Measurement of the angle-angular momentum uncertainty of a light beam

The summary form only given. One of the many forms of the uncertainty principle concerns angular position and angular momentum. We demonstrate this in the case of light: the more the angular position of a light beam is restricted by passing it through a radial aperture, the larger the spread in the beam's angular-momentum components. We prepare laser beams in different angular momentum states by reflecting them from a phase hologram, which determines the orbital-angular-momentum state, and passing them through a quarter-wave plate, which determines the spin state. We can measure the angular-momentum components in the beam in the form of resonances of a novel beam-rotating ring resonator. Our results are in broad agreement with the predictions of the uncertainty principle.