A Fine Point on Light's Angular Momentum

Miles Padgett, Johannes Courtial, and Les Allen have written an interesting review of the angular momentum properties of light (Physics Today, May 2004, page 35). In it, they note that if the spin and orbital components of a circularly polarized and helically phased beam add together to give a nonzero total angular momentum, the resulting beam can act as an optical wrench and cause a transparent particle (they must have meant a partially absorbing particle) to rotate. The authors state that no rotation results if the spin and orbital components cancel each other. Note that in the latter case, if one examines the transverse components of the Poynting vector or linear momentum across the doughnut beam profile, one finds that these vectors are still present but point in one annular direction on the inner side and in the opposite annular direction on the outer side of the annular intensity profile. Thus they cancel out in total. I suppose this phenomenon might be thought of as a way to create optical shear and perhaps could even be used as an optical hole cutter, hydraulic stirrer, or bottle-cap remover.

Padgett and Allen reply: In our experiment, the particle was Teflon and had an absorption of a few percent, which meant it could be trapped within optical tweezers. In the review, we called it transparent to contrast it with the earlier work of H. He and coworkers.¹In hindsight, as Anthony Siegman suggests, we should have described it as "slightly, or partially, absorbing."

Both the spin and orbital angular momentum of a beam can always be calculated from the transverse components of linear momentum. This transverse linear momentum arises both from the azimuthal phase gradient (orbital AM) and a combination of the beam's intensity gradient and polarization (spin AM). For circularly polarized annular beams, as Siegman correctly describes, the azimuthal linear momentum from the spin contribution has equal and opposite senses on the inner and outer edges of the ring. As a consequence the particle spins, as shown in Figure 4 of our article. A detailed consideration can be found in reference 2.