Utilizing phase delays of an integrated pixel-array structure to generate orbital-angular-momentum beams with tunable orders and a broad bandwidth

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 h 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).