Gradient-Based Optimization of Optical Vortex Beam Emitters

Vortex beams are stable solutions of Maxwell's equations that carry phase singularities and orbital angular momentum, unique properties that give rise to many applications in the basic sciences, optical communications, and quantum technologies. Scalable integration and fabrication of vortex beam emitters will allow these applications to flourish and enable new applications not possible with traditional optics. Here we present a general framework to generate integrated vortex beam emitters using photonic inverse design. We experimentally demonstrate generation of vortex beams with angular momentum spanning -3$\hbar$ to 3$\hbar$. We show the generality of this design procedure by designing a vortex beam multiplexer capable of exciting a custom vortex beam fiber. Finally, we produce foundry-fabricated beam emitters with wide-bandwidths and high-efficiencies that take advantage of a multi-layer heterogeneous integration.