The orbital angular momentum of light represents a fundamentally new optical degree of freedom. Unlike linear momentum, or spin angular momentum, which is associated with the polarization of light, orbital angular momentum arises as a subtler and more complex consequence of the spatial distribution of the intensity and phase of an optical field — even down to the single photon limit. Consequently, researchers have only begun to appreciate its implications for our understanding of the many ways in which light and matter can interact, or its practical potential for quantum information applications. This article reviews some of the landmark advances in the study and use of the orbital angular momentum of photons, and in particular its potential for realizing high-dimensional quantum spaces.Peer ReviewedPostprint (published version

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.

We put forward schemes to prepare photons in multi-dimensional vector states of orbital angular momentum. We show realizable light distributions that yield prescribed states with finite or infinite normal modes. In particular, we show that suitable light vortex-pancakes allow the add-drop of specific vector projections. We suggest that such photons might allow the generation of engineered quNits in multi-dimensional quantum information systems.