Integration of holograms into multimode waveguides allows the implementation of arbitrary unitary mode transformations and unitary matrix-vector multiplication. Theoretical analysis is used to justify a design approach to implement specific functions in these devices. Based on this approach, a compact mode-order converter, a Hadamard transformer, and a spatial pattern generator-correlator are proposed and analyzed. Beam propagation simulations are used to verify the theoretical calculations and

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... to address bandwidth, scalability, and fabrication criteria. Optical pattern generators were successfully fabricated using standard photolithographic techniques to demonstrate the feasibility of the devices.