Conservation Of Orbital Angular Momentum Research Articles

Kepler's law for optical beams.

It is well known that optics and classical mechanics are intimately related. One of the most important concepts in classical mechanics is that of a particle in a central potential that leads to the Newtonian description of the planetary dynamics. Within this, a relevant result is Kepler's second law that is related to the conservation of orbital angular momentum, one of the fundamental laws in physics. In this paper, we demonstrate that it is possible to find the conditions that allow us to state Kepler's second law for optical beams with orbital angular momentum by analyzing the streamlines of their energy flow. We find that the optical Kepler's law is satisfied only for cylindrical symmetric beams in contrast to the classical mechanics situation that is satisfied for the other conic geometries, namely, parabolic, elliptical and hyperbolic. We propose a novel approach to confirm our analytic results: we observe the propagation of the Arago's spot created by a beam with orbital angular momentum as a local "light-tracer" instead of looking at the propagation of the whole beam. The observed patterns fully agree with the prediction of our formalism.

Controlled-not gate with orbital angular momentum in a rare-earth-ion-doped solid

We experimentally demonstrate a controlled-not (CNOT) gate with vortex beams carrying orbital angular momentum (OAM) via light storage in a solid driven by electromagnetically induced transparency (EIT). We use vortex beams with different topological charges to perform EIT storage in the double lambda atomic system, the stored information is transferred into a new information channel. The topological charge of the generated signal field is determined by those of the applied fields. The OAM conservation is satisfied in this EIT storage of the double lambda system. By imposing different OAMs into the control and probe fields, we obtain a CNOT gate using EIT storage. This demonstration can be useful for better understanding and developing the OAM applications in the interactions between the OAM and the mediums.

Suppression of Penning ionization by orbital angular momentum conservation

The efficient suppression of autoionizing collisions is a stringent requirement to achieve quantum degeneracy in metastable rare gases. Here, we report on the suppression of Penning ionization in collisions between metastable He and laser-excited Li atoms. Our results show that the suppression is achieved by the conservation of both the total electron spin and $\mathrm{\ensuremath{\Lambda}}$, i.e., the projection of the total molecular orbital angular momentum along the internuclear axis. Our findings suggest that $\mathrm{\ensuremath{\Lambda}}$ conservation can be used as a more general means of reaction control, in particular, to improve schemes for the simultaneous laser cooling and trapping of metastable He and alkali-metal atoms.

Probing the reciprocal lattice associated with a triangular slit to determine the orbital angular momentum for a photon.

The orbital angular momentum conservation of light reveals different diffraction patterns univocally dependent on the topological charge of the incident light beam when passing through a triangular aperture. It is demonstrated that these patterns, which are accessed by observing the far-field measurement of the diffracted light, can also be obtained using few photon sources. In order to explain the observed patterns, we introduce an analogy of this optical phenomenon with the study of diffraction for the characterization of the crystal structure of solids. We demonstrate that the finite pattern can be associated with the reciprocal lattice obtained from the direct lattice generated by the primitive vectors composing any two of the sides of the equilateral triangular slit responsible for the diffraction. Using the relation that exists between the direct and reciprocal lattices, we provide a conclusive explanation as to why the diffraction pattern of the main maxima is finite. This can shed a new light on the investigation of crystallographic systems.

Digital laser for on-demand intracavity selective excitation of second harmonic higher-order modes.

In this article, we demonstrate selective excitation of second harmonic higher-order modes inside a diode end-pumped solid-state laser resonator that comprises of a nonlinear potassium titanyl phosphate (KTP) crystal and a digitally addressed holographic end-mirror in a form of a reflective phase-only spatial light modulator (SLM). The emitted second harmonic higher-order modes at 532 nm are generated by an intracavity nonlinear KTP crystal that is pumped by high-order fundamental modes operating at 1064 nm. The fundamental modes are digitally controlled by displaying a computer-generated hologram in the form of a grey-scale image to the SLM screen for on-demand high-order modes. The phase matching of the fundamental mode to the generated frequency-doubled mode is achieved by controlling the phase of the digital hologram to either achieve a high or quasi-degree of orbital angular momentum conservation. We show that we can intracavity generate frequency-doubled high-order Laguerre-Gaussian modes and Hermit-Gaussian modes that are either quasi or fully reproducible in the far-field. To the best of our knowledge, this is the first laser to generate frequency-doubled on-demand higher-order modes inside the cavity at the visible (green) wavelength of 532 nm.

Generation of hyper-entangled photons in a hot atomic vapor.

A source of hyper-entangled photons plays a vital role in quantum information processing, owing to its high information capacity. In this Letter, we demonstrate a convenient method to generate polarization and orbital angular momentum (OAM) hyper-entangled photon pairs via spontaneous four-wave mixing (SFWM) in a hot $ ^{87}{\rm Rb} $87Rb atomic vapor. The polarization entanglement is achieved by coherently combining two SFWM paths with the aid of two beam displacers that constitute a phase self-stabilized interferometer, and OAM entanglement is realized by taking advantage of the OAM conservation condition during the SFWM process. Our hyper-entangled biphoton source possesses high brightness and high nonclassicality and may have broad applications in atom-photon-interaction-based quantum networks.

Nonlinear optical vortex coronagraph.

A nonlinear optical vortex coronagraph (n-OVC) based on sum-frequency generation (SFG) in a periodically poled lithium niobate (PPLN) crystal is presented. We demonstrate an n-OVC by mixing the image of an on-axis point source ($ {\lambda _s} = 1.6\;{\unicode{x00B5}{\rm m}} $λs=1.6µm) inside the PPLN crystal with a pump beam (${\lambda _p} = 1064\;{\rm nm}$λp=1064nm) imprinted with a helical phase profile from a vector vortex mask (topological charge ${l} = 2$l=2). Due to quasi-phase matching and orbital angular momentum conservation, a coronagraphic image is produced at the SFG wavelength (${\lambda _{\rm up}}\sim 630\;{\rm nm}$λup∼630nm). We validate that the n-OVC is tunable to signal wavelength but only requires a vortex mask operating at the pump wavelength. The acceptance bandwidth of the SFG process provides the n-OVC a degree of achromaticity even with a monochromatic vortex mask. The n-OVC exhibits an inner working angle of $ \sim {\lambda _s}/{D}$∼λs/D and an experimental contrast of ${{10}^{ - 4}}$10-4 at $3{\lambda _s}/{D}$3λs/D.

Second-harmonic generation of asymmetric Bessel-Gaussian beams carrying orbital angular momentum.

Nonlinear processes of laser beams carrying orbital angular momentum (OAM) offer a means to generate new wavelengths and to manipulate OAM charge numbers. We demonstrate the second-harmonic generation (SHG) of asymmetric Bessel-Gaussian (BG) beams carrying OAM of both integer and fractional charge numbers. Experimental results show a good one-to-one correspondence of the charge numbers and compliance with the OAM conservation law. The SHG conversion process and efficiency with different combined charge numbers are also discussed.

Nonlinear four-wave mixing with enhanced diversity and selectivity via spin and orbital angular momentum conservation

Light that can carry orbital angular momentum (OAM) has found a variety of applications in super-resolution microscopy, optical communications, and laser machining, bringing up the need for pure OAM light generation at on-demand power levels and wavelengths. Parametric four-wave mixing is a promising platform for such source generation, and while investigations of higher-order fiber modes have revealed enhanced phase-matching possibilities, the role of the angular momentum of light in this process has not yet been substantially considered. Here, with a specially designed ring-core fiber in which over 16 OAM modes can be stably guided, we demonstrate the first experiments, to our knowledge, investigating nonlinear four wave mixing between OAM modes in an optical fiber. The large modal space as well as spin and OAM conservation rules enable a high diversity of phase matching conditions while also providing high selectivity. We report parametric wavelength translations of over 438 nm and the ability to obtain kilowatt peak-power level ∼ nanosecond pulses of pure OAM beams at user defined colors.

Tunable ultraviolet vortex source based on a continuous-wave optical parametric oscillator

We report a continuous-wave (cw) optical parametric oscillator (OPO) generating optical vortices tunable in the ultraviolet (UV). Based on MgO:sPPLT as the nonlinear crystal, the singly resonant OPO is pumped by a cw vortex beam in the green, and deploying intracavity sum-frequency generation (SFG) between the undepleted pump and the Gaussian resonant signal in the crystal of BiB3O6, it can generate optical vortices of order, luv=1 and 2, tunable across 332-344nm in the UV with a maximum power of 12mW. Due to conservation of orbital angular momentum in the parametric process, the OPO also produces a non-resonant idler output beam in a vortex spatial profile of order li=1 and 2, identical to the pump vortex, with the signal beam in Gaussian distribution. The idler vortex is tunable across 1172-1338nm with maximum output power of 1.3W.

Direct observation of OAM correlations from spatially entangled bi-photon states.

We present spatially-resolved observations of orbital angular momentum (OAM) conservation, via a Laguerre-Gauss (LG) basis decomposition, of spatially-entangled photon pairs produced in type-I collinear spontaneous parametric downconversion (SPDC). These results were obtained with a novel detection system for OAM-entangled photon pairs that combines a projective measurement for the signal photon to a specific value of the azimuthal index ls, with a spatially-resolved measurement for the idler photon using an intensified charge coupled (ICCD) camera. In combination with far-field diffraction of the idler photon through a triangular aperture, we are able to obtain: i) the spatial structure of the heralded idler photon, as governed by the user-selected topological charge of the signal photon; ii) the OAM spectrum; and iii) the topological charge (both magnitude and sign) for the heralded idler photon.

Orbital-Angular-Momentum Multiplexed Continuous-Variable Entanglement from Four-Wave Mixing in Hot Atomic Vapor.

Multiplexing is crucial for the data-carrying capacity of information communication systems. Orbital angular momentum (OAM) with a topological charge ℓ (ℓ integer) provides a degree of freedom to realize multiplexing. In this Letter, we report an experimental implementation of OAM multiplexed continuous variables (CV) entanglement based on a four-wave mixing (FWM) process, in which 13 pairs of entangled Laguerre-Gauss (LG) modes, LG_{ℓ,pr} and LG_{-ℓ,conj}, are simultaneously and deterministically generated, where ℓ (ℓ integer) is the topological charge corresponding to the OAM mode and pr (conj) indicates a probe (conjugate) beam. In the meanwhile, we experimentally show that there is no entanglement between the modes of LG_{ℓ,pr} and LG_{ℓ,conj} (ℓ≠0). These results clearly confirm the conservation of OAM in the FWM process from the viewpoint of a CV system. In addition, we investigate the entanglement properties of three types of coherent superposition of OAM modes. In the end, we also study the effect of the pump beam radius on the number of OAM multiplexing. Such OAM multiplexed CV entanglement provides a new perspective and platform to study CV quantum information protocols.

High harmonic generation with Laguerre–Gaussian beams

We summarize the development of high harmonic generation (HHG) with linearly polarized Laguerre–Gaussian (LG) beams and their superpositions to explain the non-perturbative aspects of HHG. Furthermore, we show that circularly polarized extreme ultraviolet vortices with well-defined orbital angular momentum (OAM) can be generated by HHG with bicircular LG beams. We introduce photon diagrams in order to explain how to calculate the OAM and the polarization of the generated harmonics by means of simultaneous conservation of spin angular momentum and OAM. Moreover, we show how the intensity ratio of the driving fields in HHG with bicircular LG beams further enhances the generation of circularly polarized twisted attosecond pulse trains.

Tunable vector-vortex beam optical parametric oscillator

Vector-vortex beams, having both phase and polarization singularities, are of great interest for a variety of applications. Generally, such beams are produced through systematic control of phase and polarization of the laser beam, typically external to the source. However, efforts have been made to generate vector-vortex beams directly from the laser source. Given the operation of the laser at discrete wavelengths, vector-vortices are generated with limited or no wavelength tunability. Here, we report an experimental scheme for the direct generation of vector-vortex beams. Exploiting the orbital angular momentum conservation and the broad wavelength versatility of an optical parametric oscillator, we systematically control the polarization of the resonant beam using a pair of intracavity quarter-wave plates to generate coherent vector-vortex beam tunable across 964–990 nm, with output states represented on the higher-order Poincaré sphere. The generic experimental scheme paves the way for new sources of structured beams in any wavelength range across the optical spectrum and in all time-scales from continuous-wave to ultrafast regime.

Direct Generation of Narrow-band Hyperentangled Photons.

In quantum communication and photonic quantum information processing, the requirement of quantum repeaters and quantum memory often imposes a strict bandwidth prerequisite for the entangled photons. At the same time, there is ever more increasing demand for entangling more degrees of freedom, i.e., hyperentanglement, for a photon pair. In this Letter, we report the direct generation of narrow-band orbital angular momentum (OAM) and polarization hyperentangled photons from cold atoms. The narrow-band photon pair is naturally entangled in polarization and OAM, in addition to time-frequency, degrees of freedom due to spin and orbital angular momentum conservation conditions in the spontaneous four-wave mixing process in a cold atom ensemble. The narrow-band hyperentangled photon pair source reported here is expected to play important roles in quantum memory-based long-distance quantum communication.

Conservation of the spin angular momentum in second-harmonic generation with elliptically polarized vortex beams

Spin-to-orbital angular momentum conversion and orbital angular momentum conservation in the harmonic generation process have been extensively investigated. However, very few studies have focused on the spin angular momentum (SAM) conservation in the nonlinear optical process. Herein, we investigate the SAM characteristics of the second-harmonic waves with weakly focused elliptically polarized vortex beams (EPVBs). It is shown that the chirality of the second-harmonic wave is always opposite to that of the fundamental wave. Moreover, the absolute value of SAM satisfies the conservation law in the second-harmonic process generated by weakly focused EPVBs. The results are in good agreement with the experimental observations.

The quantum centripetal force on a free particle confined to the surface of a sphere and a cylinder

The momentum operator for a spin-less particle when confined to a 2D surface embedded into 3D space acquires a geometrical component proportional to the mean curvature that renders it Hermitian. As a consequence, the quantum force operator for a particle confined to spherical and cylindrical surfaces, and free otherwise, derived by applying the Heisenberg equation of motion is found to have an apparently no-radial component in addition to the standard classical radial centripetal force. This component which renders the force operator Hermitian is shown to be essential for the vanishing of the torque the force exerts on the particle and so for the conservation of orbital angular momentum and energy. It is demonstrated that the total force is in fact radial as should be the case for a torque-less one and so can be identified as the quantum centripetal force.

Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin–orbit momentum conservation

Optical interactions are governed by both spin and angular momentum conservation laws, which serve as a tool for controlling light-matter interactions or elucidating electron dynamics and structure of complex systems. Here, we uncover a form of simultaneous spin and orbital angular momentum conservation and show, theoretically and experimentally, that this phenomenon allows for unprecedented control over the divergence and polarization of extreme-ultraviolet vortex beams. High harmonics with spin and orbital angular momenta are produced, opening a novel regime of angular momentum conservation that allows for manipulation of the polarization of attosecond pulses-from linear to circular-and for the generation of circularly polarized vortices with tailored orbital angular momentum, including harmonic vortices with the same topological charge as the driving laser beam. Our work paves the way to ultrafast studies of chiral systems using high-harmonic beams with designer spin and orbital angular momentum.

Conservation of orbital angular momentum for high harmonic generation of fractional vortex beams.

This work demonstrates conservation of average orbital angular momentum for high harmonic generation of fractional vortex beams. High harmonics are generated in reflected light beams in a three-dimensional particle-in-cell simulation. The average orbital angular momentum of the beam is calculated when a relativistic linearly polarized fractional vortex beam impinges on a solid foil. The harmonic generation progress can be well explained by using the vortex oscillating mirror model. Both simulation and theoretical analysis show that the average orbital momentum of the nth harmonic is n times that of the fundamental frequency beam. This provides evidence that the average orbital angular momentum obeys momentum conservation during the harmonic generation of fractional vortex beams.

Whistler modes in highly nonuniform magnetic fields. II. Propagation in three dimensions

In a large laboratory plasma, the properties of whistler modes are investigated in highly nonuniform magnetic fields. In an extension to previous measurements in two dimensions (2D), the present work shows new phenomena such as wave splitting in the third dimension and shedding of cross-field helicon-like modes. Three-dimensional (3D) data also permit the correct calculations of the field derivatives (∇⋅, ∇×), helicity density (J ⋅ B), Hall electric fields, phase and energy flow, and out-of-plane field structures, which are not visible from 2D data. Novel findings are the loss of the angular momentum of an m = 1 helicon mode, the splitting of a single wave packet into two wave packets in the direction of the loop axis, and the shedding of perpendicular whistler modes with angular momentum. The 3D effects cannot be explained by nonuniformities in the density and the 2D ambient magnetic field B0. They may arise from the conservation of orbital angular momentum whose direction changes along a curved magnetic field. It results in a precessional motion which creates asymmetries in the third dimension. Further effects are the interference of oppositely propagating helicon modes on circular field lines which creates linear polarization near the conjugate point of the antenna. Detached whistler modes are excited in the oscillating near-zone field. The waves propagate nearly perpendicular to the ambient field. The field polarization is right-hand circular around the oblique wave vector k but not around B0. Since the wave field is force-free the wave magnetic field lines form twisted field lines or writhed flux tubes. From streamlines of hodogram normals, it is shown that the wave exhibits a helical phase flow similar to helicon modes. These observations show the complexity of whistler modes in nonuniform magnetic fields, even under the simplest conditions of a uniform, unbounded plasma and linear waves. The results may be of interest to other laboratory plasmas and space plasmas in nonuniform magnetic fields. Meaningful comparisons require 3D field data which are rarely available.