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Spiraling light: from donut modes to a Magnus effect analogy

R. J. C. Spreeuw

Published Nov 1, 2021• 9 citations
Publisher

Abstract

The insight that optical vortex beams carry orbital angular momentum (OAM), which emerged in Leiden about 30 years ago, has since led to an ever expanding range of applications and follow-up studies. This paper starts with a short personal account of how these concepts arose. This is followed by a description of some recent ideas where the coupling of transverse orbital and spin angular momentum (SAM) in tightly focused laser beams produces interesting new effects. The deflection of a focused light beam by an atom in the focus is reminiscent of the Magnus effect known from aerodynamics. Momentum conservation dictates an accompanying light force on the atom, transverse to the optical axis. As a consequence, an atom held in an optical tweezer will be trapped at a small distance of up to λ/2π away from the optical axis, which depends on the spin state of the atom and the magnetic field direction. This opens up new avenues to control the state of motion of atoms in optical tweezers as well as potential applications in quantum gates and interferometry.

DOI
10.1515/nanoph-2021-0458

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The insight that optical vortex beams carry orbital angular momentum (OAM), which emerged in Leiden about 30 years ago, has since led to an ever expanding range of applications and follow-up studies. This paper starts with a short personal account of how these concepts arose. This is followed by a description of some recent ideas where the coupling of transverse orbital and spin angular momentum (SAM) in tightly focused laser beams produces interesting new effects. The deflection of a focused light beam by an atom in the focus is reminiscent of the Magnus effect known from aerodynamics. Momentum conservation dictates an accompanying light force on the atom, transverse to the optical axis. As a consequence, an atom held in an optical tweezer will be trapped at a small distance of up to λ/2π away from the optical axis, which depends on the spin state of the atom and the magnetic field direction. This opens up new avenues to control the state of motion of atoms in optical tweezers as well as potential applications in quantum gates and interferometry.
Abstract The insight that optical vortex beams carry orbital angular momentum (OAM), which emerged in Leiden about 30 years ago, has since led to an ever expanding range of applications and follow‐up studies. This paper starts with a short personal account of how these concepts arose. This is followed by a description of some recent ideas where the coupling of transverse orbital and spin angular momentum (SAM) in tightly focused laser beams produces interesting new effects. The deflection of a focused light beam by an atom in the focus is reminiscent of the Magnus effect known from aerodynamics. Momentum conservation dictates an accompanying light force on the atom, transverse to the optical axis. As a consequence, an atom held in an optical tweezer will be trapped at a small distance of up to λ /2 π away from the optical axis, which depends on the spin state of the atom and the magnetic field direction. This opens up new avenues to control the state of motion of atoms in optical tweezers as well as potential applications in quantum gates and interferometry.
It is shown that a circular dipole can deflect the focused laser beam that induces it and will experience a corresponding transverse force. Quantitative expressions are derived for Gaussian and angular top hat beams, while the effects vanish in the plane wave limit. The phenomena are analogous to the Magnus effect, pushing a spinning ball onto a curved trajectory. The optical case originates in the coupling of spin and orbital angular momentum of the dipole and the light. In optical tweezers the force causes off-axis displacement of the trapping position of an atom by a spin-dependent amount up to λ/2π, set by the direction of a magnetic field. This suggests direct methods to demonstrate and explore these effects, for instance, to induce spin-dependent motion.
The study of optical beams with orbital angular momentum (OAM) has gained the interest of researchers since the seminal work of the Woerdman group in Leiden in 1992. These beams have been used as optical tweezers, as a tool for high-resolution nanoscopy, as a new instrument for increased angular resolution measurement, and as a resource for increased channel capacity in optical communications and high-dimensional information carrier for diverse applications in quantum information science among others. In this presentation, I will introduce beams with OAM, their properties and peculiarities. I will talk about how these beams are generated with a focus on the coherent generation of these kinds of beams using sum-frequency generation. I will discuss the applications of these beams in detecting spinning object, and as pointer states to probe joint weak value in weak measurements. I will end my talk with possible directions for this field of research.
Light carrying orbital angular momentum (OAM)---known as vortex beams---has broadened the scope of understanding and applications of light's angular momentum. Optical tweezers using OAM, often referred to as optical spanners, have significantly expanded the tunability of optical manipulation. A key frontier now lies in understanding how vortex beams interact with quantum states of matter. In this work, we numerically investigate the dynamics of a superconductor under vortex beam illumination and demonstrate the transfer of angular momentum from light to the superconducting collective mode, resulting in mechanical rotation. Our findings open a pathway for optical manipulation in the quantum regime, which we term the quantum optical spanner.
A photon can be considered both a particle and a wave in quantum mechanics. Quantum optics deals with such quantum mechanical properties of a photon. One such property that has been of particular interest recently is that of light’s momentum, specifically its linear momentum and orbital angular momentum (OAM). Light carrying both types of momentum are of particular utility to the life sciences. Linear momentum (LM) photons have the ability to directly manipulate particles. For example, photons with these properties can be used to separate one specific particle from a group. One can then more closely observe its properties. OAM photons have the potential to unravel DNA strands using the torque of the photons to further observe certain specific physical properties. Light carrying OAM has also shown promise in the field of information technology as a new means of sending large amounts of data over long distances securely and extremely quickly. Because photons behave quantum mechanically, the encryptions are much more difficult to decode, and since the information is being sent as light it clearly travels at the speed of light. This paper will provide background on the quantum optics of particle manipulation and the results from experimental studies performed on this topic. The results show evidence of light with both types of momentum being created and used to manipulate particles. We generated light with both types of momentum, trapped particles with optical tweezers, and measured the force on the particles with a high speed video camera, optical tweezers, and computer programs that we used to track the particles.
In 1992, Les Allen and coworkers within Han Woerdman's group realized that light beams with an azimuthal phase dependence described by an additional exp(iℓθ) term, where ℓ can take any integer value and θ is the angular position within the beam, carry an orbital angular momentum. This orbital angular momentum is additional to the spin angular momentum associated with circular polarization. These azimuthally phased beams comprise ℓ intertwined helical phase fronts, skewed with respect to the beam axis, meaning that at all positions within the beam cross section, the wavefront normal and associated momentum density has a well-defined azimuthal component. The insight of Allen and coworkers was that for all beams described in this way, when integrated over the beam cross section, the orbital angular momentum (OAM) is ℓℏ per photon. Laguerre-Gaussian and high-order Bessel beams are both examples of mode families having these properties. A further feature of these beams is that the phase singularity on the beam axis precludes a nonzero on-axis intensity and therefore all such beams with ℓ ≠0 have an annular intensity cross section (see Fig. 4.1). The circulation of the optical momentum and energy around the singularity leads them also to be called optical vortices. The further recognition that beams carrying defined amounts of OAM could be created within the laboratory means that over the last 15 years they have formed the basis of many investigations, ranging from the transfer of OAM to microscopic particles (in optical spanners or optical wrenches) to studies of the fundamental properties of light in both the classical and quantum regimes. However, although OAM is an immensely useful concept, one must emphasize that all its properties are simply those predicted by standard electromagnetic theory. The purpose of this chapter is to consider how sets of helical laser modes carrying OAM can be used for information transfer.