Orbital Angular Momentum States Research Articles

Visualizing a single wavefront dislocation induced by orbital angular momentum in graphene

Phase singularities are phase-indeterminate points where wave amplitudes are zero, which manifest as phase vertices or wavefront dislocations. In the realm of optical and electron beams, the phase singularity has been extensively explored, demonstrating a profound connection to orbital angular momentum. Direct local imaging of the impact of orbital angular momentum on phase singularities at the nanoscale, however, remains challenging. Here, we study the role of orbital angular momentum in phase singularities in graphene, particularly at the atomic level, through scanning tunneling microscopy and spectroscopy. Our experiments demonstrate that the scatterings between different orbital angular momentum states, which are induced by local rotational symmetry-breaking potentials, can generate additional phase singularities, and result in robust single-wavefront dislocations in real space. Our results pave the way for exploring the effects of orbital degree of freedom on quantum phases in quasiparticle interference processes.

Spin Unlocked Vortex Beam Generation on Nonlinear Chiroptical Metasurfaces.

Optical vortices with spin and orbital angular momentum (SAM and OAM) states offer multiple degrees of freedom for manipulating optical fields and thus enable great potentials in optical information processing. Recently, the optical metasurface has become an important platform for vortex beam generation and steering. However, the strong spin-orbit interaction on such metasurfaces usually leads to spin locked OAM generation, which limits the complete control of the angular momentum state of light. Here, we propose to solve this constraint using geometric phase controlled nonlinear chiroptical metasurfaces. The metasurface consists of two types of plasmonic meta-atoms which have opposite handedness and exhibit a strong spin-dependent circular dichroism effect. By encoding specific phase singularities and phase gradients to different channels, we experimentally demonstrate the spin unlocked second harmonic beam steering. The proposed nonlinear chiroptical metasurfaces may have important applications in developing multifunctional nonlinear optical devices.

Quantum Limit for the Emittance of Dirac Particles Carrying Orbital Angular Momentum

In this article, we highlight that the interaction potential confining Dirac particles in a box must be invariant under the charge conjugation to avoid the Klein paradox, in which an infinite number of negative-energy particles are excited. Furthermore, we derive the quantization rules for a relativistic particle in a cylindrical box, which emulates the volume occupied by a beam of particles with a non-trivial aspect ratio. We apply our results to the evaluation of the quantum limit for emittance in particle accelerators. The developed theory allows the description of quantum beams carrying Orbital Angular Momentum (OAM). We demonstrate how the degeneracy pressure is such to increase the phase–space area of Dirac particles carrying OAM. The results dramatically differ from the classical evaluation of phase–space areas, that would foresee no increase in emittance for beams in a coherent state of OAM. We discuss the quantization of the phase–space cell’s area for single Dirac particles carrying OAM, and, finally, provide an interpretation of the beam entropy as the measure of how much the phase–space area occupied by the beam deviates from its quantum limit.

Spatiotemporal optical vortex reconnections of multi-vortices

Vortex reconnections are ubiquitous events found in diverse media. Here we show that vortex reconnections also occur between spatiotemporal vortices in optical waves. Since vortices exhibit orbital angular momentum (OAM), the reconnections of optical vortices create a variety of connected OAM states. Dispersion and diffraction can cause different reconnection pairs, depending on the orientation of the vortices. The transverse crossing of two vortices with a topological charge of one can produce unique vortex loop reconnection patterns. Higher topological charges result in arrays of vortex loops and connection points. Crossing of three vortices produces spherical structures made of three symmetrical vortex arms. A three vortices reconnection with higher topological charges develops complicated patterns similar to turbulence cascade phenomena in other media. Studying optical vortex interactions may bring insight into vortex reconnections in other fields. We also provide experimental results of two-vortex loop interaction.

Orbital angular momentum sensing of composite vortex light in a single-layer graphene system

This paper explores the impact of orbital angular momentum (OAM) in composite vortex light on the absorption and dispersion characteristics of a weak probe light interacting with a single-layer graphene system. Through systematic investigation, we demonstrate the exceptional control achievable over absorption and dispersion profiles by manipulating the OAM of light. Under resonance conditions for the probe light, transparent regions emerge in the spatial profile of probe absorption, and the number of these transparent regions can be precisely regulated by adjusting the OAM number of the composite vortex light. Conversely, in the case of off-resonance probe light, amplified regions surface in the absorption spectrum, with the number of these regions controllable by the OAM state of the composite vortex light. These findings hold significant implications for optical communication systems, offering a valuable tool for the detection and measurement of the OAM number of composite vortex light, and paving the way for advancements in tailored signal processing and communication technologies.

Controlled Generation of High‐Purity Scalar Orbital Angular Momentum States from a High‐Power Single‐Crystal Fiber Laser

AbstractThe orbital angular momentum (OAM) of light, which is associated with the rotation of the phase structure, gives rise to numerous novel physical phenomena inlight–matter interactions. However, the direct generation of scalar OAM lasers with power‐handling capability and controllable states at the source remains challenging owing to mode degeneracy, handedness selection, and nonlinear thermal effects, which can even lead to topological charge splitting. This paper proposes a novel approach that allows spatial mode‐conversion‐controlled laser oscillation in a high‐gain OAM laser cavity with an integrated spiral‐face output coupler (SFOC). By adapting position‐dependent resonant modes, scalar optical vortices with a record power level (>60 W), high purity (>90%), and controllable OAM states (ħ or −8ħ) are demonstrated. Further, the dynamic process of OAM generation and evolution in the cavity is revealed. The concept presented herein opens a new route for the generation of OAM laser sources toward high power levels and holds promise for advancing classical and quantum optics, particularly in the area of light–matter interactions.

Taxonomy of hybridly polarized Stokes vortex beams.

Structured beams carrying topological defects, namely phase and Stokes singularities, have gained extensive interest in numerous areas of optics. The non-separable spin and orbital angular momentum states of hybridly polarized Stokes singular beams provide additional freedom for manipulating optical fields. However, the characterization of hybridly polarized Stokes vortex beams remains challenging owing to the degeneracy associated with the complex polarization structures of these beams. In addition, experimental noise factors such as relative phase, amplitude, and polarization difference together with beam fluctuations add to the perplexity in the identification process. Here, we present a generalized diffraction-based Stokes polarimetry approach assisted with deep learning for efficient identification of Stokes singular beams. A total of 15 classes of beams are considered based on the type of Stokes singularity and their associated mode indices. The resultant total and polarization component intensities of Stokes singular beams after diffraction through a triangular aperture are exploited by the deep neural network to recognize these beams. Our approach presents a classification accuracy of 98.67% for 15 types of Stokes singular beams that comprise several degenerate cases. The present study illustrates the potential of diffraction of the Stokes singular beam with polarization transformation, modeling of experimental noise factors, and a deep learning framework for characterizing hybridly polarized beams.

Orbital angular momentum-mediated machine learning for high-accuracy mode-feature encoding

Machine learning with optical neural networks has featured unique advantages of the information processing including high speed, ultrawide bandwidths and low energy consumption because the optical dimensions (time, space, wavelength, and polarization) could be utilized to increase the degree of freedom. However, due to the lack of the capability to extract the information features in the orbital angular momentum (OAM) domain, the theoretically unlimited OAM states have never been exploited to represent the signal of the input/output nodes in the neural network model. Here, we demonstrate OAM-mediated machine learning with an all-optical convolutional neural network (CNN) based on Laguerre-Gaussian (LG) beam modes with diverse diffraction losses. The proposed CNN architecture is composed of a trainable OAM mode-dispersion impulse as a convolutional kernel for feature extraction, and deep-learning diffractive layers as a classifier. The resultant OAM mode-dispersion selectivity can be applied in information mode-feature encoding, leading to an accuracy as high as 97.2% for MNIST database through detecting the energy weighting coefficients of the encoded OAM modes, as well as a resistance to eavesdropping in point-to-point free-space transmission. Moreover, through extending the target encoded modes into multiplexed OAM states, we realize all-optical dimension reduction for anomaly detection with an accuracy of 85%. Our work provides a deep insight to the mechanism of machine learning with spatial modes basis, which can be further utilized to improve the performances of various machine-vision tasks by constructing the unsupervised learning-based auto-encoder.

Multiplication of orbital angular momentum via multi-plane light conversion.

The multiplication of orbital angular momentum (OAM) modes using optical coordinate transformation is useful for OAM optical networks, but the scalability of this scheme is limited by the ray model. Here, we propose an alternative scheme for the scalable multiplication of OAM modes based on modified multi-plane light conversion (MPLC) that can extend azimuthal and radial indices of OAM modes supported by the multipliers and unlock a new degree of freedom for radial high-order OAM states that has been restricted in the zero order. The multiplication for 20 OAM modes with radial index p = 0 and 10 OAM modes with radial index p = 1 is performed in simulation and experiment. The 3-dB optical bandwidth corresponding to the purity of OAM modes covers the entire C-band experimentally. This novel, to the best of our knowledge, approach to manipulating OAM states provides valuable insights and flexible strategies for high-capacity OAM optical communication and high-dimensional optical quantum information processing.

The Spiral Spectrum of a Laguerre–Gaussian Beam Carrying the Cross-Phase Propagating in Weak-to-Strong Atmospheric Turbulence

In communication links, the presence of atmospheric turbulence leads to crosstalk between the orbital angular momentum (OAM) states, thereby limiting the performance of information transmission. Thus, knowledge of the effect of turbulence on the spiral spectrum (also named the OAM spectrum) is of utmost importance in the field of optical communications. However, most of the existing studies are limited to weak turbulence calculation models. In this paper, based on the extended Huygens–Fresnel integral, the analytical expression is derived for the mutual coherence function of a Laguerre–Gaussian beam carrying the cross-phase and propagating through weak-to-strong anisotropic Kolmogorov atmospheric turbulence; subsequently, the analytical expression is used to study the behavior of the spiral spectrum. The discrepancies in the spiral spectrum between weak and strong turbulence are comparatively studied. The influences of the cross-phase and the anisotropy of turbulence on the spiral spectrum are investigated through numerical examples. Our results reveal that the cross-phase determines the distribution of the spiral spectrum. The spiral spectrum can be tuned to multiple OAM modes through the adaptation of the cross-phase coefficient. Moreover, increasing the cross-phase coefficient can reduce both the discrepancies of the spiral spectrum under two computational methods and the effects of the anisotropic factors of turbulence on the spiral spectrum.

Wavelength-tunable Tm:Y2O3 ceramic vortex laser with a changeable orbital angular momentum state.

Wavelength-tunable orbital angular momentum (OAM) lasers with controllable topological charges have the potential for serving as light sources for large-capacity optical communication by combining conventional wavelength division multiplexing (WDM) with OAM mode-division multiplexing (OAM-MDM). In this study, we demonstrate a wavelength-tunable Tm-bulk laser that can control OAM states in the 2-µm spectral range. The excitation conditions for different Laguerre-Gaussian (L G 0,l ) modes in a bulk laser cavity are theoretically determined by measuring the spatial propagation dynamics of the annular pump beam. As a proof-of-principle study, we experimentally generate OAM states of |ℏ| and |2ℏ| from a T m:Y 2 O 3 ceramic laser with a tunable emission wavelength using a Lyot filter (LF). The spatial properties of the scalar optical vortices are well conserved during wavelength tuning, indicating the feasibility of our approach for producing wavelength-tunable structured light. These OAM laser sources, which are characterized by their robustness and compactness, have potential applications in various areas such as optical communications, quantum optics, super-resolution microscopes, and more.

Performance of Orbital Angular Momentum Communication for a Non-Uniformly Correlated High-Order Bessel–Gaussian Beam in a Turbulent Atmosphere

We derived the formula for the detection probability, signal-to-noise ratio (SNR), and average bit error rate (BER) for the signal orbital angular momentum (OAM) state carried via non-uniformly correlated high-order Bessel–Gaussian beam propagation in a turbulent atmosphere. The wavelength, receiver aperture, beam width, strength of the turbulent atmosphere, and topological charge effect on detection probability, SNR, and average BER of the signal OAM state were demonstrated numerically. The results show that the signal OAM state with low topological charge, a small receiver aperture, a narrow beam width, and a long wavelength can improve the performance of optical communications systems under conditions of weak atmospheric turbulence. Our results will be useful in long-distance free space optical (FSO) communications.

Underwater entanglement propagation of auto-focusing Airy beams.

In underwater wireless optical communication, orbital angular momentum (OAM) states suffer from turbulence distortions. This study aims to investigate the effectiveness of auto-focusing and OAM entanglement of the beams in reducing the turbulence effects. We implement the single-phase approximation and the extended Huygens-Fresnel principle to derive the detection probability of the entangled Airy beams under unstable oceanic turbulence. The results show that auto-focusing can protect the signal OAM mode and suppress modal crosstalks, while entangled OAM states can further enhance the resistance against oceanic turbulence around the focus position. The numerical analysis demonstrates that after the auto-focusing position, the beams evolve in completely opposite directions, indicating that the focal length should be modulated according to the length of a practical link to enhance received signals. These findings suggest that entangled auto-focusing vortex beams may be a desirable light source in underwater communication systems.

Orbital angular momentum splitter of light based on beam displacer

In recent years, the high-dimensional properties of the orbital angular momentum degree of freedom of light have attracted extensive attention. This degree of freedom has been studied and used in many scientific fields, especially in optical communication and quantum information. In order to fully utilize the high-dimensional properties of orbital angular momentum, non-destructive separation of different orbital angular momentum states has become a fundamental requirement. However, the existing orbital angular momentum beam-splitting systems either lack stability and cascade expansibility, or the properties of the separated orbital angular momentum states are seriously damaged, thus failing to participate in further interaction processes. In this work, we construct a miniature Mach-Zehnder interferometer based on the beam displacer, and design an orbital angular momentum beam splitter, thereby realizing the non-destructive beam splitting of orbital angular momentum mode. In the orbital angular momentum splitter, the theoretical energy loss is zero because there exists only total reflection of the beam. The beam in the miniature Mach-Zehnder interferometer passes through the same optical element, and the spatial deviation of the beam is small, so the orbital angular momentum beam splitter has good stability. In addition, because the separated orbital angular momentum state has the same propagation direction as the incident orbital angular momentum state, the beam splitter has good extensibility and is easy to use in cascade. Our research result is of great significance in using the orbital angular momentum as a high-dimensional degree of freedom in optical communication and other related fields.

Ion-acoustic waves with non-planar wavefronts

The ion-acoustic (IA) mode exhibiting various orbital angular momentum (OAM) states is examined in a plasma with drifting electrons. The constituent plasma species are modeled with a non-gyrotropic Maxwellian distribution and discussion of dispersion relation and growth rate of twisted IA waves under various conditions is presented. In the domain of kinetic model, the twisted IA waves are characterized by Laguerre-Gaussian (LG) solutions, where plasma distribution function and electric field are decomposed into axial and azimuthal components. The plasma response function is obtained under paraxial approximations and investigated for threshold condition of instability growth rate with helical electric field structures. The impact of an extra electron specie on the instability is demonstrated through a comparison of twisted waves for single and double electron species.

Three-dimensional spatial orbital angular momentum holography

The degree of freedom of orbital angular momentum of light has been used as a new information carrier in optical holographic information processing technology. However, current research on orbital angular momentum holography mainly focuses on two-dimensional orbital angular momentum holography, where the reconstructed two-dimensional holographic image is located in a certain plane in three-dimensional space. How to further implement three-dimensional spatial orbital angular momentum holographic technology and use it to increase the information capacity of holographic communication is still a blank. Here, we implement three-dimensional spatial orbital angular momentum holographic technology based on the degrees of freedom of orbital angular momentum and the positional degrees of freedom of reconstructed two-dimensional images in three-dimensional space. In other words, in the three-dimensional spatial orbital angular momentum holography, the acquisition of the target object image requires not only the correct orbital angular momentum state used for decoding, but also the correct spatial position where the object's image is detected. In addition, we further investigate the three-dimensional spatial orbit angular momentum holographic multiplexing technology and points out that this multiplexing technology can be used for information encryption. Compared with traditional two-dimensional orbital angular momentum holography, three-dimensional spatial orbital angular momentum holography uses an additional degree of freedom. Therefore, the encryption scheme based on three-dimensional spatial orbital angular momentum holographic technology can further improve the security level of information. Our simulation results and experimental results have verified the feasibility of three-dimensional spatial orbit angular momentum holographic technology and three-dimensional spatial orbit angular momentum holographic encryption technology.

Vortex circular airy beams through leaky-wave antennas

A novel method to design leaky-wave antennas radiating vortex cylindrical Airy beams at microwave frequencies is here presented. Two different approaches are adopted to produce waves with a nonzero orbital angular momentum (OAM): one based on a bull’s eye design excited by a uniform circular array of vertical coaxial probes with proper azimuthal phase delay, and one based on a single coaxial feeder exciting a multi-spiral radiator. Both of them take advantage of backward radial propagation of cylindrical leaky waves promoting circular Airy beams with vortex patterns. The OAM state can be changed by either varying the probe phasing or the number of spiral units. A reference profile is designed under transverse-electric and transverse-magnetic excitation independently. Numerical full-wave analysis are performed using different angular states to validate the antenna design, as well to highlight the different advantages of the two alternative design approaches.

Separation and detection of orbital angular momentum states of composite vortex beams in atmospheric turbulence channels

The separation and detection of compound orbital angular momentum (OAM) modes are the basis for achieving high-speed and high-capacity communication, but the atmospheric turbulence causes distortion of the phase fronts of vortex beams, which hinders the recognition of OAM modes. To solve this problem, in this work, we propose and investigate a joint scheme of combining the Gerchberg–Saxton (GS) algorithm and the phase of addition and subtraction model that can achieve high recognition accuracy and a wide range of OAM modes of compound perfect optical vortex beam under long-distance turbulence environment. At the receiving end, the GS algorithm and phase addition and subtraction are used to compensate and modulate the incident vortex light field to obtain the pre-processed light field, and then the OAM is detected by the coordinate transformation method. The simulation results show that: The detection range of the OAM of the three optical path detection model for the vortex beam transmitting 1000 m reaches −37 to +37 in the vacuum environment, and the mode purity of −37 to +37 can reach more than 0.3 when the turbulence intensity is Cn 2 = 2 × 10−15 m−2/3. The detection range of the OAM of the vortex can be further expanded by increasing the optical path. This study provides a new method for the separation and detection of OAM of composite vortex beams.

Remote transport of high-dimensional orbital angular momentum states and ghost images via spatial-mode-engineered frequency conversion

The efficient transport and engineering of photonic orbital angular momentum (OAM) lie at the heart of various related classical and quantum applications. Here, by leveraging the spatial-mode-engineered frequency conversion, we realize the remote transport of high-dimensional orbital angular momentum (OAM) states between two distant parties without direct transmission of information carriers. We exploit perfect vortices for preparing high-dimensional yet maximal O AM entanglement. Based on nonlinear sum-frequency generation working with a strong coherent wave packet and a single photon, we conduct the Bell-like state measurements for high-dimensional perfect vortices. We experimentally achieve an average transport fidelity 0.879 ± 0.048 and 0.796 ± 0.066 for a complete set of 3-dimensional and 5-dimensional OAM mutually unbiased bases, respectively. Furthermore, by exploring the full transverse entanglement, we construct another strategy of quantum imaging with interaction-free light. It is expected that, with the future advances in nonlinear frequency conversion, our scheme will pave the way for realizing truly secure high-dimensional quantum teleportation in the upcoming quantum network.

Wideband reflective metasurface for independent control of mode and circular polarization of orbital angular momentum.

Pancharatnam-Berry (PB) phase, usually utilized for phase manipulation of circularly polarized (CP) waves, has inherent symmetrical response on left-handed polarized (LCP) and right-handed polarized (RCP) for orbital angular momentum (OAM), which severely hinders its application. By modulating both propagation and PB phase allows independent control of LCP and RCP of OAM, but increases the design difficulty. Here, we propose a phase compensation scheme to independent control the CP states of OAM only utilizing PB phase, where arbitrary topological charges and deflection directions of LCP and RCP beams can be realized. Two wideband metasurfaces are designed to independent control the mode, circular polarization and beam directions of OAM at the frequency range of 10-20 GHz. This work significantly motivates the development of polarization division multiplexing in wireless communication system.