality, supporting precise analysis in scientific research. Analog optical image processing enables real-time, high-speed, energy-efficient operations but is limited to the linear regime, restricting advanced functionalities beyond conventional Fourier optics. Additionally, designing nonlocal metasurfaces for sophisticated tasks involves complex inverse-design methods and fabrication constraints. Here, we demonstrate both theoretically and experimentally, how the nonlinear response of a thin GaAs film can be tailored non-invasively to emulate a nonlocal metasurface, performing advanced image processing operations such as log-polar transformations for scale- and rotation-invariant processing without complex metasurface design. This is achieved by structuring the spatial profile of an external beam projected onto the nonlinear film. Our approach simplifies the design process, enhances precision, and paves the way for leveraging nonlinear flat optics in all-optical analog computing. It also enables new possibilities for broadband, polarization-selective, and reconfigurable image processing.