Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

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Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Optical tweezers1 are commonly used for manipulating microscopic particles, with applications in cell manipulation2, colloid research3,4,5, manipulation of micromachines6 and studies of the properties of light beams7. Such tweezers work by the transfer of momentum from a tightly focused laser to the particle, which refracts and scatters the light and distorts the profile of the beam. The forces produced by this process cause the particle to be trapped near the beam focus. Conventional tweezers use gaussian light beams, which cannot trap particles in multiple locations more than a few micrometres apart in the axial direction, because of beam distortion by the particle and subsequent strong divergence from the focal plane. Bessel beams8,9, however, do not diverge and, furthermore, if part of the beam is obstructed or distorted the beam reconstructs itself after a characteristic propagation distance10. Here we show how this reconstructive property may be utilized within optical tweezers to trap particles in multiple, spatially separated sample cells with a single beam. Owing to the diffractionless nature of the Bessel beam, secondary trapped particles can reside in a second sample cell far removed (∼3 mm) from the first cell. Such tweezers could be used for the simultaneous study of identically prepared ensembles of colloids and biological matter, and potentially offer enhanced control of ‘lab-on-a-chip’ and optically driven microstructures.

Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam

Single photons with helical phase structures may carry a quantized amount of orbital angular momentum (OAM), and their entanglement is important for quantum information science and fundamental tests of quantum theory. Because there is no theoretical upper limit on how many quanta of OAM a single photon can carry, it is possible to create entanglement between two particles with an arbitrarily high difference in quantum number. By transferring polarization entanglement to OAM with an interferometric scheme, we generate and verify entanglement between two photons differing by 600 in quantum number. The only restrictive factors toward higher numbers are current technical limitations. We also experimentally demonstrate that the entanglement of very high OAM can improve the sensitivity of angular resolution in remote sensing.

https://science.sciencemag.org/content/sci/338/6107/640.full.pdf

Quantum Entanglement of High Angular Momenta

Optical tweezers, a simple and robust implementa- tion of optical micromanipulation technologies, have become a standard tool in biological, medical and physics research labo- ratories. Recently, with the utilization of holographic beam shap- ing techniques, more sophisticated trapping configurations have been realized to overcome current challenges in applications. Holographically generated higher-order light modes, for exam- ple, can induce highly structured and ordered three-dimensional optical potential landscapes with promising applications in op- tically guided assembly, transfer of orbital angular momentum, or acceleration of particles along defined trajectories. The non- diffracting property of particular light modes enables the op- tical manipulation in multiple planes or the creation of axially extended particle structures. Alongside with these concepts which rely on direct interaction of the light field with particles, two promising adjacent approaches tackle fundamental limita- tions by utilizing non-optical forces which are, however, induced by optical light fields. Optoelectronic tweezers take advantage of dielectrophoretic forces for adaptive and flexible, massively parallel trapping. Photophoretic trapping makes use of thermal forces and by this means is perfectly suited for trapping ab- sorbing particles. Hence the possibility to tailor light fields holo- graphically, combined with the complementary dielectrophoretic and photophoretic trapping provides a holistic approach to the majority of optical micromanipulation scenarios.

https://www.uni-muenster.de/imperia/md/content/physik_ap/denz/publikationen/2013/10_woerdemann.pdf

Advanced optical trapping by complex beam shaping

The phenomenon of light's momentum was first observed in the laboratory at the beginning of the twentieth century, and its potential for manipulating microscopic particles was demonstrated by Ashkin some 70 years later. Since that initial demonstration, and the seminal 1986 paper where a single-beam gradient-force trap was realized, optical trapping has been exploited as both a rich example of physical phenomena and a powerful tool for sensitive measurement. This review outlines the underlying theory of optical traps, and explores many of the physical observations that have been made in such systems. These phenomena include 'optical binding', where trapped objects interact with one another through the trapping light field. We also discuss a number of the applications of 'optical tweezers' across the physical and life sciences, as well as covering some of the issues involved in constructing and using such a tool.

https://iopscience.iop.org/article/10.1088/0034-4885/76/2/026401/pdf

Optical trapping and binding

We report the first experimental generation of high-order Mathieu beams and confirm their propagation invariance over a limited range. In our experiment we use a computer-generated phase hologram. The peculiar behaviour of the vortices in Mathieu beams gives rise to questions about their orbital-angular-momentum content, which we calculate by performing a decomposition in terms of Bessel beams.

https://iopscience.iop.org/article/10.1088/1464-4266/4/2/368/pdf

I. Allison

Papers

Holographic generation and orbital angular momentum of high-order Mathieu beams

Holographic generation and orbital angular momentum of high-order Mathieu beams : Special issue on atoms and angular momentum of light