Modal properties of a beam carrying OAM generated by a circular array of multiple ring-resonator emitters

We investigate the modal properties of a beam carrying orbital angular momentum (OAM) generated by a circular array (ring) of multiple micro-ring emitters (rings) analytically and via simulation. In such a "ring-of-rings" structure, N emitters generate N optical vortex beams with the same OAM-order l₀ at the same wavelength. The output beam is a coherent combination of the N vortex beams located at different azimuthal positions, having the same radial displacement. We derive an analytical expression for the output optical field and calculate the OAM-order power spectrum of the generated beam. The analytical expression and simulation results show that (1) the OAM spectrum of the output beam composes equidistant OAM spectral components, symmetrically surrounding l₀ with a spacing equal to N; (2) the envelope of the OAM spectrum broadens with an increased radius of the circular array or the value of l₀; and (3) the OAM components of the generated beam could be tuned either by changing the value of l₀, corresponding to different spectrum envelopes, or by adding different linear phase delays to the micro-ring emitters, which does not affect the envelope of the OAM spectrum.