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We study the relationship between the input phase delays and the output mode orders when using a pixel-array structure fed by multiple single-mode waveguides for tunable orbital-angular-momentum (OAM) beam generation. As an emitter of a free-space OAM beam, the designed structure introduces a transformation function that shapes and coherently combines multiple (e.g., four) equal-amplitude inputs, with the kth input carrying a phase delay of (k−1)Δφ. The simulation results show that (1) the generated OAM order ? is dependent on the relative phase delay Δφ; (2) the transformation function can be tailored by engineering the structure to support different tunable ranges (e.g., l={−1},{−1,+1},{−1,0,+1}, or {−2,−1,+1,+2}); and (3) multiple independent coaxial OAM beams can be generated by simultaneously feeding the structure with multiple independent beams, such that each beam has its own Δφ value for the …