Programmable unitary on dense spatially-tiled pixel-mode array with multi-plane light conversion

Programmable linear unitary transformations on arrays of spatially localized optical modes is leading a paradigm shift in photonic quantum computing, optical neural networks, and segmented-aperture interferometry. We show that multi-plane light conversion (MPLC)—a widely studied technique for spatial-mode transformations—can implement such unitaries across spatially tiled "pixel modes" upon Rayleigh–Sommerfeld diffraction theory. This approach enables programmable linear optics with a far more compact form factor than integrated waveguide arrays, and allows cascading or parallelizing standard n×m pixel-mode unitaries as building blocks. We analyze realizations of known unitaries and study how loss and crosstalk scale with plane number, spacing, and intermediate field bulge, and highlight applications in photonic quantum computing (e.g., cluster-state stitching) and super-additive optical communications.