  Vortices are topologically stable singularities at the center of a swirl of
energy. Optical vortices are conventionally formed using diffractive optics or
by bespoke optical elements. We report room temperature integrated lasers
directly generating and multiplexing coherent beams carrying arbitrarily large
orbital angular momenta (OAM). The OAM beams are created using two-dimensional
topological-rings formed by circular boundaries between topologically distinct
photonic materials that naturally radiate vortices in the third dimension. We
also demonstrate the planar multiplexing of OAM beams using concentric lasers.
Our experimental demonstration reveals a subtle connection between topological
matter and topological light and provides opportunities in microscopy,
metrology, high-capacity communications, and quantum information processing.
