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.
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