Controlling Random Waves with Digital Building Blocks Based on Supersymmetry

Harnessing multimode waves allows high information capacity through modal expansions. Although passive multimode devices for broadband responses have been demonstrated in momentum or frequency domains, the difficulty in achieving collective manipulation of all eigenmodes has hindered the implementation of digital multimode devices such as switching. Here we propose building blocks for digital switching of spatially random waves based on parity-converted supersymmetric pairs of multimode potentials. We reveal that unbroken supersymmetric transformations of any parity-symmetric potential derive the parity reversal of all eigenmodes, which allows the complete isolation of random waves in the "off" state. With two representative solvable potentials, building blocks for binary and many-valued logics are then demonstrated for random waves: a harmonic pair for binary switching of arbitrary wave fronts and a Pöschl-Teller pair for multilevel switching which implements fuzzy membership functions. Our results realizing the transfer of arbitrary wave fronts between wave elements will lay the foundation of high-bandwidth data processing.