Theoretical model for angular grating-based integrated optical vortex beam emitters

We develop a theoretical model for the recently reported integrated optical vortex beam emitters that incorporate angular gratings in microring resonators. Using azimuthally polarized dipole oscillators to represent emissions scattered from the grating elements that are located along the inner wall of the ring waveguide, we obtain expressions for far-field components under the paraxial approximation. The results show that the emission is of the form of cylindrical vector Bessel beams with exactly defined optical orbital angular momentum, and can have azimuthal, radial, and longitudinal field components after propagation. The calculation results for field distributions in both near and far zone agree well with the experimental results.