Implementation of discrete unitary transformations by multimode waveguide holograms

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