Orbital Angular Momentum Components Research Articles

Engineering Orbital Angular Momentum in Structured Beams in General Astigmatic Systems via Symplectic Matrix Approach

We studied theoretically and experimentally the propagation of structured Laguerre–Gaussian (sLG) beams through an optical system with general astigmatism based on symplectic ABCD transforms involving geometry of the second-order intensity moments symplectic matrices. The evolution of the coordinate submatrix ellipses accompanying the transformation of intensity patterns at different orientations of the cylindrical lens was studied. It was found that the coordinate submatrix W and the twistedness submatrix M of the symplectic matrix P degenerate in the astigmatic sLG beam with simple astigmatism, which sharply reduces the number of degrees of freedom, while general astigmatism removes the degeneracy. Nevertheless, degeneracy entails a simple relationship between the coordinate element Wxy and the twistedness elements Mxy and Myx of the submatrix M, which greatly simplifies the measurement of the total orbital angular momentum (OAM), reducing the full cycle of measurements of the Hermite–Gaussian (HG) mode spectrum (amplitudes and phases) of the structured beam to the only measurement of the intensity moment. Moreover, we have shown that Fourier transform by a spherical lens enables us to suppress the astigmatic OAM component and restore the original free-astigmatic sLG beam structure. However, with further propagation, the sLG beam restores its astigmatic structure while maintaining the maximum OAM.

High-SNR 3D dark-field microscopy based on orbital angular momentum extraction

A 3D dark-field microscopy with high signal-to-noise ratio (SNR) is realized by demodulating the orbital angular momentum (OAM) information of the compound signal from the sample. Under ordinary Gaussian beam illumination containing pure 0th-order OAM component, the scattering of the sample extends the input light energy to non-zero order ones. In order to extract the specific order of OAM component, a forked-grating hologram with opposite wavefront is applied in the detection path. The SNR with 4.5 times enhancement is observed experimentally compared with conventional dark-field imaging in that the demodulation of the dark-field signal in OAM domain realizes a comparatively more thorough separation of reflected and scattered light. A spatial resolution of better than 0.78 μm is achieved. The 3D sectioning ability inherited from confocal configuration is verified by volumetric imaging of the defects of a fused silica sample with topological charge m = 0, 1, 2. The analysis of multiple orders tends to provide indications for specific characteristics of the samples such as the structural chirality and symmetry.

Spin and orbital angular momentum of coherent photons in a waveguide

Spin angular momentum of a photon corresponds to a polarisation degree of freedom of lights, and such that various polarisation properties are coming from macroscopic manifestation of quantum-mechanical properties of lights. An orbital degree of freedom of lights is also manipulated to form a vortex of lights with orbital angular momentum, which is also quantised. However, it is considered that spin and orbital angular momentum of a photon cannot be split from the total orbital angular momentum in a gauge-invariant way. Here, we revisit this issue for a coherent monochromatic ray from a laser source, propagating in a waveguide. We obtained the helical components of spin and orbital angular momentum by the correspondence with the classical Ponyting vector. By applying a standard quantum field theory using a coherent state, we obtained the gauge-independent expressions of spin and orbital angular momentum operators. During the derivations, it was essential to take a finite cross-sectional area into account, which leads the finite longitudinal component along the direction of the propagation, which allows the splitting. Therefore, the finite mode profile was responsible to justify the splitting, which was not possible as far as we were using plane-wave expansions in a standard theory of quantum-electrodynamics (QED). Our results suggest spin and orbital angular momentum are well-defined quantum-mechanical freedoms at least for coherent photons propagating in a waveguide and in a vacuum with a finite mode profile.

Effective polarization in proton-induced α knockout reactions

The effective polarization of the residual nucleus in the proton-induced $\alpha$ knockout reaction is investigated within the distorted wave impulse approximation framework. The strong absorption of the emitted $\alpha$ particle results in strong selectivity on the reaction "position" depending on the third component of the single-particle orbital angular momentum of the $\alpha$ particle inside a nucleus, hence on the spin direction of the reaction residue. This is caused by a mechanism that is similar to the Maris effect, the effective polarization in the proton-induced proton knockout reactions. However, as a distinct feature of the effective polarization in the $\alpha$ knockout process, the spin degrees of freedom of the reacting particles play no role. The $\alpha$ knockout process with complete kinematics can be a useful polarization technique for the residual nucleus, without actively controlling the spin of the proton.

Imaging-Based Quantum Tomography of Orbital-Angular-Momentum-Multiplexed Continuous-Variable Entangled States

Multiplexing techniques combine multiple signals into one channel, in order to increase the channel capacity and speed. Here we propose a correlation-based imaging method to efficiently measure the quantum states of orbital-angular-momentum (OAM)-multiplexed Gaussian light. The covariance matrices for all OAM components of the multiplexed Gaussian light can be efficiently reconstructed by one homodyne measurement on each beam. We also show that the proposed scheme can be simplified and implemented with only two charge coupled device detectors.

Sorting orbital angular momentum of photons through a multi-ring azimuthal-quadratic phase.

Beams carrying orbital angular momentum (OAM) already play significant roles in many domains. Here we propose a practical design of an OAM beam splitter based on a single phase-only multi-ring azimuthal-quadratic diffraction optical element that can sort different OAM components into various spatial positions, and OAM state probing is also achieved. The performance is demonstrated through proof-of-principle experiments and shows favorable results. Furthermore, the intensity proportion of each OAM component, namely the OAM spectrum, is also diagnosed. This work offers high applicability and practicability for the recognition and separation of photon OAM, and thus paves the way for many advanced scenarios such as quantum communication, holographic encryption, and remote sensing.

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.

Generation of spiral optical vortex with varying OAM for micro-manipulation

Since the confirmation of orbital angular momentum (OAM) decades ago, numerous studies have led to a new understanding of optical effects and various applications. Here we propose a concept of the spiral optical vortex (SOV) which contains multiple OAM modes from inside to outside along the spiral intensity field. Theoretically, by linking the azimuthal spiral phase with the beam radius, the SOV can be generated. The corresponding OAM spectrum of the SOV are analyzed theoretically and measured experimentally. We also demonstrate the evolution characteristics of the SOV over the propagation distance. The OAM components of the SOV have also been investigated and measured based on the fundamental Laguerre–Gaussian mode experimentally. The experiment results show that the micro-particle can be transmitted along with the spiral intensity distribution of the SOV to the center. This proposal may paves a new way in the generation of the spiral light field and stimulate new applications in light field modulation and microparticles manipulation.

Orbital angular momentum comb generation from azimuthal binary phases

Since Allen et al. demonstrated 30 years ago that beams with helical wavefronts carry orbital angular momentum (OAM), the OAM of beams has attracted extensive attention and stimulated lots of applications in both classical and quantum physics. Akin to an optical frequency comb, a beam can carry multiple various OAM components simultaneously. A series of discrete, equally spaced, and equally weighted OAM modes comprise an OAM comb. Inspired by the spatially extended laser lattice, we demonstrate both theoretically and experimentally an approach to producing OAM combs through azimuthal binary phases. Our study shows that transition points in the azimuth determine the OAM distributions of diffracted beams. Multiple azimuthal transition points lead to a wide OAM spectrum. Moreover, an OAM comb with any mode spacing is achievable through reasonably setting the position and number of azimuthal transition points. The experimental results fit well with theory. This work presents a simple approach that opens new prospects for OAM spectrum manipulation and paves the way for many applications including OAM-based high-security encryption and optical data transmission, and other advanced applications.

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.

Orbital angular momentum sidebands in second harmonic generation of a vortex beam by a nonlinear crystal with inhomogeneous refractive index

The manipulation of the orbital angular momentum (OAM) spectrum in new wavelengths generated by frequency conversion has a wide range of applications in quantum information technology and modern communications. Here, the second harmonic generation of a vortex beam in a nonlinear crystal with an inhomogeneous refractive index is considered. It is shown that by using a segmented oven and generating a controllable temperature gradient along the thickness of the nonlinear crystal, a transverse phase mismatch can be induced in the vortex beam. Accordingly, the OAM spectrum of the vortex beam can be changed by generating new OAM components in the spectrum. Compared with the nonlinear Bragg diffraction method, the presented method has the advantage of longer interaction length and higher efficiency.

Adjusted EfficientNet for the diagnostic of orbital angular momentum spectrum.

Orbital angular momentum (OAM) is one of multiple dimensions of beams. A beam can carry multiple OAM components, and their intensity weights form the OAM spectrum. The OAM spectrum determines complex amplitude distributions of a beam and features unique characteristics. Thus, measuring the OAM spectrum is of great significance, especially for OAM-based applications. Here we employ a deep neural network combined with a phase-only diffraction optical element to measure the OAM spectrum. The diffraction optical element is designed to diffract incident beams into distinct patterns corresponding to OAM distributions. Then, the EfficientNet, a kind of deep neural network, is adjusted to adapt and analyze the diffraction pattern to calculate the OAM spectrum. The favorable experimental results show that our proposal can reconstruct the OAM spectra with high precision and speed, works well for different numbers of OAM channels, and is also robust to Gaussian noise and random zooming. This work opens a new, to the best of our knowledge, ability for OAM spectrum recognition and will find applications in a number of advanced domains including large capacity optical communications, quantum key distribution, optical trapping, rotation detection, and so on.

Modal properties of a beam carrying OAM generated by a circular array of multiple ring-resonator emitters.

We investigate the modal properties of a beam carrying orbital angular momentum (OAM) generated by a circular array (ring) of multiple micro-ring emitters (rings) analytically and via simulation. In such a "ring-of-rings" structure, N emitters generate N optical vortex beams with the same OAM-order l0 at the same wavelength. The output beam is a coherent combination of the N vortex beams located at different azimuthal positions, having the same radial displacement. We derive an analytical expression for the output optical field and calculate the OAM-order power spectrum of the generated beam. The analytical expression and simulation results show that (1) the OAM spectrum of the output beam composes equidistant OAM spectral components, symmetrically surrounding l0 with a spacing equal to N; (2) the envelope of the OAM spectrum broadens with an increased radius of the circular array or the value of l0; and (3) the OAM components of the generated beam could be tuned either by changing the value of l0, corresponding to different spectrum envelopes, or by adding different linear phase delays to the micro-ring emitters, which does not affect the envelope of the OAM spectrum.

Machine-learning recognition of light orbital-angular-momentum superpositions

We develop a method to characterize arbitrary superpositions of light orbital angular momentum (OAM) with high fidelity by using astigmatic transformation and machine-learning processing. In order to identify each superposition unequivocally, we combine two intensity measurements. The first one is the direct image of the input beam, which is invariant for positive and negative OAM components. The second one is an image obtained using an astigmatic transformation, which allows distinguishing between positive and negative topological charges. Samples of these image pairs are used to train a convolution neural network and achieve high-fidelity recognition of arbitrary OAM superpositions.

Conversion of spin and orbital angular momentum in the third harmonic generation process in the bulk of an isotropic medium

The interaction between spin and orbital components of the angular momentum of an elliptically polarized beam with helicoidal phase profile and arbitrary axially symmetric intensity profile in the third-harmonic generation process is investigated. The third-harmonic beam is generated in an isotropic medium with cubic nonlinearity within undepleted pump approximation. The conservation of the total projections of both the spin angular momentum and orbital angular momentum components in four-wave mixing is demonstrated for interacting waves.

Experimental Demonstration of an Electrostatic Orbital Angular Momentum Sorter for Electron Beams.

The component of orbital angular momentum (OAM) in the propagation direction is one of the fundamental quantities of an electron wave function that describes its rotational symmetry and spatial chirality. Here, we demonstrate experimentally an electrostatic sorter that can be used to analyze the OAM states of electron beams in a transmission electron microscope. The device achieves postselection or sorting of OAM states after electron-material interactions, thereby allowing the study of new material properties such as the magnetic states of atoms. The required electron-optical configuration is achieved by using microelectromechanical systems technology and focused ion beam milling to control the electron phase electrostatically with a lateral resolution of 50nm. An OAM resolution of 1.5ℏ is realized in tests on controlled electron vortex beams, with the perspective of reaching an optimal OAM resolution of 1ℏ in the near future.

Exploring the Spatial Features of Electronic Transitions in Molecular and Biomolecular Systems by Swift Electrons

We devise a new kind of experiment that extends the technology of electron energy loss spectroscopy to probe (supra-)molecular systems: by using an electron beam in a configuration that avoids molecular damage and a very recently introduced electron optics setup for the analysis of the outcoming electrons, one can obtain information on the spatial features of the investigated excitations. Physical insight into the proposed experiment is provided by means of a simple but rigorous model to obtain the transition rate and selection rule. Numerical simulations of DNA G-quadruplexes and other biomolecular systems, based on time dependent density functional theory calculations, point out that the conceived new technique can probe the multipolar components and even the chirality of molecular transitions, superseding the usual optical spectroscopies for those cases that are problematic, such as dipole-forbidden transitions, at a very high spatial resolution.

Selective Orbital Imaging of Excited States with X-Ray Spectroscopy: The Example of α -MnS

Herein we show that non-resonant inelastic x-ray scattering involving an $s$ core level is a powerful spectroscopic method to characterize the excited states of transition metal compounds. The spherical charge distribution of the $s$ core hole allows the orientational dependence of the intensities of the various spectral features to produce a spatial charge image of the associated multiplet states in a straightforward manner, thereby facilitating the identification of their orbital character. In addition, the $s$ core hole does not add an extra orbital angular momentum component to the multiplet structure so that the well-established Sugano-Tanabe-Kamimura diagrams can be used for the analysis of the spectra. For $\alpha$-MnS we observe the spherical charge density corresponding to its high spin $3d^5$ ($^6A_1$) ground state configuration and we were able to selectively image its excited states and identify them as $t_{2g}$ ($^5T_2$) and $e_g$ ($^5E$) with an energy splitting $10Dq$ of 0.78\,eV.

Twisting and tweezing the spin wave: on vortices, skyrmions, helical waves, and the magnonic spiral phase plate

Spin waves are the low-energy excitations of magnetically ordered materials. They are key elements in the stability analysis of the ordered phase and have a wealth of technological applications. Recently, we showed that spin waves of a magnetic nanowire may carry a definite amount of orbital angular momentum components along the propagation direction. This helical, in addition to the chiral, character of the spin waves is related to the spatial modulations of the spin-wave phase across the wire. It, however, remains a challenge to generate and control such modes with conventional magnetic fields. Here, we make the first proposal for magnetic spiral phase plate by appropriately synthesizing two magnetic materials that have different speeds of spin waves. It is demonstrated with full-numerical micromagnetic simulations that despite the complicated structure of demagnetization fields, a homogeneous spin wave passing through the spiral phase plate attains the required twist and propagates further with the desired orbital angular momentum. While excitations from the ordered phase may have a twist, the magnetization itself can be twisted due to internal fields and forms what is known as a magnetic vortex. We point out the differences between both types of magnetic phenomena and discuss their possible interaction.

Propagation of converging polarization singular beams through atmospheric turbulence.

We report investigations on propagation of converging vector beams containing C-point and V-point polarization singularities through atmospheric turbulence. The C-point singularity is generated by superposition of the l=0 and l=1 orbital angular momentum (OAM) states, whereas the V-point singularity is generated by a superposition of the l=-1 and l=1 OAM states in orthogonal polarizations. The propagation of these beams through extended atmosphere is modeled by placing random phase screens along a 2 km propagation path. The random phase screens were generated using the FFT method with von Karman spectrum and Cn2=10-14 m-2/3. The quality of intensity profile of the focused vector beams after propagation through turbulence is assessed using the instantaneous signal-to-noise ratio and the on-axis scintillation index measurements. Our simulation results show that although both the C-point and V-point beams perform better than their scalar OAM components, C-point beams are seen to maintain much better beam intensity profile compared to the V-point beams. This observation is explained in terms of the OAM diversity of the individual polarization states and the correlation of their associated speckle patterns. The results presented here are important for engineering laser beams that can maintain a robust intensity profile on propagation through long-range atmospheric turbulence.