The ubiquitous photonic wheel

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate here a paraxial vector Gaussian beam with an infinite number of polarization singularities residing evenly on a straight line. The intensity distribution is derived analytically and the polarization singularities are shown to exist only in the initial plane and in the far field. The azimuthal angle of the polarization singularities is shown to increase in the far field by π/2. We obtain the longitudinal component of the spin angular momentum (SAM) density and show that it is independent of the azimuthal angle of the polarization singularities. Upon propagation in free space, an infinite number of C-points is generated, where polarization is circular. We show that the SAM density distribution has a shape of four spots, two with left and two with right elliptic polarization. The distance to the transverse plane with the maximal SAM density decreases with decreasing distance between the polarization singularities in the initial plane. Generating such alternating areas with positive and negative SAM density, despite linear polarization in the initial plane, manifests the optical spin Hall effect. Application areas of the obtained results include designing micromachines with optically driven elements.

Two linked gear wheels in a micromachine can be simultaneously rotated in opposite directions by using a laser beam that has in its section areas the spin angular momentum (SAM) of the opposite sign. However, for instance, a cylindrical vector beam has zero SAM in the focus. We alter a cylindrical vector beam so as to generate areas in its focus where the SAM is of opposite signs. The first alteration is adding to the cylindrical vector beam a linearly polarized beam. Thus, we study superposition of two rotationally symmetric beams: those with cylindrical and linear polarization. We obtain an expression for the SAM and prove two of its properties. The first property is that changing superposition coefficients does not change the shape of the SAM density distribution, whereas the intensity changes. The second property is that maximal SAM density is achieved when both beams in the superposition have the same energy. The second perturbation is adding a spatial carrier frequency. We study the SAM density of a cylindrical vector beam with a spatial carrier frequency. Due to periodic modulation, upon propagation in space, such a beam is split into two beams, having left and right elliptic polarization. Thus, in the beam transverse section, areas with the spin of different signs are separated in space, which is a manifestation of the spin Hall effect. We demonstrate that such light beams can be generated by metasurfaces, with the transmittance depending periodically on one coordinate.

Vector optical fields (VOFs) with space-variant polarizations have attracted great attention in various areas, and the VOFs have been applied to study the spin angular momentum (SAM) of the photon, leading to many new effects and applications. Here, we propose the multi-polar coordinate and design and generate the multi-polar VOF (MP-VOF) with an arbitrary even number of singularities. We further find that the SAM appears or annihilates in the focal plane, which means the processes of “0-1” and “1-0” of the SAM can be accomplished in propagation. The corresponding theoretical explanation is also provided, indicating that the SAM appears or annihilates due to the interaction of the fields at central symmetric positions on the wavefront. Moreover, the appearance of transverse SAM (also known as the “photonic wheel”) can also be achieved in tight focusing cases. In this way, we can achieve three cases of SAM under different conditions, including purely longitudinal SAM, purely transverse SAM, and three-dimensional SAM with both components. This new kind of MP-VOF significantly enriches the family of VOFs and provides new insights in studying the focal behavior of the SAM, which can be applied in realms such as spin absorbing particles in a more flexible way.

Optical spin-orbit interaction has gained much interest recently due to its universality and importance in modern photonics. In this Letter, we theoretically demonstrate that orbit-induced localized spin angular momentum (SAM) conversion can occur in the tight focusing of spin-free linearly polarized vortex beams (LPVBs). By analysis of the polarization states that are associated with the SAM density, we attribute the occurrence of such a conversion to the helical-phase-induced change of local polarization states in the focused field. In the local SAM, density can be further regulated by altering the sign and value of the orbital angular momentum in the incident LPVBs, as well as their polarization orientations. This Letter is expected to advance our understanding of optical spin-orbit coupling and benefit applications of optical microscopy and trapping.

The spin‐orbit interaction (SOI) of light generated by tight focusing in optical tweezers is regularly employed in generating angular momentum ‐ both spin and orbital ‐ the effects being extensively observed in trapped mesoscopic particles. Specifically, the transverse spin angular momentum (TSAM), which arises due to the longitudinal component of the electromagnetic field generated by tight focusing is of special interest, both in terms of fundamental studies and associated applications. This study provides an effective and optimal strategy for generating TSAM in optical tweezers by tightly focusing first‐order radially and azimuthally polarized vector beams with no intrinsic angular momentum (AM) into a refractive index stratified medium. The choice of such input fields ensures that the longitudinal spin angular momentum (LSAM) arising from the electric (magnetic) field for the radial (azimuthal) polarization is zero. As a result, the effects of the electric and magnetic TSAM are exclusively observed separately in the case of input first‐order radially and azimuthally polarized vector beams on single optically trapped birefringent particles. This research opens up new and simple avenues for exotic and complex particle manipulation in optical tweezers.

Light carries intrinsic spin angular momentum (SAM) when the electric or magnetic field vector rotates over time. A familiar vector equation calculates the direction of light’s SAM density using the right-hand rule with reference to the electric and magnetic polarisation ellipses. Using Maxwell’s equations, this vector equation can be decomposed into a sum of two distinct terms, akin to the well-known Poynting vector decomposition into orbital and spin currents. We present the first general study of this spin decomposition, showing that the two terms, which we call canonical and Poynting spin, are chiral analogies to the canonical and spin momenta of light in its interaction with matter. Like canonical momentum, canonical spin is directly measurable. Both canonical and Poynting spin incorporate spatial variation of the electric and magnetic fields and are influenced by optical vortices. The decomposition allows us to show that a linearly polarised vortex beam, which has no total SAM, can nevertheless exert longitudinal chiral pressure due to equal and opposite canonical and Poynting spins.

Geometrical phase shift of the extrinsic orbital angular momentum density of light propagating in a helically wound optical fiber

A self-consistent formulation of the exchange energy density, effective exchange field, and Poynting vector is carried out, for a general ferrimagnet, in terms of the spin and orbital angular momentum densities. When there is more than one magnetic lattice or when the gyromagnetic ratios are tensor quantities, this formulation leads to an exchange energy density and Poynting vector that differ from those commonly employed. The associated boundary conditions at a surface of passive discontinuity are also discussed; power flow considerations lead to the conclusion that one of these is a dynamic boundary condition. With the help of the correspondence principle and a quasi particle interpretation of spin waves, a small-signal energy density, momentum density, and stress tensor are postulated for a ferromagnet. The associated small-signal force density (postulated to equal the divergence of the stress tensor minus the time rate of change of the momentum density) is found to be the negative of the force density that accelerates the envelope of the spin wave packet and is interpreted as a reaction force density acting upon the lattice. A prediction is made that a magnon incident upon a surface of discontinuity such as a material—air interface, will exert an exchange-radiation pressure on it.

Transverse spin angular momentum, which appears locally in the structured optical fields, has attracted much attention, owing to its extraordinary properties and potential applications. We show theoretically that, by highly focusing a vector vortex beam with azimuthally varied polarization, it is possible to trap multiple particles simultaneously and manipulate the particles' spin along the azimuthal direction. Both the direction and the magnitude of the spin angular momentum, so the spin torque on the particle, can be varied by changing the state of the input beams. Moreover, the magnitude of the spin torque can be manipulated further by changing the characteristics of the particles. Such results may be exploited in practical optical manipulation, especially for optically induced rotations.

We demonstrate that tight focusing of a circularly polarized Gaussian beam in optical tweezers leads to spin-momentum locking—with the transverse momentum density (Poynting vector) being helicity-dependent, while the transverse spin angular momentum density becomes independent of helicity. We further use a stratified medium in the path of the trapping beam in our optical tweezers setup to enhance the magnitude of the transverse momentum and the electric field intensity in the radial direction with respect to the beam axis and cause them to significantly overlap. This overlap allows us to experimentally observe the circular motion of a birefringent particle, trapped off-axis, in response to an input circularly polarized fundamental Gaussian beam carrying no intrinsic orbital angular momentum (OAM). The circular motion is dependent on the helicity of the input beam so that we can identify it as the signature of the elusive Belinfante spin in propagating light beams obtained in our optical tweezers configuration. Our results can be extended to beams carrying intrinsic OAM leading to simple routes for achieving complex manipulation of micro-machines or other mesoscopic matter using optical tweezers.

The investigations on optical angular momenta and their interactions have broadened our knowledge of light’s behavior at sub-wavelength scales. Recent studies further unveil the extraordinary characteristics of transverse spin angular momentum in confined light fields and orbital angular momentum in optical vortices. Here we demonstrate a direct interaction between these two intrinsic quantities of light. By engineering the transverse spin in the evanescent wave of a whispering-gallery-mode-based optical vortex emitter, a spin-orbit interaction is observed in generated vortex beams. Inversely, this unconventional spin-orbit interplay further gives rise to an enhanced spin-direction locking effect in which waveguide modes are unidirectionally excited, with the directionality jointly controlled by the spin and orbital angular momenta states of light. The identification of this previously unknown pathway between the polarization and spatial degrees of freedom of light enriches the spin-orbit interaction phenomena, and can enable various functionalities in applications such as communications and quantum information processing.

Light carries both longitudinal and transverse spin angular momentum. The spin can couple with its orbital counterpart, known as the spin-orbit interaction (SOI) of light. Complementary to the longitudinal SOI known previously, here we show that transverse SOI of light is inherent in the Helmholtz equation when transverse spinning light propagates in curved paths. It lifts the degeneracy of dispersion relations of light for opposite transverse spin states, analogous to the Dresselhaus effect. Transverse SOI is ubiquitous in nanophotonic systems where transverse spin and optical path bending are inevitable. It can explain anomalous effects like the dispersion relation of surface plasmon polaritons on curved paths and the energy level of whispering gallery modes. Our results reveal the analogies of spin photonics and spintronics and offer a new degree of freedom for integrated photonics, spin photonics, and astrophysics.

Spin angular momentum (SAM) and orbital angular momentum (OAM) are two important fundamental degrees of freedom of light and play crucial roles in various light–matter interactions. SAM usually makes the microparticle rotate around its axis, while OAM causes orbital motion of the microparticles around the beam axis. For an optical field with only SAM, the spin-to-orbit conversion may occur under the tightly focused condition, leading to the orbital motion of probing particles. However, it is invalid for weakly focused conditions. Here, we generated an annular optical field without intrinsic OAM by weakly focusing (i.e., negligible spin-to-orbit conversion) a circularly polarized light with a linearly varying radial phase and then observed a kind of dual orbital motion of asymmetric probing particles (Janus particles) in the focal plane. The two orbital motions have opposite directions on both sides across the strongest ring of the annular optical field. In addition to the SAM, the local angular momentum (AM) density also depends on the radial intensity gradient. The radial intensity gradient has the opposite signs on both sides across the strongest ring of the annular optical field, which results in the opposite orbital motions of trapped particles. The manipulation of the local AM density and the resulting novel dual orbital effect in the absence of intrinsic OAM provide a new scene to understand the physics underlying the light–matter interaction, paving the way to some new applications involving the sorting and delivery of microparticles.

The surface waves that propagate along the interface of a dielectric with nonlinear susceptibility of the third order and topological insulator have been considered. The optical nonlinearity of the dielectric ensures the existence of a surface wave. The density of the spin angular momentum of a surface wave has been determined for dielectrics with positive or negative linear permittivity. It has been shown that the spin angular momentum vector has a projection on the normal to the interface, which is different from the usual surface polaritons or plasmon polaritons. The discrete nature of the topological number manifests itself in the discreteness of the values of the normal and tangential components of the spin angular momentum density. The increase in the intensity of the electric field of the wave at the interface of the media changes the value of the spin angular momentum and can lead to its disappearance.

Separation of spin and orbital angular momentum states from cylindrical vector beams