N. B. Simpson

We use a Laguerre-Gaussian laser mode within an optical tweezers arrangement to demonstrate the transfer of the orbital angular momentum of a laser mode to a trapped particle. The particle is optically confined in three dimensions and can be made to rotate; thus the apparatus is an optical spanner. We show that the spin angular momentum of +/-?per photon associated with circularly polarized light can add to, or subtract from, the orbital angular momentum to give a total angular momentum. The observed cancellation of the spin and orbital angular momentum shows that, as predicted, a Laguerre-Gaussian mode with an azimuthal mode index l=1 has a well-defined orbital angular momentum corresponding to ? per photon.

Abstract We numerically model the axial trapping forces within optical tweezers arising from Laguerre–Gaussian laser modes. For an 8 μm diameter sphere suspended in water, the higher-order modes produce an axial trapping force several times larger than that of the fundamental. Partial absorption results in a transfer of the orbital angular momentum from the Laguerre–Gaussian mode to the trapped particle. This results in the rotation of the particle by what may be called an optical spanner (wrench). For an absorption coefficient of α = 5700 m−1 and a laser power of 10 mW, we find that an 8 μm diameter sphere would acquire an angular acceleration of 10 × 104 rad s−2 and a limiting angular velocity of 0.2 rad s−1.

We outline an easily reproduced experiment that allows the student to investigate the intensity and phase structure of transverse laser modes. In addition to discussing the usual Hermite–Gaussian laser modes we detail how Laguerre–Gaussian laser modes can be obtained by the direct conversion of the Hermite–Gaussian output. A Mach–Zehnder interferometer allows the phase structure of the Laguerre–Gaussian modes to be compared with the phase structure of a plane wave with the same frequency. The resulting interference patterns clearly illustrate the azimuthal phase dependence of the Laguerre–Gaussian modes, which is the origin of the orbital angular momentum associated with each of them.

The orbital angular momentum of light is distinct from the angular momentum associated with the spin or polarisation state of the light. Thus linearly polarised modes can carry angular momentum. Laguerre-Gaussian laser modes have been identified as a class of modes that can possess such orbital angular momentum. Hermite-Gaussian modes may be converted to Laguerre-Gaussian modes, characterised by two integer indices l and p, by the use of a mode converter. The l index occurs in the azimuthal phase factor eil ϕ in the field distribution of Laguerre-Gaussian beams which possess an orbital angular momentum equivalent to lħ per photon 1.

Abstract We demonstrate that the axial trapping efficiency in optical tweezers is improved by using a Laguerre-Gaussian laser mode as the trapping beam. For a wide range of particle sizes and sample cell depths, the laser power required with an l = 3 Laguerre-Gaussian mode is reduced by a factor of two compared with that of the fundamental mode. This is important for biological applications where a reduction in the laser power lessens the risk of damage to living samples.