Component Of Angular Momentum Research Articles

Spin-orbit interactions in plasmonic crystals probed by site-selective cathodoluminescence spectroscopy.

The study of spin-orbit coupling (SOC) of light is crucial to explore the light-matter interactions in sub-wavelength structures. By designing a plasmonic lattice with chiral configuration that provides parallel angular momentum and spin components, one can trigger the strength of the SOC phenomena in photonic or plasmonic crystals. Herein, we explore the SOC in a plasmonic crystal, both theoretically and experimentally. Cathodoluminescence (CL) spectroscopy combined with the numerically calculated photonic band structure reveals an energy band splitting that is ascribed to the peculiar spin-orbit interaction of light in the proposed plasmonic crystal. Moreover, we exploit angle-resolved CL and dark-field polarimetry to demonstrate circular-polarization-dependent scattering of surface plasmon waves interacting with the plasmonic crystal. This further confirms that the scattering direction of a given polarization is determined by the transverse spin angular momentum inherently carried by the SP wave, which is in turn locked to the direction of SP propagation. We further propose an interaction Hamiltonian based on axion electrodynamics that underpins the degeneracy breaking of the surface plasmons due to the spin-orbit interaction of light. Our study gives insight into the design of novel plasmonic devices with polarization-dependent directionality of the Bloch plasmons. We expect spin-orbit interactions in plasmonics will find much more scientific interests and potential applications with the continuous development of nanofabrication methodologies and uncovering new aspects of spin-orbit interactions.

Hall Effect at the Focus of an Optical Vortex with Linear Polarization.

The tight focusing of an optical vortex with an integer topological charge (TC) and linear polarization was considered. We showed that the longitudinal components of the spin angular momentum (SAM) (it was equal to zero) and orbital angular momentum (OAM) (it was equal to the product of the beam power and the TC) vectors averaged over the beam cross-section were separately preserved during the beam propagation. This conservation led to the spin and orbital Hall effects. The spin Hall effect was expressed in the fact that the areas with different signs of the SAM longitudinal component were separated from each other. The orbital Hall effect was marked by the separation of the regions with different rotation directions of the transverse energy flow (clockwise and counterclockwise). There were only four such local regions near the optical axis for any TC. We showed that the total energy flux crossing the focus plane was less than the total beam power since part of the power propagated along the focus surface, while the other part crossed the focus plane in the opposite direction. We also showed that the longitudinal component of the angular momentum (AM) vector was not equal to the sum of the SAM and the OAM. Moreover, there was no summand SAM in the expression for the density of the AM. These quantities were independent of each other. The distributions of the AM and the SAM longitudinal components characterized the orbital and spin Hall effects at the focus, respectively.

An odd feature of the “most classical” states of SU(2) invariant quantum mechanical systems

Complex and spinorial techniques of general relativity are used to determine all the states of SU(2) invariant quantum mechanical systems in which the equality holds in uncertainty relations for the components of the angular momentum vector operator in two given directions. The expectation values depend on a discrete quantum number and two parameters, one of them is the angle between two angular momentum components and the other is the quotient of two standard deviations. Allowing the angle between two angular momentum components to be arbitrary, a new genuine quantum mechanical phenomenon emerges: it is shown that although standard deviations change continuously, one of the expectation values changes discontinuously on this parameter space. Since physically neither of the angular momentum components is distinguished over the other, this discontinuity suggests that the genuine parameter space must be a double cover of this classical one: it must be diffeomorphic to a Riemann surface known in connection with the complex function z. Moreover, the angle between angular momentum components plays the role of the parameter of an interpolation between the continuous range of expectation values in the special case of orthogonal angular momentum components and the discrete point spectrum of one angular momentum component. The consequences in the simultaneous measurements of these angular momentum components are also discussed briefly.

Generalized Poincaré Beams in Tight Focus

We study the tight focus of generalized (hybrid) Poincaré beams. A conventional Poincaré beam is a coaxial superposition of two optical vortices, one with left circular polarization and a topological charge (TC) of m, while the other has a right circular polarization and a TC of −m. The generalized Poincaré beams are also composed of two optical vortices, but their TCs are different, for instance, p and q. Here, we theoretically investigate the generalized Poincaré beams with the TCs p = m + 1 and q = −m in tight focus. In this case, both transverse components of the strength vector of the initial electric field have a topological charge of 1/2, and the beam itself is a cylindrical vector beam of fractional order m + 1/2. Analytical expressions are derived for the components of the strength vectors of the electric and magnetic field at the focus as well as for the intensity distribution, the longitudinal component of the spin angular momentum (SAM), and for the components of the Poynting vector (energy flow density). We show that the intensity at the focus has 2m − 1 local maxima residing evenly in a certain circle radius with the center on the optical axis. We also demonstrate that the radial spin and orbital Hall effects occur at the focus, i.e., the longitudinal SAM component has different signs in the circles of different radii, and the azimuthal component of the transverse Poynting vector also has different signs.

The Short-Term Prediction of Length of Day Using 1D Convolutional Neural Networks (1D CNN)

Accurate Earth orientation parameter (EOP) predictions are needed for many applications, e.g., for the tracking and navigation of interplanetary spacecraft missions. One of the most difficult parameters to forecast is the length of day (LOD), which represents the variation in the Earth's rotation rate since it is primarily affected by the torques associated with changes in atmospheric circulation. In this study, a new-generation time-series prediction algorithm is developed. The one-dimensional convolutional neural network (1D CNN), which is one of the deep learning methods, is introduced to model and predict the LOD using the IERS EOP 14 C04 and axial Z component of the atmospheric angular momentum (AAM), which was taken from the German Research Centre for Geosciences (GFZ) since it is strongly correlated with the LOD changes. The prediction procedure operates as follows: first, we detrend the LOD and Z-component series using the LS method, then, we obtain the residual series of each one to be used in the 1D CNN prediction algorithm. Finally, we analyze the results before and after introducing the AAM function. The results prove the potential of the proposed method as an optimal algorithm to successfully reconstruct and predict the LOD for up to 7 days.

LAMOST meets Gaia: The Galactic open clusters

Open clusters (OCs) are born and evolve along the Milky Way (MW) plane. On them is imprinted the history of the Galactic disc, including its chemical and dynamical evolution. Chemical and dynamical properties of OCs can be derived from photometric, spectroscopic, and astrometric data of their member stars. Based on the photometric and astrometric data from the Gaia mission, the membership of stars in more than two thousand Galactic clusters has been identified in the literature. The chemical properties (e.g. metallicity) and kinematical properties (e.g. radial velocity), however, are still poorly known for many of these clusters. In synergy with the large spectroscopic survey LAMOST (data release 8) and Gaia (data release 2), we report a new comprehensive catalogue of 386 OCs. This catalogue has homogeneous parameter determinations of radial velocity, metallicity, and dynamical properties, such as orbit, eccentricity, angular momenta, total energy, and 3D Galactic velocity. These parameters enable the first radial velocity determination for 44 clusters, and the first spectroscopic [Fe/H] determination for 137 clusters. The metallicity distributions of the majority of clusters show falling trends in the parameter space of the Galactocentric radius, the total energy, and the Z component of angular momentum, except for two old groups that show flat tails in their own parameter planes. Cluster populations of ages younger and older than 500 Myr distribute diversely on the disc. The latter have a spatial consistency with the Galactic disc flare. The 3D spatial comparison between very young clusters (< 100 Myr) and nearby molecular clouds revealed a wide range of metallicity distribution along the Radcliffe gas cloud wave, indicating a possible inhomogeneous mixing or fast star formation along the wave. This catalogue will serve the community as a useful tool to trace the chemical and dynamical evolution of the MW.

Resonant jumps induced by stationary tidal perturbation: a two-for-one deal

Extreme-mass-ratio inspirals (EMRIs) are promising target sources for space-based interferometers such as LISA, Taiji, and Tianqin. Depending on the astrophysical environment, such as close perturbers or an accretion disk, EMRI orbital evolution may deviate from the predictions of general relativity in vacuum. In particular, we focus on the resonance jumps, i.e. the changes of the conserved quantities induced by a stationary perturbation to the background Kerr geometry. Using Hamiltonian formulation, we provide a closed relation between the jump in Carter constant and that in the axial component of angular momentum. It is also shown that the obtained relation is consistent with the fitting formulae computed for the tidal resonance in previous works.

Insights into propagating surface plasmons in Ag–Cu alloy thin films: Enhancement of spin angular momentum of light

Surface plasmon polaritons (SPPs) can be supported by metal–dielectric interfaces and have been exploited for various applications. Typically, most studies deal with plasmons excited in pure metallic films or homogenous alloy thin films and the understanding of plasmon behavior in films with complex microstructures is limited. In this work, we numerically study the surface plasmons that are supported at the interface of an Ag–Cu alloy film that undergoes spinodal decomposition to produce a two-phase microstructure, when an initially compositionally homogenous alloy film (with composition within spinodal limits) is processed within the miscibility gap. We use phase-field simulated spinodally decomposed microstructures for our optical simulations to study the effect of microstructure on propagating surface plasmons in Ag–Cu alloy films. We demonstrate that the far-field response is governed principally by the composition of the alloy film and is not affected by the microstructural feature size. On the contrary, near-fields are strongly dependent on the microstructure and composition of the films. The origin of inhomogenous fields is demonstrated to be the result of constructive and destructive interference of SPPs. Finally, we demonstrate the enhancement of both transverse and longitudinal components of spin angular momentum in these phase-separated alloy films. The longitudinal components can be enhanced by more than a hundred times in the alloy films as compared to the pure metal films. This study paves the way for exploiting multi-phase alloy thin films for applications in sensing, nanomanipulation, and light modulation.

Gravitational Faraday Rotation of gravitational waves by a Kerr black hole

Gravitational Faraday Rotation (GFR) is a frame-dragging effect induced by rotating massive objects, which is one of the important, yet studied characteristics of lensed gravitational waves (GWs). In this work, we calculate the GFR angle χ g of GWs in the weak deflection limit, assuming it is lensed by a Kerr black hole (BH). We find that the GFR effect changes the initial polarization state of the lensed GW. Compared with the Einstein deflection angle, the dominant term of the rotation angle χ g is a second-order correction to the polarization angle, which depends on the light-of-sight component of BH angular momentum. Such a rotation is tiny and degenerates with the initial polarization angle. In some critical cases, the GFR angle is close to the detection capability of the third-generation GW detector network, although the degeneracy has to be broken.

Polarized photoelectrons from converging vector waves

This paper investigates the spin characteristics of photoelectrons when hydrogen-like ions are centro-symmetrically irradiated with converging vector waves—a non-paraxial form of structured light. For a photon with given total angular momentum and third component thereof, photoelectrons with both helicities are obtained—in contrast to the fixed helicities produced by left- or right-circularly polarized light. The angular distribution of photoelectrons is broadly tunable through the radiation mode numbers, and opposite helicities can be extracted in synchronism.

Autonomous Wheel Off-Loading Strategies for Deep-Space CubeSats

Deep-space CubeSats missions require careful trade-offs on design drivers such as mass, volume, and cost, while ensuring autonomous operations. This work elaborates the possibility of off-loading the reaction wheels without the need of carrying a bulky and expensive reaction control system or the field-dependent magnetotorquers. The momentum accumulated along two body axes can be removed by either offsetting the main thruster with a gimbal mechanism or by tilting differentially the solar wings. The dumping on the third axis can be still accomplished by imposing a specific attitude trajectory with the motion of either the gimbal or the arrays drive mechanism. The M-Argo CubeSat is selected as case study to test the techniques along its deep-space trajectory. The strategies decision-making is autonomously carried out by a state machine. The off-loading during the cruising arcs employs the gimballed thruster and takes typically 3 h, granting a mass savings of more than 99% with respect to the usage of a reaction control system. The trajectory is shown to have negligible differences with respect to the nominal one, since the thrust is corrected accordingly. During the coasting arcs, the solar arrays are tilted and several hours are required, depending on the Sun direction and intensity, but the propellant is completely saved. Sensitivity analyses are also carried out on the initial angular momentum components and the center of mass displacement to check the robustness of the algorithms.

No general relation between phase vortices and orbital angular momentum

Simple superpositions of Laguerre–Gauss beams illustrate, counterintuitively, the difference between two quantities that are commonly conflated: the component of orbital angular momentum ⟨l⟩ in the propagation direction z, and the total topological charge S, which is the algebraic sum of the charges of vortices piercing any plane perpendicular to z. The examples illustrate two contrasting situations: ⟨l⟩ = 0, S ≠ 0, and ⟨l⟩ ≠ 0, S = 0. In the second situation, not only is the total charge zero but also there are no vortices in the infinite half-space beyond the beam waist plane z = 0.

Spin-Orbital Conversion with the Tight Focus of an Axial Superposition of a High-Order Cylindrical Vector Beam and a Beam with Linear Polarization.

In this paper, spin-orbital conversion in the tight focus of an axial superposition of a high-order (order m) cylindrical vector beam and a beam with linear polarization is theoretically and numerically considered. Although such a beam does not have a spin angular momentum in the initial plane and the third projection of its Stokes vector is equal to zero, subwavelength local regions with a transverse vortex energy flow and with the non-zero third Stokes projection (the longitudinal component of the spin angular momentum) are formed in the focal plane for an odd number m. This means that such a beam with an odd m has regions of elliptical or circular polarization with alternating directions of rotation (clockwise and counterclockwise) in the focus. For an even m, the field is linearly polarized at every point of the focal plane, and the transverse energy flux is absent. These beams can be used to create a micromachine in which two microparticles in the form of gears are captured in the focus of the beam into neighboring local areas in which the energy flow rotates in different directions, and therefore, these gears will also rotate in different directions.

Composition of low-lying J=32± Δ -baryons

A Poincar\'e-covariant quark+diquark Faddeev equation is used to develop insights into the structure of the four lightest $(I,J^P=\tfrac{3}{2},\tfrac{3}{2}^\pm)$ baryon multiplets. Whilst these systems can contain isovector-axialvector and isovector-vector diquarks, one may neglect the latter and still arrive at a reliable description. The $(\tfrac{3}{2},\tfrac{3}{2}^+)$ states are the simpler systems, with features that bear some resemblance to quark model pictures, \emph{e.g}., their most prominent rest-frame orbital angular momentum component is $\mathsf S$-wave and the $\Delta(1600)\tfrac{3}{2}^+$ may reasonably be viewed as a radial excitation of the $\Delta(1232)\tfrac{3}{2}^+$. The $(\tfrac{3}{2},\tfrac{3}{2}^-)$ states are more complex: the $\Delta(1940)\tfrac{3}{2}^-$ expresses little of the character of a radial excitation of the $\Delta(1700)\tfrac{3}{2}^-$; and whilst the rest-frame wave function of the latter is predominantly $\mathsf P$-wave, the leading piece in the $\Delta(1940)\tfrac{3}{2}^-$ wave function is $\mathsf S$-wave, in conflict with quark model expectations. Experiments that can test these predictions, such as large momentum transfer resonance electroexcitation, may shed light on the nature of emergent hadron mass.

Evolution of the chiral rotation mode in rhodium isotopes

Self-consistent solutions for the chiral rotation in the rhodium isotopes $^{102--107}\mathrm{Rh}$ are obtained within the three-dimensional tilted axis cranking covariant density functional theory. The orientation of angular momenta is determined self-consistently by minimizing the total Routhian surface calculations with respect to the azimuth angle $\ensuremath{\varphi}$ and polar angle $\ensuremath{\theta}$ for a given rotational frequency. It is found that when neutrons are added the critical rotational frequency ${\ensuremath{\omega}}_{\text{crit}}$ of the appearance of chiral aplanar rotation decreases, which can be attributed to the neutrons in $(gd)$ shells having smaller and larger angular momentum components along the short and medium axes, respectively. The theoretical results agree well with the experimental energy spectra, electromagnetic transition probabilities, as well as the kinetic and dynamic moments of inertia.

Rotating and vibrating symmetric-top molecule RaOCH3 in fundamental P, T -violation searches

We study the influence of the rotations and vibrations of the symmetric-top ${\mathrm{RaOCH}}_{3}$ molecule on its effectiveness as a probe for the $\mathcal{P}, \mathcal{T}$-violating effects, such as the electron electric dipole moment and the scalar-pseudoscalar electron-nucleon interaction. The corresponding enhancement parameters ${E}_{\mathrm{eff}}$ and ${E}_{\mathrm{s}}$ are computed for the ground and first excited rovibrational states with different values of the angular momentum component $K$. For the lowest $K$ doublet with ${v}_{\ensuremath{\perp}}=0$ and $K=1$ the values are ${E}_{\mathrm{eff}}=47.647\phantom{\rule{0.28em}{0ex}}\mathrm{GV}/\mathrm{cm}$ and ${E}_{\mathrm{s}}=62.109\phantom{\rule{0.16em}{0ex}}\mathrm{kHz}$. The results show larger deviation from the equilibrium values than in triatomic molecules.

Interconversion between OAM and SAM in five-wave mixing process in medium with the fourth-order optical susceptibility

We investigate the interconversion between spin components of the angular momentum (SAM) and orbital components of the angular momentum (OAM) of collinear elliptically polarized monochromatic fundamental beams with frequencies ω1 and ω2 in the five-wave mixing process in homogeneous isotropic nonracemic mixtures of chiral molecules with nonlinear fourth-order susceptibility. Fundamental beams have helicoidal wavefronts and arbitrary radial distributions of intensity. The discovered non-conservation of the total SAM and OAM projections on the direction of propagation of the interacting waves during the generation of radiation at the frequency 3ω1 - ω2 compensate each other, ensuring the conservation of the total angular momentum projection. A straightforward classical and quantum interpretation of the results is given.

Transfer matrices and solution of the problem of stochastic dynamics of aerosol clusters by Monte Carlo method

Abstract A Monte Carlo algorithm based on the use of transfer matrices is developed to describe the stochastic dynamics of the rotational--translational motion of aerosol clusters taking into account fluctuations in the molecular fluxes of the gas medium. In the general case, the cluster is immersed into a rarefied gas medium, the temperatures of its surfaces may differ from the temperature of the surrounding gas, for example, due to absorption of visible and infrared radiation. The motion of the cluster is described based on Langevin motion equations. The algorithm allows one to calculate parameters of the probability distribution of a six-dimensional vector consisting of components of the momentum and angular momentum vectors transmitted to the cluster by molecular flows. The numerical method allows one to apply preliminary analytical averaging modulo velocities of molecules for both the average values of the components of momentum and angular momentum and their correlation characteristics, which significantly reduces the calculation time.

Non-asymptotic Coqblin–Schrieffer interaction between local f[formula omitted]-states

The magnetism of many cerium-based compounds has been studied considering the hybridization of its local f1 state with itinerant electrons, a mechanism that originates an anisotropic RKKY-type interaction between two neighboring local moments. The orbital degrees of freedom of the f-levels play a fundamental role in this mechanism, as shown in the well-known and broadly used Coqblin–Schrieffer formalism, which, however, is valid only for ions very far apart, yields an effective Hamiltonian that is not hermitian and does not reflect the interchange symmetry when applied for two identical ions. Therefore, the off-diagonal terms of the interaction energy do not exhibit the Friedel oscillations typical of the RKKY interactions. Through an exact evaluation of Ruderman–Kittel-like integrals, we extended such formalism to any ionic separation, corrected the non-hermiticity and the lack of ionic interchange symmetry, which recovered the Friedel oscillations. These improvements strongly impact the contribution of each angular momentum component to the ionic interaction-energy and hence whether ferro- or anti-ferromagnetic alignment is favored. As an example, we calculated the temperature dependence of the magnetic susceptibility for a simple system of Ce-Ce free dimers and show that striking differences exist when compared with the susceptibility evaluated using the original Coqblin–Schrieffer formalism.

Antikaon-nucleon interaction within three-dimensional approach: Homogeneous and inhomogeneous Lippmann-Schwinger equations

The Λ(1405) resonance below the antikaon-nucleon threshold is studied by solving homogeneous and inhomogeneous Lippmann-Schwinger equations for local K‾N Yukawa and Gaussian potentials within three-dimensional approach. In this method, unlike the partial wave method, in which the number of considered partial waves needs to increase with enhancing energy, the calculations are performed without decomposition into angular momentum components. Also, the behavior of the transition matrix in on-shell, half-off-shell, and fully off-shell modes for various energies is investigated.