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 k th input carrying a phase delay of ( k − 1 ) Δ φ . The simulation results show that (1) the generated OAM order ℓ is dependent on the relative phase delay Δ φ ; (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 Δ φ value for the four inputs. Moreover, there is a trade-off between the tunable range and the mode purity, bandwidth, and crosstalk, such that the increase of the tunable range leads to (a) decreased mode purity (from 91% to 75% for l = − 1 ), (b) decreased 3 dB bandwidth of emission efficiency (from 285 nm for l = { − 1 } to 122 nm for l = { − 2 , − 1 , + 1 , + 2 } ), and (c) increased crosstalk within the C-band (from − 23.7 to − 13.2 d B when the tunable range increases from 2 to 4).