Beams of light carrying orbital angular momentum, such as vortex beams, have many applications in imaging and micromanipulation. We focus on applications in communication, in particular for quantum key distribution, where the security of communication channels is enhanced with the laws of quantum mechanics. However, this procedure requires superpositions of vortex beams. We want to generate such beams using integrated optics components due to their small size and their advantages in scalability and stability. Angular gratings, which are ring resonators with an embedded Bragg grating, are integrated structures known to generate vortex beams. We propose that a ring resonator with two embedded Bragg gratings, each on the inner and outer sidewalls, would generate a superposition of vortex beams. We verify this claim through analytical models, simulations and experiments.