Angular Momentum Density Research Articles

Vanishing Poynting Observers and Electromagnetic Field Classification in Kerr and Kerr-Newman Spacetimes

We consider electromagnetic fields having an angular momentum density in a locally nonrotating reference frame in Schwarzschild, Kerr, and Kerr-Newman spacetimes. The nature of such fields is assessed with two families of observers, the locally nonrotating ones and those of vanishing Poynting flux. The velocity fields of the vanishing-Poynting observers in the locally nonrotating reference frames are determined using the 3 + 1 decomposition formalism. From a methodological point of view and considering a classification of the electromagnetic field based on its invariants, it is convenient to separate the consideration of the vanishing-Poynting observers into two cases corresponding to the pure and nonpure fields; additionally, if there are regions where the field rotates with the speed of light (light surfaces), it becomes necessary to split these observers into two subfamilies. We present several examples of relevance in astrophysics and general relativity, such as pure rotating dipolar-like magnetic fields and the electromagnetic field of the Kerr-Newman solution. For the latter example, we see that vanishing-Poynting observers also measure a vanishing super-Poynting vector, confirming recent results in the literature. Finally, for all nonnull electromagnetic fields, we present the 4-velocity fields of vanishing Poynting observers in an arbitrary spacetime.

Superkicks and the photon angular and linear momentum density

We address the problem of determining the physically correct definition of the momentum and angular momentum densities in a spatially structured electromagnetic field, given that the expressions are not the same when one uses the canonical energy-momentum tensor instead of the symmetric Belinfante energy-momentum tensor in electrodynamics. This has important consequences for the interaction of matter with structured light, for example, twisted photons, and would give drastically different results for forces and angular momenta induced on small test objects. We show, with numerical estimates of the size of the effects, situations where the canonical and symmetrized forms induce very different torques or (superkick) recoil momenta on small objects or atomic rotors, over a broad range of circumstances.

Lorentzian Taub-NUT spacetimes: Misner string charges and the first law

Motivated by recent activities in Lorentzian Taub-NUT space thermodynamics, we calculate conserved charges of these spacetimes. We find additional mass, nut, angular momentum, electric and magnetic charge densities distributed along Misner string. These additional charges are needed to account for the difference between the values of the above charges at horizon and at infinity. We propose an unconstrained thermodynamical treatment for Taub-NUT spaces, where we introduce the nut charge $n$ as a relevant thermodynamic quantity with its chemical potential \phi_n. The internal energy in this treatment is M-n\phi_n rather than the mass M. This approach leads to an entropy which is a quarter of the area of the horizon and all thermodynamic quantities satisfy the first law, Gibbs-Duhem relation as well as Smarr's relation. We found a general form of the first law where the quantities depend on an arbitrary parameter. Demanding that the first law is independent of this arbitrary parameter or invariant under electric-magnetic duality leads to a unique form which depends on Misner string electric and magnetic charges. Misner string charges play an essential role in the first law, without them the first law is not satisfied.

Toroidal vortices of light

Toroidal vortices, also known as vortex rings, are whirling, closed-loop disturbances that form a characteristic ring shape in liquids and gases and propagate in a direction that is perpendicular to the plane of the ring. They are well-studied structures and commonly found in various fluid and gas flow scenarios in nature, for example in the human heart, underwater air bubbles and volcanic eruptions1–3. Here we report the experimental observation of a photonic toroidal vortex as a new solution to Maxwell’s equations, generated by the use of conformal mapping4–7. The resulting light field has a helical phase that twists around a closed loop, leading to an azimuthal local orbital angular momentum density. The preparation of such an intriguing state of light may offer insights for exploring the behaviour of toroidal vortices in other disciplines and find important applications in light–matter interactions, optical manipulation, photonic symmetry and topology, and quantum information8–17.

Spin Hall effect of fractional order radially polarized beam in its tight focusing

Different from the traditional radially polarized beams, the fractional order radially polarized beam possess the symmetry broken structure of the polarization state distribution. The symmetry broken of the optical beams’ intrinsic structure can lead to the spin–orbit coupling of light. In this paper, we investigate the tight focusing of the fractional order radially polarized beam and show some interesting phenomena induced by the symmetry broken structure of the polarization state distribution. Firstly, the intensity and the spin angular momentum density are split in the focal plane, and the focal field intensity distribution can be controlled (split or focused) by modulating the initial phase of the polarization state. Furthermore, just like the spin angular momentum, the orbital angular momentum density also is split into two opposite parts (positive and negative). Though, the evolutions of the spin and the orbital angular momentum are different: as the change of the initial phase of the polarization state, the spin angular momentum distribution just is rotated slightly, yet the orbital angular momentum distribution is reversed. All these phenomena can be considered as the manifestations of the spin Hall effect of the fractional order radially polarized beam. Our results provide further potential applications of the vector beams in the focal field shaping.

Angular momentum and generalized parton distributions for the proton with basis light-front quantization

We study the unpolarized and the helicity-dependent generalized parton distributions (GPDs) for the valence quarks of the proton in both momentum space and position space within the basis light-front quantization (BLFQ) framework. The GPDs for the valence quarks are computed from the eigenvectors of a light-front effective Hamiltonian in the valence Fock sector consisting of a three-dimensional confinement potential and a one-gluon exchange interaction with fixed coupling. Employing these GPDs, we obtain the spatial distributions of quark angular momentum inside the proton. In our BLFQ approach, we explore various definitions of angular momentum density and illustrate the differences between them arising from terms that integrate to zero. We also discuss the flavor contributions to the quark angular momentum densities.

Ultrafast Spin‐to‐Orbit and Orbit‐to‐Local‐Spin Conversions of Tightly Focused Hybridly Polarized Light Pulses

Spin–orbit interaction (SOI) has provided a new viable roadmap for the development of spin‐based photonics devices. However, existing strategies to control the SOI focus commonly on tailoring the spatial dimension of light fields yet neglecting the inherent temporal one. Herein, ultrafast temporal effects on both spin‐to‐orbit and orbit‐to‐local‐spin conversions based on the time‐assistant vectorial diffractive theory and the fast Fourier transformation are first presented. Such interconversions depend upon whether the incident hybridly vectorial light pulse carries vortex phase or not in a single high numerical aperture geometry. For the case of the absence of vortex phase, it is found that it enables orbit angular momentum‐carrying transverse component fields, and the resultant orbit angular momentum embedded within focused light fields remains constantly revolving as time elapses, which indicates that the controllable spin‐to‐orbit conversion occurs. By contrast, it is revealed that hybridly polarized vectorial‐vortex light pulses allow access to the locally excited circular polarization at the focus, and this induced local circular polarization is independent of ultrafast varying time, whereas the resulting spin angular momentum density components experience the alternation between the appearance and annihilation over time, thus giving rise to the tunable orbit‐to‐local‐spin conversion. These exotic ultrafast interconversions not only breathe a new life into the area of ultrafast photonics, but refresh our understanding on the paradigm of photonic SOI.

Surface stress tensor and junction conditions on a rotating null horizon

The general form of the surface stress tensor of an infinitesimally thin shell located on a rotating null horizon is derived, when different interior and exterior geometries are joined there. Although the induced metric on the surface must be the same approached from either side, the first derivatives of the metric need not be. Such discontinuities lead to a Dirac $\delta$-distribution in the Einstein tensor localized on the horizon. For a general stationary axisymmetric geometry the surface stress tensor can be expressed in terms of two geometric invariants that characterize the surface, namely the discontinuities $[\kappa]$ and $[\cal J]$ of the surface gravity $\kappa$ and angular momentum density $\cal J$. The Komar energy and angular momentum are given in coordinates adapted to the Killing symmetries, and the surface contributions to each determined in terms of $[\kappa]$ and $[\cal J]$. Guided by these, a simple modification of the original Israel junction conditions is verified directly from the Einstein tensor density to give the correct finite result for the surface stress, when the normal $\boldsymbol n$ to the surface is allowed to tend continuously to a null vector. The relation to Israel's original junction conditions, which fail on null surfaces, is given. The modified junction conditions are suitable to the matching of a rotating `black hole' exterior to any interior geometry joined at the Kerr null horizon surface, even when the surface normal is itself discontinuous and the Barrab\`es-Israel formalism is also inapplicable. This joining on a rotating null horizon is purely of the matter shell type and does not contain a propagating gravitational shock wave.

Simulation of a rotating strong gravity that reverses time

In this research we simulated how time can be reversed with a rotating strong gravity. At first, we assumed that the time and the space can be distorted with the presence of a strong gravity, and then we calculated the angular momentum density of the rotating gravitational field. For this simulation we used Einstein’s field equation with spherical polar coordinates and the Euler’s transformation matrix to simulate the rotation. We also assumed that the stress-energy tensor that is placed at the end of the strong gravitational field reflects the intensities of the angular momentum, which is the normal (perpendicular) vector to the rotating axis. The result of the simulation shows that the angular momentum of the rotating strong gravity changes its directions from plus (the future) to minus (the past) and from minus (the past) to plus (the future), depending on the frequency of the rotation.

Spin-orbit Hall effect in the tight focusing of a radially polarized vortex beam.

When the first-order radially polarized vortex beam propagates in an uniaxial crystal, the spin and the orbital angular momentum parts can be separated. It is called the optical spin-orbit Hall effect. In this study, we investigate the tight focusing of the radially polarized vortex beam theoretically and find the spatial separation of the spin and the orbital angular momentum parts occurs in the focal plane when the polarization order equals 1 and the vortex charge equals 1 (or -1). Moreover, when the initial phase of the polarization state takes π/2, the spatial separation of intensity in the focal plane corresponds to the spatial separation of the spin and the orbital angular momentum parts. This phenomenon can be considered as a manifestation of the optical spin-orbit Hall effect in the tight focusing of radially polarized vortex beam. Also, we show that, when the polarization order is greater than 1, the initial phase change of polarization state just leads to the rotation of the focal field and the spin and the orbital angular momentum density in the focal plane. Our results provide the potential application in the field of optical micro-manipulation.

Optical spin sorting chain.

Transverse spin angular momentum of light is a key concept in recent nanophotonics to realize unidirectional light transport in waveguides by spin-momentum locking. Herein we theoretically propose subwavelength nanoparticle chain waveguides that efficiently sort optical spins with engineerable spin density distributions. By arranging high-refractive-index nanospheres or nanodisks of different sizes in a zigzag manner, directional optical spin propagation is realized. The origin of efficient spin transport is revealed by analyzing the dispersion relation and spin angular momentum density distributions, being attributed to guided modes that possess transverse spin angular momenta. In contrast to conventional waveguides, the proposed asymmetric waveguide can spatially separate up- and down-spins and locate one parity inside and the other outside the structure. Moreover, robustness against bending the waveguide and its application as an optical spin sorter are presented. Compared to previous reports on spatial engineering of local spins in photonic crystal waveguides, we achieved miniaturization of the entire footprint down to the subwavelength scale.

Focal field properties of toroidal double-mode vector beams

Integer-order vector beams maintain their polarization properties under the paraxial diffraction condition. Fractional-order vector beam with irregular phase change that leading to changeable focusing properties has aroused huge interest research. Herein, we proposed and experimentally generated a double-mode concentric annular fractional vector beam. Based on the modal superposition, the intensity and spin angular momentum (SAM) density are characterized by periodic changes from rotational symmetry to axial symmetry as the topological coefficient increases. These results reveal that the fractional topological coefficients have a great potential degree of freedom. The experimental results are exploited in this work to emphasize the important connection between fractional coefficient and SAM density.

Influence of initial phase of polarization on tight focusing of vector beam

Generally, the influence of initial phase of polarization distribution of incident vector beams always is ignored in its tight focusing, because it just induce the whole rotation of polarization distribution. In this paper, we show some distinctive effects induced by the initial azimuthal phase of polarization distribution in the tight focusing of radially polarized and azimuthal-variant hybrid vector beams. For these two types of vector beams, the initial azimuthal phase of polarization distribution induces two types rotation, the whole polarization rotation and the combined polarization rotation including the polarization distribution rotation and phase difference rotation, respectively. Furthermore, two methods are presented for modulating energy flow density and spin angular momentum density in the focal region, the synchronous and asynchronous rotation, which denote two polarization unit vectors with the same or different initial phase. Our results indicate the light–matter interaction can be induced by the polarization distribution rotation of incident vector beams in its tight focusing, and provide a possible connection with the rotational Doppler effect of optical vector beams.

Parametric characterization of vortex cosine-hyperbolic-Gaussian beams

Based on the moments method, the analytical expressions for the beam propagation factor, the kurtosis parameter and the orbital angular momentum density distribution of a vortex cosh-Gaussian beam (vChGB) propagating in free space are derived. According to the obtained expressions, the beam propagation factor is determined by the decentered parameter b and the vortex charge m of the beam. The kurtosis parameter and the orbital angular momentum density are determined by the decentered parameter b, the vortex charge m and the propagation distance. Numerical examples are presented to illustrate and discuss the influences of the parameters b and m on the propagation characteristics of vChGB upon propagation in free space. This research could be beneficial to the applications involving vChGBs in optical communications, beam splitting, and micromanipulation of particles.

Spin density in partially coherent surface-plasmon-polariton vortex fields

We examine the spin angular momentum (SAM) density associated with the recently introduced [Phys. Rev. A 100, 053833 (2019)], partially coherent surface-plasmon-polariton (SPP) vortex fields at a metal-air interface. We show that the vortices appearing in such structured SPP fields induce a SAM density both in the interface plane and in the direction normal to the interface. We find that the radial and azimuthal SAM densities are caused solely by the SPP electric-field correlations. However, besides the intrinsic spin component induced by the complex SPP wave vector, the azimuthal SAM density remarkably carries also a spin component created by the elementary SPPs comprising the partially coherent vortex field. The normal SAM density, on the other hand, arises mainly due to the SPP magnetic-field correlations. Our analysis specifically demonstrates that the state of coherence of the partially coherent SPP vortex field plays an essential role in shaping the SAM density distributions. Our findings can find applications to near-field particle manipulation and in spin-based integrated photonic circuit design.

Novel twist-three transverse-spin sum rule for the proton and related generalized parton distributions

We derive a new twist-3 partonic sum rule for the transverse spin of the proton, which involves the well-know quark spin structure function gT(x)=g1(x)+g2(x), the less-studied but known transverse gluon polarization density ΔGT(x), and quark and gluon canonical orbital angular momentum densities associated with transverse polarization. This is the counter part of the sum rule for the longitudinal spin of the proton derived by Jaffe and Manohar previously. We relate the partonic canonical orbital angular momentum densities to a new class of twist-3 generalized parton distribution functions which are potentially measurable in deep-virtual exclusive processes. We also discuss in detail an important technicality related to the transverse polarization in the infinite momentum frame, i.e., separation of intrinsic contributions from the extrinsic ones. We apply our finding to the transverse-space distributions of partons, angular momentum, and magnetic moment, respectively, in a transversely polarized proton.

Functional Meta Lenses for Compound Plasmonic Vortex Field Generation and Control.

Surface plasmon polaritons carrying orbital angular momentum are of great fundamental and applied interest. However, common approaches for their generation are restricted to having a weak dependence on the properties of the plasmon-generating illumination, providing a limited degree of control over the amount of delivered orbital angular momentum. Here we experimentally show that by tailoring local and global geometries of vortex generators, a change in helicity of light imposes arbitrary large switching in the delivered plasmonic angular momentum. Using time-resolved photoemission electron microscopy we demonstrate pristine control over the generation and rotation direction of high-order plasmonic vortices. We generalize our approach to create complex topological fields and exemplify it by studying and controlling a "bright vortex", exhibiting the breakdown of a high-order vortex into a mosaic of unity-order vortices while maintaining the overall angular momentum density. Our results provide tools for plasmonic manipulation and could be utilized in lab-on-a-chip devices.

Double bracket formulation for the distribution function approach to multibead-chain suspensions

A suspension of elastic chains of small beads in a Newtonian fluid is a common model for a viscoelastic polymer solution. The configuration of these multibead chains is described by a distribution function that evolves according to a Liouville or Fokker–Planck equation. The evolution of these multibead-chain suspensions is described using a double bracket formulation with a Hamiltonian functional. The conservative part of the dynamics is described by a Poisson bracket, and the dissipative part by an additional symmetric bracket. We treat the configuration space of multibead chains as a higher order tangent bundle. Lifting the fluid velocity field to the bundle leads naturally to a semidirect product Lie–Poisson bracket for the conservative dynamics. The elastic stress exerted by the multibead chains on the fluid then follows directly from the same Hamiltonian functional that governs the internal dissipative mechanics of the multibead chains. For chains with three or more beads, the possible bending of the chain introduces an angular momentum flux that is absent for chains with two beads. This flux appear as an asymmetric elastic stress whose antisymmetric part is the divergence of a rank-3 tensor, as in the Cosserats’ theory of couple stresses in media with no internal angular momentum density. We investigate the possibility of an exact closure, passing from a distribution function description to a closed internal state variable description of the fluid suspension, and obtain some sufficient conditions for their existence. The resulting exactly closable models are generalisations of the upper-convected Maxwell model to Hookean bead–spring chains instead of Hookean bead–spring pairs.

Real spin angular momentum and acoustic spin torque in a topological phononic crystal

The topological one-way waveguide mode of the acoustic wave has recently been demonstrated in various meta-structure systems. Here, we show that in a topological phononic crystal with a symmetry-broken acoustic unit cell, the topological state possesses not just a “spin-like” pseudospin mode but also real spin angular momentum. By rotating the double-square units, the band of the phononic crystal will become inverse and induce both topological phase transition and spin angular momentum reversal. As such, by putting two topologically different systems together, the spin angular momentum dependent one-way interface modes can be selectively excited by acoustic spin sources, exhibiting robust transport protected by tight spin-momentum locking. The spin angular momentum density distribution in the unit cell and edge states shows that in addition to the pseudospin, there is a strong correlation between the real spin angular momentum and topological properties in this acoustic system, producing the topologically selective acoustic torque. Revealing the real spin angular momentum and associated acoustic spin torque properties of these topological phononic and acoustic systems will give people a more general understanding about symmetric breaking wave systems and help people to explore more potential applications of acoustic spins in various topological systems.

Twisted Spatiotemporal Optical Vortex Random Fields

We present twisted spatiotemporal optical vortex (STOV) beams, which are partially coherent light sources that possess a coherent optical vortex and a random twist coupling their space and time dimensions. These beams have controllable partial coherence and transverse orbital angular momentum (OAM), which distinguishes them from the more common spatial vortex and twisted beams (known to carry longitudinal OAM) in the literature and should ultimately make them useful in applications such as optical communications and optical tweezing. We present the mathematical analysis of twisted STOV beams, deriving the mutual coherence function and linear and angular momentum densities. We simulate the synthesis of twisted STOV beams and investigate their free-space propagation characteristics. We discuss how to physically generate twisted STOV fields and lastly conclude with a summary and brief discussion of future research.