Programmable pixel-mode linear interferometers using multi-plane light conversion

Programmable linear optical interferometers are a core primitive in optical signal processing, quantum information processing, and photonic computing. Existing photonic-integrated implementations realize arbitrary M-mode unitaries using Mach--Zehnder-interferometer meshes whose footprint and accumulated loss scale with O\(M²\) optical components. Here we analyze and experimentally demonstrate a programmable architecture for implementing linear optical transformations directly on spatially tiled free-space pixel modes using multi-plane light conversion (MPLC). In this architecture, M spatial modes arranged on a transverse lattice undergo a unitary transformation and are mapped to M output modes of identical geometry through a sequence of programmable phase masks separated by free-space propagation segments. Numerical simulations show that arbitrary M-mode unitaries can be compiled to a desired high fidelity using a number of phase planes that scales approximately linearly with M. Using a spatial-light-modulator-based MPLC, we experimentally demonstrate programmable interferometers acting on up to 16 spatial pixel modes, including tunable beamsplitters, Hadamard unitaries, spatial permutations, boosted-Bell-measurement unitaries, and partial unitaries on select subsets of modes. These results establish MPLC-based pixel-mode interferometers as a promising architecture for programmable linear optics with applications in classical and quantum optical interconnects, photonic switching, and quantum information processing.