Optical vortices, angular momentum, and Heisenberg's uncertainty relationship

Light beams with helical phasefronts are characterized by an azimuthal phase. The centre of these beams is often termed an optical vortex and the surrounding annulus of high intensity carries an orbital angular momentum with a ratio between angular momentum and energy corresponding to per photon. Such beams can induce rotation in microscopic objects and, when they are rotated, undergo a frequency shift. The light’s orbital angular momentum is a valid description and measurement on both a macroscopic scale and at the level of single photons. Most recently, orbital angular momentum has been shown to be subject to an uncertainty relationship between angular momentum and angular position.