Intrinsic Orbital Angular Momentum Research Articles

Second-harmonic generation of spatiotemporal optical vortices and conservation of orbital angular momentum

A spatiotemporal optical vortex (STOV) is an intrinsic optical orbital angular momentum (OAM) structure in which the OAM vector is orthogonal to the propagation direction [Optica 6, 1547 (2019)OPTIC82334-253610.1364/OPTICA.6.001547] and the optical phase circulates in space-time. Here, we experimentally and theoretically demonstrate the generation of the second harmonic of a STOV-carrying pulse along with the conservation of STOV-based OAM. Our experiments verify that photons can have intrinsic orbital angular momentum perpendicular to their propagation direction.

Quark spin and orbital angular momentum from proton generalized parton distributions

We calculate the leading-twist helicity-dependent generalized parton distributions (GPDs) of the proton at finite skewness in the Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics (QCD). From these (and previously calculated helicity-independent GPDs) we obtain the spin decomposition of the proton, including predictions for quark intrinsic spin and orbital angular momentum. The inclusion of multiple species of diquarks is found to have a significant effect on the flavor decomposition, and resolving the internal structure of these dynamical diquark correlations proves essential for the mechanical stability of the proton. At a scale of $Q^2=4\,$GeV$^2$ we find that the up and down quarks carry an intrinsic spin and orbital angular momentum of $S_u=0.534$, $S_d=-0.214$, $L_u=-0.189$, and $L_d=0.210$, whereas the gluons have a total angular momentum of $J_g=0.151$. The down quark is therefore found to carry almost no total angular momentum due to cancellations between spin and orbital contributions. Comparisons are made between these spin decomposition results and lattice QCD calculations.

High-Harmonic Generation and Spin-Orbit Interaction of Light in a Relativistic Oscillating Window.

When a high power laser beam irradiates a small aperture on a solid foil target, the strong laser field drives surface plasma oscillation at the periphery of this aperture, which acts as a "relativistic oscillating window." The diffracted light that travels though such an aperture contains high-harmonics of the fundamental laser frequency. When the driving laser beam is circularly polarized, the high-harmonic generation (HHG) process facilitates a conversion of the spin angular momentum of the fundamental light into the intrinsic orbital angular momentum of the harmonics. By means of theoretical modeling and fully 3D particle-in-cell simulations, it is shown the harmonic beams of order n are optical vortices with topological charge |l|=n-1, and a power-law spectrum I_{n}∝n^{-3.5} is produced for sufficiently intense laser beams, where I_{n} is the intensity of the nth harmonic. This work opens up a new realm of possibilities for producing intense extreme ultraviolet vortices, and diffraction-based HHG studies at relativistic intensities.

Detection of magnetic impurities using electron vortex beams

Electron vortex beams generated by a transmission electron microscope (TEM) are employed to study magnetic properties of an impurity often embedded in materials. Compared to the optical wave, a higher spatial resolving power of electron waves enables the detection of impurities on the nanoscale. Here, we investigate theoretically the interaction of the twisted electrons and the magnetic impurity in which the magnetic dipole moment is taken as a demonstration element. In addition to the usual optical phase, the inhomogeneous vector potential generated by the magnetic dipole moment makes an additional contribution to the intrinsic orbital angular momentum of the twisted electrons, resulting in a dipole-dependent Gouy phase shift. By interfering the outgoing twisted electron beam with a reference cylindrical wave, one can determine the magnitude and orientation of the magnetic dipole directly via the rotational and deformed interference pattern. Furthermore, the pattern is shown to be sensitive to the width of the beam in the focal plane, which provides an effective way to reveal the influence of impurities on the twisted electrons more intuitively and distinctly. The obtained results demonstrate the usefulness of the twisted electron beams for probing the nanoscale magnetism of impurity by TEM, while the proposed model provides the conceptual basis for future developments of the TEM method.

Symmetric spin splitting of elliptically polarized vortex beams reflected at air-gold interface via pseudo-Brewster angle.

A simple expression of the transverse spatial spin splitting of light-carrying intrinsic orbital angular momentum (IOAM) is theoretically derived for reflections at strong absorbing media surfaces. By introducing an asymmetric spin splitting (ASS) factor, the transverse spatial symmetric spin splitting (SSS) and ASS of an arbitrary polarized vortex beam can be distinguished. Here, the transverse spatial SSS of an elliptically polarized vortex beam with a phase difference of 90° is predicted when the incident angle is close to the pseudo-Brewster angle. Remarkably, the larger transverse spatial SSS reaches 1100 nm for the incident circularly polarized LG beam with l=3. It is noteworthy that the transverse spatial SSS can be flexibly manipulated by changing the polarized angle, meaning it is theoretically possible to realize fully polarization-controllable transverse spatial SSS for elliptically polarized incident vortex beams. These results could potentially be applied to precision polarization metrology and edge-enhanced imaging.

Edge current and orbital angular momentum of chiral superfluids revisited

Cooper pairs in chiral superfluids carry quantized units of relative orbital angular momentum (OAM). Various predictions of the intrinsic OAM density or the macroscopic OAM of a two-dimensional chiral superfluid differ by several orders of magnitude, which constitute the so-called Angular Momentum Paradox. Following several previous studies, we substantiate the semiclassical Bogoliubov-de Gennes theory of the single-particle edge current and OAM in two-dimensional chiral superfluids in the BCS limit. The analysis provides a simple intuitive understanding for the vanishing of OAM for a non-p-wave chiral superfluid (such as $d+id$) confined in a rigid potential. When generalized to anisotropic chiral superconductors and three-dimensional chiral superfluids, the theory similarly returns an accurate description. We also present a detailed numerical study of the chiral phases in the BEC limit. Our study suggests that, in both BCS and BEC phases the relative OAM of the individual Cooper pairs contribute to the total OAM additively, and that in both phases the corresponding macroscopic OAM density distribution is localized at the boundary.

Direct observation of the effects of spin dependent momentum of light in optical tweezers

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

Phase Singularities to Polarization Singularities

Polarization singularities are superpositions of orbital angular momentum (OAM) states in orthogonal circular polarization basis. The intrinsic OAM of light beams arises due to the helical wavefronts of phase singularities. In phase singularities, circulating phase gradients and, in polarization singularities, circulatingϕ12Stokes phase gradients are present. At the phase and polarization singularities, undefined quantities are the phase andϕ12Stokes phase, respectively. Conversion of circulating phase gradient into circulating Stokes phase gradient reveals the connection between phase (scalar) and polarization (vector) singularities. We demonstrate this by theoretically and experimentally generating polarization singularities using phase singularities. Furthermore, the relation between scalar fields and Stokes fields and the singularities in each of them is discussed. This paper is written as a tutorial-cum-review-type article keeping in mind the beginners and researchers in other areas, yet many of the concepts are given novel explanations by adopting different approaches from the available literature on this subject.

Effective dynamics for a spin-1/2 particle constrained to a space curve in an electric and magnetic field

We consider the dynamics of a spin-1/2 particle constrained to move in an arbitrary space curve with an external electric and magnetic field applied. With the aid of gauge theory, we successfully decouple the tangential and normal dynamics and derive the effective Hamiltonian. A new type of quantum potential called SU(2) Zeeman interaction appears, which is induced by the electric field and couples spin and intrinsic orbital angular momentum. Based on the Hamiltonian, we discuss the spin precession for zero intrinsic orbital angular momentum case and the energy splitting caused by the SU(2) Zeeman interaction for a helix as examples, showing the combined effect of geometry and external field. The new interaction may bring new approaches to manipulate quantum states in spintronics.

Geometric Phase and Intensity-Controlled Extrinsic Orbital Angular Momentum of Off-Axis Vortex Beams

Smooth control of the intrinsic orbital angular momentum (OAM) carried by a beam of light is important for $e.g.$ optical tweezers, communication, and quantum information processing, while control of extrinsic OAM is useful for $e.g.$ super-resolution microscopy and light-matter interaction with atoms, molecules, and condensates. This study presents a technique to control intrinsic and extrinsic OAM in a single-path configuration that is free from mechanical errors. By managing the relative intensity and Pancharatnam-Berry phase difference between two orthogonal spatial modes with orthogonal polarizations, one may tune the net transverse linear momentum to yield variable extrinsic OAM.

Measuring the Topological Charge of Orbital Angular Momentum Beams by Utilizing Weak Measurement Principle

According to the principle of weak measurement, when coupling the orbital angular momentum (OAM) state with a well-defined pre-selected and post-selected system of a weak measurement process, there will be an indirect coupling between position and topological charge (TC) of OAM state. Based on this we propose an experiment scheme and experimentally measure the TC of OAM beams from −14 to 14 according to the weak measurement principle. After the experiment the intrinsic OAM of the beams changed very little. Weak measurement, Topological Charge, OAM beams.

Surface transverse linear momenta accompanying the reflection and refraction of a paraxial light beam

The reflection and transmission of a paraxial light beam carrying the spin and intrinsic orbital angular momenta (IOAMs) at a plane interface between two isotropic transparent media is considered. The surface transverse linear momenta (STLMs), i.e., the momenta that are localized near the interface and whose direction is perpendicular to the plane of incidence, are investigated. The IOAM-dependent and spin-dependent STLMs of the beams of homogeneous and inhomogeneous plane waves as well as the interference STLMs in the first medium are calculated. A detailed comparison of these STLMs is made. The way of experimental investigation of STLMs based on the relation between the global STLM and the transverse shift of the center of gravity of the global electromagnetic field is discussed.

(Invited) Open-Cage Fullerene C60 Derivatives Encapsulating a Paramagnetic Molecule

Organic electron spin systems have received much attention owing to their broad interests in medicine, quantum device, molecular magnetism, and etc. Fullerene C60 has an inner space which is suitable to accommodate a variety of small molecules. In this work, we constructed organic electron spin systems, O2@openC60 and NO@openC60, by encapsulation of the molecules inside an open-cage C60 derivative with high crystallinity and solubility. In the case of O2@openC60, the EPR signals were observed and the paramagnetic behaviour was demonstrated above 3 K without an antiferromagnetic transition.[1] In the case of NO@openC60, however, sharp 1H NMR signals were observed with remarkable paramagnetic shifts despite the encapsulation of the paramagnetic molecule. Although an NO molecule is known to be inactive in ESR measurements due to the intrinsic orbital angular momentum, the ESR signal of NO@openC60 was detected below 40 K owing to the symmetry breaking.[2] [1] A Stable, Soluble, and Crystalline Supramolecular System with a Triplet Ground State Futagoishi, T.; Aharen, T.; Kato, T.; Kato, A.; Ihara, T.; Tada, T.; Murata, M.; Wakamiya, A.; Kageyama, H.; Kanemitsu, Y.; Murata, Y. Angew. Chem. Int. Ed. 2017, 56, 4261-4265. [2] Construction of a Metal-Free Electron Spin System by Encapsulation of an NO Molecule inside an Open-Cage Fullerene C60 Derivative Hasegawa, S.; Hashikawa, Y.; Kato, T.; Murata, Y. Angew. Chem. Int. Ed. 2018, 57, 12804-12808.

Siberian Snake-Like Behavior for an Orbital Polarization of a Beam of Twisted (Vortex) Electrons

The orbital polarization of twisted electrons carrying an intrinsic orbital angular momentum is not influenced by field perturbations in arbitrary magnetic fields. This property means an existence of the Siberian snake-like behavior for an orbital polarization of a beam of twisted electrons in cyclotrons with the main magnetic field and magnetic focusing. As a result, the acceleration of twisted electron beams in cyclotrons necessary for their applications in high-energy-physics experiments considerably simplifies.

Electric Quadrupole Moment and the Tensor Magnetic Polarizability of Twisted Electrons and a Potential for their Measurements.

For a twisted (vortex) Dirac particle in nonuniform electric and magnetic fields, the relativistic Foldy-Wouthuysen Hamiltonian is derived including high order terms describing new effects. The result obtained shows for the first time that a twisted spin-1/2 particle possesses a tensor magnetic polarizability and a measurable (spectroscopic) electric quadrupole moment. We have calculated the former parameter and have evaluated the latter one for a twisted electron. The tensor magnetic polarizability of the twisted electron can be measured in a magnetic storage ring because a beam with an initial orbital tensor polarization acquires a horizontal orbital vector polarization. The electric quadrupole moment is rather large and strongly influences the dynamics of the intrinsic orbital angular momentum (OAM). Three different methods of its measurements, freezing the intrinsic orbital angular momentum and two resonance methods, are proposed. The existence of the quadrupole moment of twisted electrons can lead to practical applications.

Dynamics of an orbital polarization of twisted electron beams in electric and magnetic fields

Relativistic classical and quantum dynamics of twisted (vortex) Dirac particles in arbitrary electric and magnetic fields is constructed. The relativistic Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived. Methods for the extraction of an electron vortex beam with a given orbital polarization and for the manipulation of such a beam are developed. The new effect of a radiative orbital polarization of a twisted electron beam in a magnetic field resulting in a nonzero average projection of the intrinsic orbital angular momentum on the field direction is predicted.

Large centroid shifts of vortex beams reflected from multi-layers

Gaussian beams reflected from a multi-layered dielectric experience a shift in their centroid that is different than that from a single interface. This has been previously investigated for linearly polarized beams and, to a much lesser extent, beams with spin angular momentum. Here a combination of theoretical and computational analysis is used to provide a unified quantification of these shifts in layered dielectrics, for light endowed with an intrinsic orbital angular momentum (OAM)—i.e. vortex beams. Two geometries are considered: air/glass/air and glass/air/glass multi-layers. Destructive interference causes singular lateral shifts in the centroid of the reflected vortex beam for which spin alone produces only a mild modulation. In the case of total internal reflection, both spin and intrinsic OAM contribute to an enhancement of these lateral shifts as the interlayer thickness is decreased. This is just the opposite of the trend associated with longitudinal shifts. We find that vortex beams undergo centroid shifts up to tens of microns, more than an order of magnitude larger than for Gaussian beams.

Spectroscopy of fractional orbital angular momentum states.

We present an approach for measuring the orbital angular momentum (OAM) of light tailored towards applications in spectroscopy and non-integer OAM values. It is based on the OAM sorting method (Berkhout et al., Phys. Rev. Lett. 105, 153601 (2010)). We demonstrate that mixed OAM states and fractional OAM states can be identified using moments of the sorted output intensity distribution and OAM states with integer and non-integer topological charge can be clearly distinguished. Furthermore the difference between intrinsic OAM and total OAM for fractional OAM states is highlighted and the importance of the orientation of the fractional OAM beam is shown. All experimental results show good agreement with simulations. Finally we discuss possible applications of this method for spectroscopy of semiconductor systems such as exciton-polaritons in microcavities.

Evolution of orbital angular momentum in three-dimensional structured light

Light beams with an azimuthal phase dependency of $e^{i\ell\phi}$ have helical phase fronts and thus carry orbital angular momentum (OAM), a strictly conserved quantity with propagation. Here, we engineer quasi three-dimensional (3D) structured light fields and demonstrate unusual scenarios in which OAM can vary locally in both sign and magnitude along the beam's axis, in a controlled manner, under free-space propagation. To reveal the underlying mechanisms of this phenomenon, we perform full modal decomposition and reconstruction of the generated beams to describe the evolution of their intrinsic OAM and topological charge with propagation. We show that topological transition and the associated variation in local OAM rely on the creation, movement, and annihilation of local vortex charges without disturbing the global net charge of the beam, thus conserving the global OAM while varying it locally. Our results may be perceived as an experimental demonstration of the Hilbert Hotel paradox, while advancing our understanding of topological deformations in general.

Quantum gyroelectric effect: Photon spin-1 quantization in continuum topological bosonic phases

Topological phases of matter arise in distinct fermionic and bosonic flavors. The fundamental differences between them are encapsulated in their rotational symmetries - the spin. Although spin quantization is routinely encountered in fermionic topological edge states, analogous quantization for bosons has proven elusive. To this end, we develop the complete electromagnetic continuum theory characterizing 2+1D topological bosons, taking into account their intrinsic spin and orbital angular momentum degrees of freedom. We demonstrate that spatiotemporal dispersion (momentum and frequency dependence of linear response) captures the matter-mediated interactions between bosons and is a necessary ingredient for topological phases. We prove that the bulk topology of these 2+1D phases is manifested in transverse spin-1 quantization of the photon. From this insight, we predict two unique bosonic phases - one with even parity $C=\pm 2$ and one with odd $C=\pm 1$. To understand the even parity phase $C=\pm 2$, we introduce an exactly solvable model utilizing non-local optical Hall conductivity and reveal a single gapless photon at the edge. This unidirectional photon is spin-1 helically quantized, immune to backscattering, defects, and exists at the boundary of the $C=\pm 2$ bosonic phase and any interface - even vacuum. The contrasting phenomena of transverse quantization in the bulk, but longitudinal (helical) quantization on the edge is addressed as the quantum gyro-electric effect (QGEE). We also validate our bosonic Maxwell theory by direct comparison with the supersymmetric Dirac theory of fermions. To accelerate the discovery of such bosonic phases, we suggest two new probes of topological matter with broken time-reversal symmetry: momentum-resolved electron energy loss spectroscopy and cold atom near-field measurement of non-local optical Hall conductivity.