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Harnessing multimode waves allows high information capacity through modalexpansions. Although passive multimode devices including waveguides, couplers,and multiplexers have been demonstrated for broadband responses in momentum orfrequency domains, collective switching of multimodes remains a challenge, dueto the difficulty in imposing consistent dynamics on all eigenmodes. Here weovercome this limitation by realizing digital switching of spatially randomwaves, based on supersymmetric pairs of multimode potentials. We reveal thatsupersymmetric transformations of any parity-symmetric potential derive theparity reversal of all eigenmodes, which allows the complete isolation ofrandom waves at the 'off' state. Building blocks for binary and many-valuedlogics are then demonstrated for random waves: a harmonic pair for binaryswitching of arbitrary wavefronts and a P\"oschl-Teller pair for multi-levelswitching which implements the fuzzy membership function. Our resultsestablishing global phase matching conditions for multimode dynamics will laythe foundation of multi-channel digital photonics.

Digital building blocks for controlling random waves based on supersymmetry