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The issue of gauge choice in the Landau problem and the physics of canonical and mechanical orbital angular momenta
One intriguing issue in the nucleon spin decomposition problem is the existence of two types of decompositions, which are representably characterized by two different orbital angular momenta (OAMs) of quarks. The one is the mechanical OAM, while the other is the so-called gauge-invariant canonical (g.i.c.) OAM, the concept of which was introduced by Chen et al. An especially delicate quantity is the g.i.c. OAM, which must be distinguished from the ordinary (gauge-variant) canonical OAM. We find that, owing to its analytically solvable nature, the famous Landau problem offers an ideal tool to understand the difference and the physical meaning of the above three OAMs, i.e. the standard canonical OAM, g.i.c. OAM, and the mechanical OAM. We analyze these three OAMs in two different formulations of the Landau problem, first in the standard (gauge-fixed) formulation and second in the gauge-invariant (but path-dependent) formulation of DeWitt. Especially interesting is the latter formalism. It is shown that the choice of path has an intimate connection with the choice of gauge, but they are not necessarily equivalent. Then, we answer the question about what is the consequence of a particular choice of path in DeWitt’s formalism. This analysis also clarifies the implication of the gauge symmetry hidden in the concept of g.i.c. OAM. Finally, we show that the finding above offers a clear understanding about the uniqueness or non-uniqueness problem of the nucleon spin decomposition, which arises from the arbitrariness in the definition of the so-called physical component of the gauge field.
Nonequilibrium Quasiparticle Dynamics in Bi-Based Superconductors Measured by Modulation Photoexcitation Spectroscopy
We develop an orbital angular momentum (OAM) excitation pump-probe (Pp) spectroscopy and perform experiments on a Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+δ} (Bi2212) superconductor. The OAM modulation for the pump is realized by using a transverse mode conversion technique which allows to modulate the chirality of the optical OAM with a fixed polarization. The result reveals a difference of the OAM-dependent transient reflectivity changes below T{sub c}, indicating that the pump OAM can break the chiral symmetry of the superconducting (SC) state. The OAM dependences of the transient signal imply that the quasi-particle (QP) excitation with OAM enhances the SC with opposite chirality and/or suppress the SC with equal chirality. The temperature dependence of the OAM dynamics shows virtually no pairing fluctuation that usually appears in the QP dynamics observed by conventional Pp, suggesting that the nonequilibrium OAM dynamics is sensitive to the delocalized OAM associated with long range order.
A FDTD Solution of Scattering of Laser Beam with Orbital Angular Momentum by Dielectric Particles: Far-Field Characteristics
Electromagnetic (EM) beams with orbital angular momentum (OAM) may have great potential applications in communication technology and in remote sensing of the Earth-atmosphere system and outer planets. Study of their interaction with optical lenses and dielectric or metallic objects, or scattering of them by particles in the Earth-atmosphere system, is a necessary step to explore the advantage of the OAM EM beams. In this study, the 3-dimensional (3D) scattered-field (SF) finite-difference time domain (FDTD) technique with the convolutional perfectly matched layer (CPML) absorbing boundary conditions (ABC) is applied to calculate the scattering of the purely azimuthal (the radial mode number is assumed to be zero) Laguerre–Gaussian (LG) beams with the OAM by dielectric particles. We found that for OAM beam׳s interaction with dielectric particles, the forward-scattering peak in the conventional phase function (P11) disappears, and light scattering peak occurs at a scattering angle of ~15° to 45°. The disappearance of forward-scattering peak means that, in laser communications most of the particle-scattered noise cannot enter the receiver, thus the received light is optimally the original OAM-encoded signal. This feature of the OAM beam also implies that in lidar remote sensing of the atmospheric particulates, most of the multiple-scattering energy will be off lidar sensors, and this may result in an accurate profiling of particle layers in the atmosphere or in the oceans by lidar, or even in the ground when a ground penetration radar (GPR) with the OAM is applied. This far-field characteristics of the scattered OAM light also imply that the optical theorem, which is derived from plane-parallel wave scattering case and relates the forward scattering amplitude to the total cross section of the scatterer, is invalid for the scattering of OAM beams by dielectric particles.
Generation of extreme-ultraviolet beams with time-varying orbital angular momentum
Light fields carrying orbital angular momentum (OAM) provide powerful capabilities for applications in optical communications, microscopy, quantum optics, and microparticle manipulation. We introduce a property of light beams, manifested as a temporal OAM variation along a pulse: the self-torque of light. Although self-torque is found in diverse physical systems (i.e., electrodynamics and general relativity), it was not realized that light could possess such a property. We demonstrate that extreme-ultraviolet self-torqued beams arise in high-harmonic generation driven by time-delayed pulses with different OAM. We monitor the self-torque of extreme-ultraviolet beams through their azimuthal frequency chirp. Lastly, this class of dynamic-OAM beams provides the ability for controlling magnetic, topological, and quantum excitations and for manipulating molecules and nanostructures on their natural time and length scales.
ORBITAL ANGULAR MOMENTUM BEAMS RESEARCH USING A FREE-ELECTRON LASER OSCILLATOR
Orbital angular momentum (OAM) photon beams are excellent tools for non-contact optical manipulation of mat- ter in a broad photon energy range. A free-electron laser (FEL) oscillator is well-suited for studying OAM beams with various features including a wide spectral coverage, wavelength tunability, two-color lasing, polarization control, etc. Here, we report the first experimental demonstration of superposed OAM beams from an oscillator FEL. Lasing at around 458 nm, we have generated superposed OAM beams up to the fourth order as a superposition of two pure OAM modes with opposite helicities. These generated beams have a good beam quality, a high degree of circular polarization, and high power. Using external rf modulation with frequen- cies from 1 to 30 Hz, we also developed a pulsed mode operation of the OAM beams with a highly reproducible temporal structure. FEL operation showcased in this work can be extended to higher photon energies, e.g. using a future x-ray FEL oscillator. The operation of such an OAM FEL also paves the way for the generation of OAM gamma-ray beams via Compton scattering.
Photons, phonons, and plasmons with orbital angular momentum in plasmas
Exact eigen modes with orbital angular momentum (OAM) in the complex media of unmagnetized homogeneous plasmas are studied. Three exact eigen modes with OAM are derived, i.e., photons, phonons, and plasmons. The OAM of different plasma components are closely related to the charge polarities. For photons, the OAM of electrons and ions are of the same magnitude but opposite direction, and the total OAM is carried by the field. For the phonons and plasmons, their OAM are carried by the electrons and ions. Lastly, the OAM modes in plasmas and their characteristics can be explored for potential applications in plasma physics and accelerator physics.
Parametric amplification of orbital angular momentum beams based on light-acoustic interaction
A high fidelity amplification of beams carrying orbital angular momentum (OAM) is very crucial for OAM multiplexing and other OAM-based applications. Here, we report a demonstration of stimulated Brillouin amplification for OAM beams, and the energy conversion efficiency of photon-phonon coupling and the phase structure of amplified signals are investigated in collinear and noncollinear frame systems, respectively. Our results demonstrate that the OAM signals can be efficiently amplified without obvious noise introduced, and the modes of output signal are independent of the pump modes or the geometrical frames. Meanwhile, an OAM state depending on the optical modes and the geometrical frames is loaded into phonons by coherent light-acoustic interaction, which reveals more fundamental significance and a great application potential in OAM-multiplexing.
Scattering of twisted particles: Extension to wave packets and orbital helicity
High-energy photons and other particles carrying nonzero orbital angular momentum (OAM) emerge as a new tool in high-energy physics. Recently, it was suggested to generate high-energy photons with nonzero OAM (twisted photons) by the Compton backscattering of twisted optical photons on relativistic electron beams. Twisted electrons in the intermediate energy range have also been demonstrated experimentally; twisted protons and other particles can, in principle, be created in a similar way. Collisions of energetic twisted states can offer a new look at particle properties and interactions. A theoretical description of twisted particle scattering developed previously treated them as pure Bessel states and ran into difficulty when describing the OAM of the final twisted particle at nonzero scattering angles. Here we develop further this formalism by incorporating two additional important features. First, we treat the initial OAM state as a wave packet of a finite transverse size rather than a pure Bessel state. This realistic assumption allows us to resolve the existing controversy between two theoretical analyses for nonforward scattering. Second, we describe the final twisted particle in terms of the orbital helicity: the OAM projection on its average direction of propagation rather than on the fixed reaction axis. Using this formalism, we determine to what extent the twisted state is transferred from the initial to final OAM particle in a generic scattering kinematics. As a particular application, we prove that in the Compton backscattering the orbital helicity of the final photon stays close to the OAM projection of the initial photon.
Orbital angular momenta of quarks and gluons in the nucleon -model-dependent versus model-independent extractions-
We demonstrate that there exist two kinds of gauge-invariant decompositions of the nucleon spin, which are physically inequivalent. The quark and gluon orbital angular momenta (OAMs) appearing in one decomposition are basically the canonical OAMs, while the quark and gluon OAMs appearing in another decomposition are called the dynamical OAMs. It is shown that the dynamical OAMs of quarks and gluons in the nucleon can be related to definite high-energy deep-inelastic-scattering observables. On the other hand, we conjecture that the canonical OAMs of quarks and gluon in the nucleon are model-dependent quantities, which is meaningful only within a specific theoretical model of the nucleon.
Antiferromagnetic real-space configuration probed by dichroism in scattered x-ray beams with orbital angular momentum
X-ray beams with orbital angular momentum (OAM) are a promising tool for x-ray characterization techniques. Beams with OAM have a helicity - an azimuthally varying phase - which leads to a gradient of the light field. New material properties can be probed by utilizing the helicity of an OAM beam. Here, we demonstrate a dichroic effect in resonant diffraction from an artificial antiferromagnet with a topological defect. We found that the scattered OAM beam has circular dichroism at the antiferromagnetic Bragg peak whose sign is coupled to its helicity, which reveals the real-space configuration of the antiferromagnetic ground state. Thermal cycling of the artificial antiferromagnet can change the ground state, as indicated by reversal of the sign of circular dichroism. This result is one of the first demonstrations of a soft x-ray spectroscopy characterization technique utilizing the OAM of x rays. In conclusion, this helicity-dependent circular dichroism exemplifies the potential to utilize OAM beams to probe matter in a way that is inaccessible using currently available x-ray techniques.
Optical attenuation mechanism upgrades, MOBLAS, and TLRS systems
This poster presentation describes the Optical Attenuation Mechanism (OAM) Upgrades to the MOBLAS and TLRS Crustal Dynamics Satellite Laser Ranging (CDSLR) systems. The upgrades were for the purposes of preparing these systems to laser range to the TOPEX/POSEIDON spacecraft when it will be launched in the summer of 1992. The OAM permits the laser receiver to operate over the expected large signal dynamic range from TOPEX/POSEIDON and it reduces the number of pre- and post-calibrations for each satellite during multi-satellite tracking operations. It further simplifies the calibration bias corrections that had been made due to the pass-to-pass variation of the photomultiplier supply voltage and the transmit filter glass thickness. The upgrade incorporated improvements to the optical alignment capability of each CDSLR system through the addition of a CCD camera into the MOBLAS receive telescope and an alignment telescope onto the TLRS optical table. The OAM is stepper motor and microprocessor based; and the system can be controlled either manually by a control switch panel or computer controlled via an EIA RS-232C serial interface. The OAM has a neutral density (ND) range of 0.0 to 4.0 and the positioning is absolute referenced in steps of 0.1 ND. Both the fixed transmit filter and the daylight filter are solenoid actuated with digital inputs and outputs to and from the OAM microprocessor. During automated operation, the operator has the option to overide the remote control and control the OAM system via a local control switch panel.
Improving Ocean Angular Momentum Estimates Using a Model Constrained by Data
Ocean angular momentum (OAM) calculations using forward model runs without any data constraints have, recently revealed the effects of OAM variability on the Earth's rotation. Here we use an ocean model and its adjoint to estimate OAM values by constraining the model to available oceanic data. The optimization procedure yields substantial changes in OAM, related to adjustments in both motion and mass fields, as well as in the wind stress torques acting on the ocean. Constrained and unconstrained OAM values are discussed in the context of closing the planet's angular momentum budget. The estimation procedure, yields noticeable improvements in the agreement with the observed Earth rotation parameters, particularly at the seasonal timescale. The comparison with Earth rotation measurements provides an independent consistency check on the estimated ocean state and underlines the importance of ocean state estimation for quantitative. studies of the variable large-scale oceanic mass and circulation fields, including studies of OAM.
Does Orbital Angular Momentum Have Effect on Laser’s Scattering by Molecular Atmosphere?
Lasers with orbital angular momentum (OAM) have potential applications in communication technology, manipulation of particles, and remote sensing. Because of its unusual light-scattering properties, the OAM laser’s interaction with a molecular atmosphere must be studied to ensure that it is not lossy for communication or remote-sensing applications that involve its transmission through an atmospheric environment. In this study, the finite-difference time-domain (FDTD) method [21] is applied to calculate the light scattering of the purely azimuthal (the radial mode number is assumed to be zero) Laguerre-Gaussian (LG) beams with OAM by very small dielectric particles. Not like Lorentz-Mie solutions, the FDTD method can calculate for particles off the central axis of the LG beam. It is found that when the particles are very small, and the topological charge number of the OAM of a laser is not extremely large, the laser’s OAM has little effect on the scattering phase function. This suggests that Rayleigh theory can be applied directly to calculate the light scattering by atmospheric molecules. The transmission of a laser beam with OAM in a molecular atmosphere is not different from that of a regular Gaussian beam.
Orbital angular momentum at small $x$ revisited
We revisit the problem of the small Bjorken-x asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton utilizing the revised small-x helicity evolution derived recently in [1]. We relate the quark and gluon OAM distributions at small x to the polarized dipole amplitudes and their (first) impact-parameter moments. To obtain the OAM distributions, we derive novel small-x evolution equations for the impact-parameter moments of the polarized dipole amplitudes in the double-logarithmic approximation (summing powers of α s ln 2 (1/x) with α s the strong coupling constant). We solve these evolution equations numerically and extract the leading large-N c , small-x asymptotics of the quark and gluon OAM distributions, which we determine to be ${L}_{q+\overline{q}}\left(x,{Q}^2\right)\sim {L}_G\left(x,{Q}^2\right)\sim \Delta \Sigma \left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {\left(\frac{1}{2}\right)}^{3.66\sqrt{\frac{\alpha_s{N}_c}{2_π}}}$in agreement with [2] within the precision of our numerical evaluation. (Here N c is the number of quark colors.) We also investigate the ratios of the quark and gluon OAM distributions to their helicity distribution counterparts in the small-x region.
Multiple copies of orbital angular momentum states through second-harmonic generation in a two-dimensional periodically poled LiTaO{sub 3} crystal
We experimentally demonstrate multiple copies of optical orbital angular momentum (OAM) states through quasi-phase-matched (QPM) second-harmonic (SH) generation in a 2D periodically poled LiTaO{sub 3} (PPLT) crystal. Since the QPM condition is satisfied by involving different reciprocal vectors in the 2D PPLT crystal, collinear and noncollinear SH beams carrying OAMs of l{sub 2} are simultaneously generated by the input fundamental beam with an OAM of l{sub 1}. The OAM conservation law (i.e., l{sub 2} = 2l{sub 1}) holds well in the experiment, which can tolerate certain phase-mismatch between the interacting waves. Our results provide an efficient way to obtain multiple copies of the wavelength-converted OAM states, which can be used to enhance the capacity in optical communications.
Conversion of the optical orbital angular momentum in a plasmon-assisted second-harmonic generation
We experimentally demonstrate the plasmon-assisted second-harmonic generation of an optical orbital angular momentum (OAM) beam. Because of the shape resonance, the plasmons in a periodic array of rectangular metal holes greatly enhance the nonlinear optical conversion of an OAM state. The OAM conservation (i.e., 2l{sub 1} = l{sub 2} with l{sub 1} and l{sub 2} being the OAM numbers of the fundamental and second-harmonic waves, respectively) holds well under our experimental configuration. Our results provide a potential way to realize nonlinear optical manipulation of an OAM mode in a nano-photonic device.
Modeling of high intensity orbital angular momentum beams for laser–plasma interactions
In this work, we explore the field of high intensity orbital angular momentum (OAM) beams, their generation with spiral phase mirrors, and the theory behind modeling both ideal and realistic beams. We explore OAM beam asymmetries introduced by aberrations in the beam, manufacturing defects, and bandwidth. A full three-dimensional description of the paraxial Laguerre–Gaussian (LG) modes suitable for modeling beams down to f/2 focal geometries is derived. A perturbative approach to modeling asymmetric OAM beams is introduced showing that only three LG modes are sufficient to model a wide variety of OAM asymmetries. The models are compared with experimental results followed by a discussion on the future of high intensity OAM beams in plasma physics.