Creating well-defined orbital angular momentum states with a random turbulent medium

Previous work by Allen, demonstrated that optical beams possess orbital angular momentum. Other work has shown that a random, phase-only disturbance can impart ± 1 orbital angular momentum states to propagating waves. However, the field preceding the formation of these ± 1 states was unknown. In this paper, we identify the unique field that leads to the formation of a pair of branch points, indicators of orbital angular momentum. This field is then verified in a bench-top optical experiment.