Light-induced rotation of absorbing microscopic particles by transfer of angular momentum from light to the material raises the possibility of optically driven micromachines. The phenomenon has been observed using elliptically polarized laser beams or beams with helical phase structure. But it is difficult to develop high power in such experiments because of overheating and unwanted axial forces, limiting the achievable rotation rates to a few hertz. This problem can in principle be overcome by using transparent particles, transferring angular momentum by a mechanism first observed by Beth in 1936, when he reported a tiny torque developed in a quartz waveplate due to the change in polarization of transmitted light. Here we show that an optical torque can be induced on microscopic birefringent particles of calcite held by optical tweezers. Depending on the polarization of the incident beam, the particles either become aligned with the plane of polarization (and thus can be rotated through specified angles) or spin with constant rotation frequency. Because these microscopic particles are transparent, they can be held in three-dimensional optical traps at very high power without heating. We have observed rotation rates in excess of 350 Hz.Comment: 4 pages, 4 figure

manuscript received pri r rejective articles can be trappe in t e ar d h dark central minimum of a doughnut laser beam d h 1 ram. Such beams carry angular momentum ed usin a hi h efficiency computer generate o ogram. uc d ith the central phase singularity even when linearly due to the h helical wave-front structure associate wit t e cen ra b tion of this angular momentum transferred polarized. rapp Tra ed abso tive particles spin due to a sorp ion o an be reversed b changing the sign of the singularity. from the singularity beam. The direction of spin can e reverse y c a PACS numbers: 42.25.Md, 42.40.My It is well known that a circularly polarized beam carries angular momentum. Each photon of such a beam has the optical angular momentum are hard to observe in most circumstances as they represent extremely small quantities. The angular momentum flux carried by a circularly polarized 10 mW He-Ne laser beam is of the order of 10-18 mN. The first attempt to measure the torque produced by the optical angular momentum was made b B h [1] 59 years ago. Beth reported that his results agreed with theory in sign and magnitude. More recent y Santamato et al. [2] observed the light induced rotation of liquid crystal molecules, Chang and Lee [3] calculated the optical torque acting on a weakly absorbing optically levitated sphere, and Ashkin and Dziedzic [4] observed rotation of particles optically levitated in air.A linearly polarized wave containing a central phase singularity also carries angular momentum associated with its helical structure. Figure 1 shows this structure for a TEMot beam [5]. Each photon carries I Tt angular momentum where l is called the topological charge of the singularity. This contribution to the angular momentum is sometimes referred to as "orbital angular momentum" to d h t f om "spin" angular momentum associated aistinguis i ro with circular polarization [6,7]. Allen et al. [6] have proposed to measure the angular momentum carried by a doughnut laser beam by measuring the torque acting on an optical device which reverses the chirality of the beam. We have demonstrated in a previous paper [8] that black or rejective particles of sizes of 1 -2 p, m can be trapped optically in a liquid by higher order doughnuts produced by high efficiency computer generated holograms. We also mentioned that some bigger absorptive particles were set into rotation by slightly defocused doughnuts.In this paper we report on further experiments concerned with the transfer of angular momentum to absorptive particles and their subsequent rotation. The detection is performed using a video camera. A large number of small particles have been trapped and have been recorded. Our results clearly show that the rotation directions of all these trapped particles agree with the sign of the doughnut.In this Letter we analyze the results of the rotating particles in terms of possible torques acting on a trapped absorptive particle. ! / f ofa TEM qr, tu e e e (~" t" ' '"'] beam containing a first order phase singularity. FIG. 1. Snapsho...

Laser beams that contain phase singularities can be generated with computer-generated holograms, which in the simplest case have the form of spiral Fresnel zone plates.There has recently been considerable interest in optical fields that exhibit phase singularities, which manifest themselves as isolated dark spots in the modal patterns of certain lasers. Each dark spot has a topological charge that represents the number of 2vr accumulated when the phase gradient is integrated around it. The wave fronts near a singularity have a helical structure, while the field at the singularity must be zero because of the ambiguous phase; hence the dark spot.It has been shown theoretically how, under the influence of nonlinear interactions, frequencydegenerate transverse modes can lock together with a fixed phase difference to produce stable patterns that contain one or more of the singularities.' Such modal patterns have also been observed experimentally. 2 -4 Uncontrolled generation of random arrays of singularities has also been reported. 5 Here we report a means of generating such singularities in a controlled way, using only the simplest equipment, which amounts to the use of a computergenerated hologram, or zone plate. The hologram that is simulated is that of a modal pattern that contains a set of phase singularities using a reference plane wave. The technique can be extended to produce patterns of great complexity, but in this Letter we mainly concentrate on the circularly symmetric doughnut mode. If one interferes two coherent optical fieldsEl exp(iol) and E 2 exp(i0 2 ), the resultant spatial intensity pattern is modulated by a 2ElE 2 cos ((k + 02) term, which represents the interference fringes.The desired interference pattern is between a plane wave and the lowest-order hybrid doughnut mode, 3

Almost a hundred years ago, two different expressions were proposed for the energy-momentum tensor of an electromagnetic wave in a dielectric. Minkowski's tensor predicted an increase in the linear momentum of the wave on entering a dielectric medium, whereas Abraham's tensor predicted its decrease. Theoretical arguments were advanced in favour of both sides, and experiments proved incapable of distinguishing between the two. Yet more forms were proposed, each with their advocates who considered the form that they were proposing to be the one true tensor. This paper reviews the debate and its eventual conclusion: that no electromagnetic wave energy-momentum tensor is complete on its own. When the appropriate accompanying energy-momentum tensor for the material medium is also considered, experimental predictions of all the various proposed tensors will always be the same, and the preferred form is therefore effectively a matter of personal choice.

The divergence of quantum and classical descriptions of particle motion is clearly apparent in quantum tunnelling between two regions of classically stable motion. An archetype of such non-classical motion is tunnelling through an energy barrier. In the 1980s, a new process, 'dynamical' tunnelling, was predicted, involving no potential energy barrier; however, a constant of the motion (other than energy) still forbids classically the quantum-allowed motion. This process should occur, for example, in periodically driven, nonlinear hamiltonian systems with one degree of freedom. Such systems may be chaotic, consisting of regions in phase space of stable, regular motion embedded in a sea of chaos. Previous studies predicted dynamical tunnelling between these stable regions. Here we observe dynamical tunnelling of ultracold atoms from a Bose-Einstein condensate in an amplitude-modulated optical standing wave. Atoms coherently tunnel back and forth between their initial state of oscillatory motion (corresponding to an island of regular motion) and the state oscillating 180 degrees out of phase with the initial state.