Programmable Multidimensional Diffraction Engineering via an Optically Addressed Nested Fourier Metasurface.

Free-space optical routing and programmable Fourier optical processing are promising for next-generation photonic information systems. Here, we propose an optically addressed nested Fourier metasurface (OA-NFM) platform for dynamically switchable, multidimensional optical routing and diffraction-channel engineering without dense electrical interconnects. By integrating a Fourier-coefficient-based inverse-design method with a nested Fourier metasurface architecture, the proposed platform enables simultaneous control of diffraction channels and polarization states. By spatially multiplexing Fourier-engineered mode regions within nested supercells and activating them through digital light processing (DLP)-based optical addressing, the OA-NFM achieves programmable momentum-space redistribution, sideband clustering, and angular-channel engineering via controllable superlattice diffraction. The local Fourier mode defines the target diffraction response, while the global nested array factor controls the angular distribution of clustered sidebands. Simulations show that individually optimized modes achieve diffraction efficiencies up to 45% with polarization fidelities above 0.99. The OA-NFM achieves diffraction efficiencies up to 37% within the ± 1.1° receiver window, excluding losses from the DMD and projection optics. NRZ-OOK simulations confirm BERs below the hard-decision FEC threshold (10-3) at 25 Gbps across the 1500-1600 nm band. This work demonstrates a promising platform for optical switching, free-space routing, and multidimensional photonic information processing.