Separation Of Angular Momentum Research Articles

Separation and detection of orbital angular momentum states of composite vortex beams in atmospheric turbulence channels

The separation and detection of compound orbital angular momentum (OAM) modes are the basis for achieving high-speed and high-capacity communication, but the atmospheric turbulence causes distortion of the phase fronts of vortex beams, which hinders the recognition of OAM modes. To solve this problem, in this work, we propose and investigate a joint scheme of combining the Gerchberg–Saxton (GS) algorithm and the phase of addition and subtraction model that can achieve high recognition accuracy and a wide range of OAM modes of compound perfect optical vortex beam under long-distance turbulence environment. At the receiving end, the GS algorithm and phase addition and subtraction are used to compensate and modulate the incident vortex light field to obtain the pre-processed light field, and then the OAM is detected by the coordinate transformation method. The simulation results show that: The detection range of the OAM of the three optical path detection model for the vortex beam transmitting 1000 m reaches −37 to +37 in the vacuum environment, and the mode purity of −37 to +37 can reach more than 0.3 when the turbulence intensity is Cn 2 = 2 × 10−15 m−2/3. The detection range of the OAM of the vortex can be further expanded by increasing the optical path. This study provides a new method for the separation and detection of OAM of composite vortex beams.

Spin-orbit optical Hall effect in π-vector fields.

Given the tremendous increase of data in digital era, vector vortex light with strongly coupled spin and orbital angular momenta of photons have attracted great attention for high-capacity optical applications. To fully utilize such rich degrees of freedom of light, it is highly anticipated to separate the coupled angular momentum with a simple but powerful method, and the optical Hall effect becomes a promising scheme. Recently, the spin-orbit optical Hall effect has been proposed in terms of general vector vortex light using two anisotropic crystals. However, angular momentum separation for π-vector vortex modes, another important part in vector optical fields, have not been explored and it remains challenging to realize broadband response. Here, the wavelength-independent spin-orbit optical Hall effect in π-vector fields has been analyzed based on Jones matrices and verified experimentally using a single-layer liquid-crystalline film with designed holographic structures. Every π-vector vortex mode can be decoupled into spin and orbital components with equal magnitude but opposite signs. Our work could enrich the fields of high-dimensional optics.

Shaping focal field by grafted polarization.

In this paper, we propose a novel (to our knowledge) vector beam by combining the radially polarized beams with the different polarization orders, which is called the grafted polarization vector beam (GPVB). Compared with the tight focusing of traditional cylindrical vector beams, GPVB can present more flexible focal field patterns by adjusting the polarization order of two (or more) grafted parts. Moreover, because the GPVB possesses the non-axisymmetrical polarization state distribution, which will lead to the spin-orbit coupling in its tight focusing, it can obtain the spatial separation of spin angular momentum (SAM) and orbital angular momentum (OAM) in the focal plane. The SAM and the OAM are well modulated by adjusting the polarization order of two (or more) grafted parts. Furthermore, we also find the on-axis energy flow in the tight focusing of the GPVB can be changed from positive to negative by adjusting its polarization order. Our results provide more modulation freedom and potential applications in optical tweezers and particles trapping.

On the Decomposition Theorem for Gluons

Recently, the problem of spin and orbital angular momentum (AM) separation has widely been discussed. Nowadays, all discussions about the possibility to separate the spin AM from the orbital AM in the gauge invariant manner are based on the ansatz that the gluon field can be presented in form of the decomposition where the physical gluon components are additive to the pure gauge gluon components, i.e. $A_\mu = A_\mu^{\text{phys}}+A_\mu^{\text{pure}}$. In the present paper, we show that in the non-Abelian gauge theory this gluon decomposition has a strong mathematical evidence in the frame of the contour gauge conception. In other words, we reformulate the gluon decomposition ansatz as a theorem on decomposition and, then, we use the contour gauge to prove this theorem. In the first time, we also demonstrate that the contour gauge possesses the special kind of residual gauge related to the boundary field configurations and expressed in terms of the pure gauge fields. As a result, the trivial boundary conditions lead to the inference that the decomposition includes the physical gluon configurations only provided the contour gauge condition.

Angular momentum separation in focused fractional vector beams for optical manipulation

The generation, propagation, and applications of different types of integer vector beams have been extensively investigated. However, little attention focuses on the photophysical and photomechanical properties of the fractional vector beam (FVB). Herein, we theoretically and experimentally investigate the spin angular momentum (SAM) separation and propagation characteristics of weakly focused FVBs. It is demonstrated that such a beam carrying no SAM leads to both the transverse separation of SAM and the special intensity patterns in the focal region. Furthermore, we study the intensity, SAM, and orbital angular momentum (OAM) distributions of the tightly focused FVBs. It is shown that both three-dimensional SAM and OAM are spatially separated in the focal region of tightly focused FVBs. We investigate the optical forces, spin torques, and orbital torques on a dielectric Rayleigh particle produced by the focused FVBs. The results reveal that asymmetrical spinning and orbiting motions of optically trapped particles can be realized by manipulating FVBs.

Spin-Orbit Optical Hall Effect.

The optical Hall effect manifests itself as angular momentum separation induced by the photonic spin-orbit interaction. Such a celebrated Hall effect, at the mercy of the angular momentum conservation law, has attracted tremendous interest owing to its science and potential applications in precision measurements, material characterizations, and photonic devices, as well as quantum optics. However, to date, the Hall effect only expresses angular momentum separation of the spin term (spin-spin separation) or the orbital term (orbit-orbit separation), whereas the spin-orbit angular momentum separation, named as the spin-orbit Hall effect, remains unexplored. Here we demonstrate for the first time that this spin-orbit effect could appear when the polarization state of the light beam evolves adiabatically from the equator toward the poles of the higher-order Poincaré sphere, rather than the conventional Poincaré sphere. In this scenario, the intrinsic spin and orbital components of the light beam become separated, leading to equal nonzero spin and orbital angular momenta in magnitude but with the opposite sign. We further show that the spin-orbit Hall effect can be controlled via crystal birefringence and hence holds promise for applications; e.g., it is shown that the separated orbital angular momentum could be utilized in particle manipulations.

Two-dimension and high-resolution demultiplexing of coaxial multiple orbital angular momentum beams.

A high-resolution demultiplexing method is proposed for the separation of coaxial multiple orbital angular momentum (OAM) beams which are created by a self-designed computer-generated hologram (CGH) encoded with logarithmic spiral phases. The logarithmic spiral phase, consisting of both azimuthal and radial phase, enables the two-dimensional demultiplexing of the OAM beams. The simulation and experiment results show that, with our method, the coaxial multiple OAM beams can be effectively separated in the specified plane. The overlap between the adjacent channel is greatly reduced by the high-resolution demultiplexing method, which is based on an optical geometrical transform and a coherent copy technique. The proposed method has great potential in increasing the number of spatial channels available for OAM multiplexing transmission system.

Quantum gauge transformation, gauge-invariant extension and angular momentum decomposition in Abelian Higgs model

I discuss the momentum and angular momentum decomposition problem in the Abelian Higgs model. The usual gauge-invariant extension (GIE) construction is incorporated naturally into the framework of quantum gauge transformation à la Strocchi and Wightman and with this, I investigate the momentum and angular momentum separation in a class of GIE conditions which correspond to the so-called “static gauges”. Using this language, I find that the so-called “generator criterion” does not generally hold even for the dressed physical field. In the case of U(1) symmetry breaking, I generalize the standard GIE construction to include the matter field degrees of freedom so that the usual separation pattern of momentum and angular momentum in the unitarity gauge can be incorporated into the same universal framework. When the static gauge condition could not uniquely fix the gauge, I show that this GIE construction should be expanded to take into account the residual gauge symmetry. In some cases, I reveal that the usual momentum or angular momentum separation pattern in terms of the physical dressed field variables needs some type of modification due to the nontrivial commutator structure of the underlying quantum gauge choice. Finally, I give some remarks on the general GIE constructions in connection with the possible commutator issues and modification of momentum and angular momentum separation patterns.

轨道角动量分离系统中纯相位型扇出光栅的设计

轨道角动量分离系统中纯相位型扇出光栅的设计

Trunk kinetic effort during step ascent and descent in patients with transtibial amputation using angular momentum separation

BackgroundPatients with transtibial amputation adopt trunk movement compensations that alter effort and increase the risk of developing low back pain. However, the effort required to achieve high-demand tasks, such as step ascent and descent, remains unknown. MethodsKinematics were collected during bilateral step ascent and descent tasks from two groups: 1) seven patients with unilateral transtibial amputation and 2) seven healthy control subjects. Trunk kinetic effort was quantified using translational and rotational segmental moments (time rate of change of segmental angular momentum). Peak moments during the loading period were compared across limbs and across groups. FindingsDuring step ascent, patients with transtibial amputation generated larger sagittal trunk translational moments when leading with the amputated limb compared to the intact limb (P=0.01). The amputation group also generated larger trunk rotational moments in the frontal and transverse planes when leading with either limb compared to the healthy group (P=0.01, P<0.01, respectively). During step descent, the amputation group generated larger trunk translational and rotational moments in all three planes when leading with the intact limb compared to the healthy group (P<0.017). InterpretationThis investigation identifies how differing trunk movement compensations, identified using the separation of angular momentum, require higher kinetic effort during stepping tasks in patients with transtibial amputation compared to healthy individuals. Compensations that produce identified increased and asymmetric trunk segmental moments, may increase the risk of the development of low back pain in patients with amputation.

Physical angular momentum separation for QED

We study the non-uniqueness problem of the gauge-invariant angular momentum separation for the case of QED, which stems from the recent controversy concerning the proper definitions of the orbital angular momentum and spin operator of the individual parts of a gauge field system. For the free quantum electrodynamics without matter, we show that the basic requirement of Euclidean symmetry selects a unique physical angular momentum separation scheme from the multitude of the possible angular momentum separation schemes constructed using the various gauge-invariant extensions (GIEs). Based on these results, we propose a set of natural angular momentum separation schemes for the case of interacting QED by invoking the formalism of asymptotic fields. Some perspectives on such a problem for the case of QCD are briefly discussed.

Identification of trunk and pelvis movement compensations in patients with transtibial amputation using angular momentum separation

Patients with unilateral dysvascular transtibial amputation (TTA) have a higher risk of developing low back pain than their healthy counterparts, which may be related to movement compensations used in the absence of ankle function. Assessing components of segmental angular momentum provides a unique framework to identify and interpret these movement compensations alongside traditional observational analyses. Angular momentum separation indicates two components of total angular momentum: (1) transfer momentum and (2) rotational momentum. The objective of this investigation was to assess movement compensations in patients with dysvascular TTA, patients with diabetes mellitus (DM), and healthy controls (HC) by examining patterns of generating and arresting trunk and pelvis segmental angular momenta during gait. We hypothesized that all groups would demonstrate similar patterns of generating/arresting total momentum and transfer momentum in the trunk and pelvis in reference to the groups (patients with DM and HC). We also hypothesized that patients with amputation would demonstrate different (larger) patterns of generating/arresting rotational angular momentum in the trunk. Patients with amputation demonstrated differences in trunk and pelvis transfer angular momentum in the sagittal and transverse planes in comparison to the reference groups, which indicates postural compensations adopted during walking. However, patients with amputation demonstrated larger patterns of generating and arresting of trunk and pelvis rotational angular momentum in comparison to the reference groups. These segmental rotational angular momentum patterns correspond with high eccentric muscle demands needed to arrest the angular momentum, and may lead to consequential long-term effects such as low back pain.

Spectral separation of optical spin based on antisymmetric Fano resonances.

We propose a route to the spectral separation of optical spin angular momentum based on spin-dependent Fano resonances with antisymmetric spectral profiles. By developing a spin-form coupled mode theory for chiral materials, the origin of antisymmetric Fano spectra is clarified in terms of the opposite temporal phase shift for each spin, which is the result of counter-rotating spin eigenvectors. An analytical expression of a spin-density Fano parameter is derived to enable quantitative analysis of the Fano-induced spin separation in the spectral domain. As an application, we demonstrate optical spin switching utilizing the extreme spectral sensitivity of the spin-density reversal. Our result paves a path toward the conservative spectral separation of spins without any need of the magneto-optical effect or circular dichroism, achieving excellent purity in spin density superior to conventional approaches based on circular dichroism.

The azimuthal component of Poynting's vector and the angular momentum of light

The usual description in basic electromagnetic theory of the linear and angular momenta of light is centred upon the identification of Poynting's vector as the linear momentum density and its cross product with position, or azimuthal component, as the angular momentum density. This seemingly reasonable approach brings with it peculiarities, however, in particular with regards to the separation of angular momentum into orbital and spin contributions, which has sometimes been regarded as contrived. In the present paper, we observe that densities are not unique, which leads us to ask whether the usual description is, in fact, the most natural choice. To answer this, we adopt a fundamental rather than heuristic approach by first identifying appropriate symmetries of Maxwell's equations and subsequently applying Noether's theorem to obtain associated conservation laws. We do not arrive at the usual description. Rather, an equally acceptable one in which the relationship between linear and angular momenta is nevertheless more subtle and in which orbital and spin contributions emerge separately and with transparent forms.

Angular momentum redistribution by SASI spiral modes and consequences for neutron star spins

In the collapsing core of massive stars, the standing accretion shock instability (SASI) can drive spiral modes that efficiently redistribute angular momentum. This process can impart a spin to the forming neutron star even when the progenitor star is non-rotating. Here we develop the first analytical description of the angular momentum redistribution driven by a spiral mode of the SASI. Our analysis, valid in the limit of small mode amplitude, shows that the angular momentum separation is driven by the Reynolds stress generated by the spiral mode. The resulting solutions compare favorably with previous three-dimensional hydrodynamic simulations of the SASI in the linear and weakly non-linear phases. Reasonable agreement is also found when extrapolating the solutions into the fully non-linear phase. A Reynolds-decomposition of the flow is performed in the saturated state of these simulations, showing that outward angular momentum transport by the Reynolds stress and the fluctuating component of the mass flux balance inward transport by advection. We derive an approximate analytic expression for the maximum angular momentum deposited in the neutron star as a function of the mass accretion rate, shock radius, shock compression ratio, and amplitude of the spiral mode at the time of explosion. Implications for the birth spin periods of neutron stars are discussed.

Separation of spin angular momentum in space-variant linearly polarized beam

We show that the spin angular momentum (SAM) flux in a space-variant linearly polarized beam can be separated in the focal plane. Such a beam carries only orbital angular momentum (OAM) and develops a net SAM flux upon focusing. The radial splitting of the SAM flux density is mediated by the phase vortex (or OAM) and can be controlled by the topological charge of the phase vortex. Optical trapping experiments verify the separation of the SAM flux density. The proposed approach enriches the manipulation of the angular momentum of light fields and inspires more designs of focus engineering, which would benefit optical micromanipulation of microscopic particles.

Gauge-invariant dynamical quantities of QED with decomposed gauge potentials

We discover an inner structure of the QED system; i.e., by decomposing the gauge potential into two orthogonal components, we obtain a new expansion of the Lagrangian for the electron-photon system, from which, we realize the orthogonal decomposition of the canonical momentum conjugate to the gauge potential with the canonical momentum's two components conjugate to the gauge potential's two components, respectively. Using the new expansion of Lagrangian and by the general method of field theory, we naturally derive the gauge invariant separation of the angular momentum of the electron-photon system from Noether theorem, which is the rational one and has the simplest form in mathematics, compared with the other four versions of the angular momentum separation available in literature. We show that it is only the longitudinal component of the gauge potential that is contained in the orbital angular momentum of the electron, as Chen et al. have said. A similar gauge invariant separation of the momentum is given. The decomposed canonical Hamiltonian is derived, from which we construct the gauge invariant energy operator of the electron moving in the external field generated by a proton [Phys. Rev. A 82, 012107 (2010)], where we show that the form of the kinetic energy containing the longitudinal part of the gauge potential is due to the intrinsic requirement of the gauge invariance. Our method provides a new perspective to look on the nucleon spin crisis and indicates that this problem can be solved strictly and systematically.

Canonical separation of angular momentum of light into its orbital and spin parts

It is shown that the photon picture of the electromagnetic field enables one to determineunambiguously the splitting of the total angular momentum of the electromagnetic fieldinto the orbital part and the spin part.

Pumping angular momentum by driven chaotic scattering

Chaotic scattering with an internal degree of freedom and the possibility of generating directed transport of angular momentum is studied in a specific model, a magnetic dipole moving in a periodically modulated magnetic field confined to a compact region in space. We show that this system is an irregular scatterer in large parts of its parameter space. If in addition all spatio-temporal symmetries are broken, directed transport of mass as well as angular momentum occurs. The sensitive parameter dependence of the corresponding currents includes frequent sign reversals. Zeros of either quantity entail the exclusive occurrence of the other and thus give rise in particular to angular-momentum separation without mass transport as a classical analogue of spin-polarized currents.

Meridional Propagation of Planetary-Scale Waves in Vertical Shear: Implication for the Venus Atmosphere

Abstract It is shown that planetary-scale waves are inherently accompanied by latitudinal momentum transport when they propagate vertically in vertically sheared zonal flows. Because of the dependence of the wave's latitudinal scale on the intrinsic phase speed, positive (negative) vertical shear should force prograde (retrograde) waves to focus equatorward and retrograde (prograde) waves to expand poleward in the course of upward propagation. Consequently, Eliassen–Palm (EP) flux vectors are tilted from the vertical and nonzero latitudinal momentum fluxes occur. The direction of momentum transport should always be equatorward (poleward) in positive (negative) vertical shear irrespective of the zonal propagation direction. The idea was applied to upwardly propagating waves in the Venusian middle atmosphere, where vertical shear of strong midlatitude jets and equatorial superrotation exist. Numerical solutions showed that Kelvin and prograde inertio-gravity waves focus equatorward and mixed Rossby–gravity and Rossby waves expand poleward below the cloud top. The former is attributed primarily to the vertical shear of the superrotation, while the latter to the vertical shear beneath the midlatitude jets. Such characteristics of planetary-scale waves will cause angular momentum separation between high and low latitudes and, at least partly, contribute to the maintenance of the superrotation.