Demonstrating the Angular Momentum of Light

Giovanni Milione John Noé

Laser Teaching Center, Department of Physics and Astronomy

It has long been known that circular polarized light carries spin angular momentum, and the small mechanical torque due to the absorption of such light was first demonstrated in a sensitive experiment by Beth in 1936. Only much more recently (1992) has it been appreciated that light beams that contain an optical vortex carry /orbital/ angular momentum, or OAM. Unlike spin angular momentum the OAM in a light beam is not restricted to two values, and OAM values of 100 or more have been reported. The wide range of possible OAM values leads to many applications, most notably in optical tweezers.

Optical vortex beams have a phase exp(ilphi) that varies with the azimuthal (clock) angle phi, where l is an integer called the topological charge of the vortex. Such beams have a dark core, since the phase is undefined (singular) at radius r = 0. The helical wavefronts associated with the vortex phase term have the consequence that the Poynting vector S = E x H that describes the direction of energy flow circles around the k vector that describes the direction of propagation. The resulting azimuthal energy flow creates the orbital angular momentum.

Optical vortex beams have been studied in a number of past projects in the Laser Teaching Center, as reported at the 2006 Research Celebration. The emphasis in these projects was on creating the vortex beams and analyzing their phase structure through interferometry. The goal of the current project is somewhat different - to /directly/ demonstrate the angular momentum properties of light.

Optical tweezers are an excellent tool for studying the angular momentum of light through torques exerted on small trapped particles, and a working tweezer setup already exists in the LTC. Moothoo et al. (Am. J. Phys., 2001) have described using a tweezer similar to ours to rotate calcite particles, in a modern version of Beth's experiment. We can create the necessary circular polarized light by successive reflections in two prisms, as described in another poster at this event, or with a cellophane waveplate, as described last year. An alternative approach is to directly detect the azimuthal energy flow, as described in two recent papers. Arlt (J. Mod. Optics, 2003) observed the propagation of an optical vortex beam that has been bisected with a razor blade, while Leach et al. (Optics Express, 2006) used a Shack-Hartmann (SH) wavefront sensor to image the varying wavefront tilt of the beam. While the laboratory has the necessary camera to recreate the first experiment it does not have a SH device. We believe however that it should be possible to make equivalent measurements by sampling portions of the beam using a simple "single-channel" SH sensor mounted on a translation stage.

Giovanni Milione
February 2007
Laser Teaching Center