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Photonic computing has the potential to harness the full degrees of freedom (DOFs) of the light field, including the wavelength, spatial mode, spatial location, phase quadrature, and polarization, to achieve a higher level of computing parallelism and scalability than digital electronic processors. While multiplexing using the wavelength and other DOFs can be readily integrated on silicon photonics platforms with compact footprints, conventional mode-division multiplexed (MDM) photonic designs occupy areas exceeding tens to hundreds of microns for a few spatial modes, significantly limiting their scalability. Here, we utilize inverse design to demonstrate an ultracompact photonic computing core that calculates vector dot products based on MDM coherent mixing. Our dot-product core integrates the functionalities of two-mode multiplexers and one multimode coherent mixer within a nominal footprint of 5  μm×3  μm. We have experimentally demonstrated computing examples on the fabricated dot-product core, including complex number multiplication and motion estimation using optical flow. The compact dot-product core design enables large-scale on-chip integration in a parallel photonic computing primitive cluster for high-throughput scientific computing and computer vision tasks. 

Photonic computing has potential advantages in speed and energy consumption yet is subject to inaccuracy due to the limited equivalent bitwidth of the analog signal. In this Letter, we demonstrate a configurable, fixed-point coherent photonic iterative solver for numerical eigenvalue problems using shifted inverse iteration. The photonic primitive can accommodate arbitrarily sized sparse matrix–vector multiplication and is deployed to solve eigenmodes in a photonic waveguide structure. The photonic iterative eigensolver does not accumulate errors from each iteration, providing a path toward implementing scientific computing applications on photonic primitives. 

Computational imaging systems with embedded processing have potential advantages in power consumption, computing speed, and cost. However, common processors in embedded vision systems have limited computing capacity and low level of parallelism. The widely used iterative algorithms for image reconstruction rely on floating-point processors to ensure calculation precision, which require more computing resources than fixed-point processors. Here we present a regularized Landweber fixed-point iterative solver for image reconstruction, implemented on a field programmable gated array (FPGA). Compared with floating-point embedded uniprocessors, iterative solvers implemented on the fixed-point FPGA gain 1 to 2 orders of magnitude acceleration, while achieving the same reconstruction accuracy in comparable number of effective iterations. Specifically, we have demonstrated the proposed fixed-point iterative solver in fiber borescope image reconstruction, successfully correcting the artifacts introduced by the lenses and fiber bundle.