Twisted light for micromanipulation and beyond

That light carries a linear momentum has been recognized at least since the time of Kepler, when it was proposed to explain why comets' tails always point away from the sun. That light carries also an angular momentum was first elucidated by Poynting in 1909.¹ He used a mechanical analogy with a revolving shaft to deduce a ratio between the energy and angular momentum carried by circularly polarized light. We would now associate Poynting's work with the ℏ spin angular momentum of the photon.

The momentum of light is an essential property with respect to atomic and molecular transitions where both the linear and angular momentum of the combined atomic/optical system are conserved. The change in angular momentum arising from a dipole transition is naturally associated with the photon's ℏ spin. Higher order transitions require larger changes in angular momentum and the spin is no longer sufficient to conserve the total angular momentum of the process. The requirement for additional optical momentum was recognized by Darwin² and others and until the mid-1990s this additional orbital angular momentum of light was associated with higher order transitions.

Figure 1. Intensity (brightness) and phase (color) cross-section of a Laguerre-Gaussian mode with ℏ angular momentum per photon.

Figure 2. Illustration of a beam with orbital angular momentum, produced by a forked hologram, causing a trapped bead to circulate.

Allen and coworkers in 1992 showed that light beams carrying well-defined angular momentum could be created in the laboratory.³ They used specific combinations of cylindrical lenses to convert the Hermite-Gaussian modes emitted from a laser into Laguerre-Gaussian modes, which comprise ℓ intertwined helical phase fronts described by a phase cross-section exp(iℓθ) (see Figure 1). The helical shape of the phase fronts means that the Poynting vector at any given point in the light beam is skewed with respect to the beam axis. This skew gives an azimuthal component to the linear momentum carried by the light at that point. When integrated over the beam cross section, this component accounts exactly for the orbital angular momentum of the light corresponding to ℓℏ per photon. Although helically phased beams were already in production by other groups, who used diffraction gratings modified to include a fork dislocation in the lines, no one had hitherto recognized the beams' momentum properties.⁴

One of the most intuitive demonstrations of optical linear momentum is optical tweezers, and the same is true for angular momentum. Optical tweezers were pioneered by Ashkin, who used tightly focused beams of light to trap and move micron-sized transparent objects suspended in a surrounding fluid.⁵ Rather than relying on the radiation pressure, the trapping mechanism arises from the deflection of light by the object, the resulting change in momentum producing a reaction force on the object. Optical tweezers are now a mainstream tool for control of microscopic objects in nano- and life sciences.⁶

Rubinsztein-Dunlop and coworkers in 1995 used a forked diffraction grating to create a helically phased beam (see Figure 2), which they then used in an optical tweezers experiment.⁷ They trapped micron-sized carbon particles that absorbed some of the trapping light and thus were pushed by the radiation pressure and held against a microscope slide. More important, the partial absorption of the light and its associated orbital angular momentum caused the particles to spin.

In our work in 1997, we used transparent particles, which allowed 3D trapping while the residual absorption was still sufficient to transfer the angular momentum from the beam to cause the spinning of a particle: the optical spanner.⁸ With larger beams, we demonstrated that the action of spin and orbital angular momentum can be distinguished. The transfer of the spin angular momentum causes the particle to spin about its own axis whereas the orbital angular momentum causes the particle to orbit at a constant radius around the beam axis. We observed both spinning and orbiting of the particles at the same time.^{9, 10}

Figure 3. A compact optical tweezers system, featuring a spatial light modulator that can create beams with angular momentum. Similar systems will soon be available from Boulder Nonlinear Systems.

Figure 3 shows the compact holographic optical tweezers system recently constructed by our lab. It includes a spatial light modulator with which we can create beams with angular momentum and aberration correction.^{11, 12} These helically phased beams can be used to increase the stiffness of optical traps: the beams' ring-shaped structure places more light around the edge of the particle.¹³ We have recently developed a new form of stereo microscope and used it to optimize the 3D stiffness of the optical trap.^{14, 15} We are currently exploring the use of helically phased beams to deflect stray particles from a measurement region, using their ring-shaped structure to create a 'shield' of light, preventing contamination of the sample volume.

Optical tweezers with a twist have introduced many researchers to the concept of orbital angular momentum not just as a physical phenomena but as a potential tool for micromanipulation.¹⁶ Optically induced rotation provides a non-contact torque that can drive micromachines and micropumps.^17–19 Indeed, spinning a particle by itself gives a microscopic method for measuring local viscosity.²⁰

Beyond optical manipulation, research on the orbital angular momentum of light has given rise to fresh interpretations of various physical concepts and related applications. We have used optical angular momentum to investigate physical concepts ranging from rotational frequency shifts, to angular uncertainty relationships, to the photon drag.^{21, 22} Use of orbital angular momentum filters within imaging systems has given a new form of edge-enhanced microscopy and within telescopes is emerging as a mechanism to suppress the light from a bright star to make neighboring planets more visible.^{23, 24} Unlike the spin angular momentum of light, which can take only one of two values, the orbital angular momentum is unbounded. This property makes it an attractive variable for encoding information, with exciting prospects for classical and quantum communications.^{25, 26}