Orbital Angular Momentum Spectrum Research Articles

Engineered 3D Vortex Array with Customized Energy and Topological Charges for Multi‐View Display

AbstractArrays of multiple vortex beams enhance parallel processing capabilities from particle manipulation to information communication. However, the spatial position, topological charge, and energy parameters of the vortex beams within the array have yet to be precisely controlled, posing significant challenges to the realization of multi‐view 3D Orbital Angular Momentum (OAM) display using vortex arrays as information carriers. To address this issue, a method for generating vortex arrays based on a phase‐only hologram, customizing the array by using the energy and OAM spectrum of each vortex beam as the loss function is developed. Experimental results indicate that a 2D array generates 100 vortex beams in the spatial frequency domain, while a 3D array in the Fresnel zone produces 252 vortex beams across 7 planes, each with 36 unprecedentedly controllable energy and topological charge vortex beams. Subsequently, images of 4 views using the 3D vortex arrays and decoded through coordinate transformation to achieve a multi‐view 3D OAM display are encoded. The results demonstrate imaging quality with Mean Peak Signal‐to‐Noise Ratio (MPSNR) of 12.7, 13.0, 13.4, and 12.2 dB in 4 views, respectively, offering promising opportunities for applications in 3D optical manipulation, high‐capacity communication, and 3D OAM holography.

Orbital angular momentum spectrum of model partially coherent beams in turbulence

The use of partial coherence has been extensively studied as a potential solution to mitigate the destructive effects of atmospheric turbulence in optical applications involving the free space propagation of light. However, in OAM-based optical systems, reducing coherence leads to the broadening of the orbital angular momentum (OAM) spectrum, consequently increasing the cross-talk between adjacent modes. In this paper, we have investigated three fundamental classes of partially coherent OAM beams under the influence of turbulence. The aim is to identify a distinct type of partially coherent beam (PCB) in which the reduction in coherence results in higher resistance of the OAM spectrum against atmospheric disturbances. It is demonstrated that, for a specific propagation distance, we can prepare a PCB in which the benefits of reducing coherence outweigh its drawbacks.

Tailoring nondiffracting fields with a non-Markovian phase imprint.

We experimentally generate nondiffracting speckles that carry non-Markovian properties by encoding the wavefront of a monochromatic laser beam with ring-shaped non-Markovian phases. The resulting non-Markovian nondiffracting fields present a ring-shaped pattern and central dark notches, which are analyzed with an expression of the orbital angular momentum spectra of the wavefront possessing ring-shaped non-Markovian phases. Furthermore, we demonstrate that the intensity profiles of these non-Markovian nondiffracting fields exhibit stability over multiple Rayleigh ranges, and their statistical properties could be controlled with the non-Markovianity of the input phase masks. This work presents an approach for simultaneously tailoring the diffracting property and non-Markovianity of optical fields and provides a deeper understanding of non-Markovian processes.

Spectral analysis of intricate orbital angular momentum modes in multiplexing communication using a residual neural network

Vortex beams carrying orbital angular momentum (OAM) modes offer a compelling avenue for increasing optical communication capacity. Despite significant efforts in OAM mode (de)multiplexing, challenges persist in signal demodulation and noise monitoring of multiplexed channels. This challenge largely stems from the absence of efficient feature extraction methods capable of analyzing the OAM spectrum, which delineates mode components and intensity weights. Herein, we introduce a novel strategy for OAM mode spectrum analysis using a residual neural network incorporating interference techniques. By introducing interference between target vortex beams and a spherical wave, resulting in the mapping of OAM distributions onto the stripe features observed in the interferogram. To effectively extract spectrum details from these interferograms, we construct a residual neural network exhibiting high feature processing capabilities, which enables precise analysis of intricate OAM mode spectrum. We demonstrate the effectiveness of this OAM spectrum analysis by obtaining the intensity weights for 15 superimposed modes ranging from −10 to +10, achieving a mean-square-error of 2.3 × 10−4. To validate its practicality, we showcase an 80-channel three-dimensional multiplexing communication system including five OAM modes, two polarizations, and eight wavelengths. The 4 Tbit/s quadrature-phase-shift-keying signals are successfully demodulated with a bit-error rate below 3.34 × 10−6. Additionally, the measured optical signal-to-noise ratio reaches 11.5 dB, indicating the potential applications of this OAM spectrum analysis strategy in signal demodulation and noise monitoring.

Polarization-controlled generation of multiple orbital angular momentum modes

By concurrently manipulating the degrees of freedom associated with polarization and orbital angular momentum (OAM), a variety of vector fields can be generated, which exhibit unique characteristics and have found extensive application in both classical and quantum optics. However, the OAM dimensions in these fields have been predominantly confined to two. Different from high-order OAM with a large topological charge, broadening the OAM dimensions beyond this limit and generating OAM spectra with multiple OAM modes can significantly enhance the scope of research. In this study, we explore vector fields with OAM dimensions exceeding ten, achieving polarization-controlled spectra in higher-dimensional OAM. Our findings not only offer a method for controlling high-dimensional OAM through polarization but also pave the way for potential applications in both classical and quantum realms utilizing high-dimensional vector states.

Scattering Field Intensity and Orbital Angular Momentum Spectral Distribution of Vortex Electromagnetic Beams Scattered by Electrically Large Targets Comprising Different Materials

In this study, we obtained the intensity and orbital angular momentum (OAM) spectral distribution of the scattering fields of vortex electromagnetic beams illuminating electrically large targets composed of different materials. We used the angular spectral decomposition method to decompose a vortex beam into plane waves in the spectral domain at different elevations and azimuths. We combined this method with the physical optics algorithm to calculate the scattering field distribution. The OAM spectra of the scattering field along different observation radii were analyzed using the spiral spectrum expansion method. The numerical results indicate that for beams with different parameters (such as polarization, topological charge, half-cone angle, and frequency) and targets with different characteristics (such as composition), the scattering field intensity distribution and OAM spectral characteristics varied considerably. When the beam parameters change, the results of scattering from different materials show similar changing trends. Compared with beams scattered by uncoated metal and dielectric targets, the scattering field of the coating target can better maintain the shape and OAM mode of beams from the incident field. The scattering characteristics of metal targets were the most sensitive to beam-parameter changes. The relationship between the beam parameters, target parameters, the scattering field intensity, and the OAM spectra of the scattering field was constructed, confirming that the spiral spectrum of the scattering field carries the target information. These findings can be used in remote sensing engineering to supplement existing radar imaging, laying the foundation for further identification of beam or target parameters.

Metasurface for Engineering Superimposed Ince-Gaussian Beams.

Ince-Gaussian beams (IGBs) are the third complete family of exact and orthogonal solutions of the paraxial wave equation and have been applied in many fields ranging from particle trapping to quantum optics. IGBs play a very important role in optics as they represent the exact and continuous transition modes connecting Laguerre-Gaussian and Hermite-Gaussian beams. The method currently in use suffers from the high cost, complexity, and large volume of the optical system. The superposition of IGBs can generate complicated structured beams with multiple phase and polarization singularities. A metasurface approach is proposed to realizing various superpositions of IGBs without relying on a complicated optical setup. By superimposing IGBs with even and odd modes, multiple phase, and polarization singularities are observed in the resultant beams. The phase and polarization singularities are modulated by setting the initial phase in the design and controlling the incident linear polarization. The compactness of the developed metasurface devices and the unique properties of the generated beams have the potential to impact many practical applications such as particle manipulation, orbital angular momentum spectrum manipulation, and optical communications.

Analytical calculation of beam profile and orbital angular momentum spectrum of Laguerre Gaussian beams reflected from a graphene plasmonic structure.

In this paper, Laguerre Gaussian (LG) beams with different topological charges are used for excitation of surface plasmon polaritons (SPPs) through a graphene layer inserted in the Otto-configuration. By utilizing the angular spectrum representation (ASR) and Lorenz-gauge vector potential, an explicit analytical expression is derived for the electromagnetic fields of the reflected beam. At the optimal excitation state of graphene SPPs, the reflected beam exhibits a distinctive field profile characterized by two identical crescent-shaped lobes separated by a vertical strip with null intensity. Furthermore, in the absence of external magnetic field, the orbital angular momentum (OAM) spectrum of the reflected beam at the optimal excitation of SPPs reveals the annihilation of central OAM mode and the generation of two equal OAM sidebands, regardless of the incident OAM topological charge. Furthermore, the phase distributions of electric field of the reflected beam confirm the existence of OAM sidebands in the vicinity of optimal SPPs excitation. As the system is taken away from the optimal excitation of SPPs by introduction of an external magnetic field or increasing the chemical potential or increasing the incident angle, both central and sideband modes appear in the OAM spectrum of the reflected beam. In this case, when the topological charge of the incident wave increases, the weight of central OAM mode decreases while the weight of sidebands increases. In contrast, in the presence of external magnetic field, at the optimal excitation of SPPs, both central OAM and sidebands modes exist in the reflected beam such that the weight of central modes increases with the external magnetic field. This effect is also confirmed by plotting the phase distributions of the reflected beam at different external magnetic fields and for different incident topological charges. Therefore, the manipulation of graphene plasmons characteristics leads to the control of OAM sideband generation.

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.

Breaking the symmetric spiral spectrum distribution of a Laguerre-Gaussian beam propagating in moderate-to-strong isotropic atmospheric turbulence.

We demonstrate that the spiral spectrum (also known as orbital angular momentum spectrum) of a Laguerre-Gaussian (LG) beam with topological charge (TC) l is asymmetrically broadened propagating through moderate-to-strong atmospheric turbulence, even the statistics of turbulence is isotropic. This phenomenon is quite different from that predicted in weak turbulence where the spiral spectrum of a disturbed LG beam is symmetric with respect to its TC number l. An explicit analytical expression of the spiral spectrum of the LG beam with l = 1 is derived based on the extend Huygens-Fresnel integral and quadratic approximation, which is used to illustrate the transition scenarios of the spiral spectrum from symmetry to asymmetry in weak-to-strong turbulence. The physical mechanism for the asymmetric spiral spectrum in moderate-to-strong turbulence is thoroughly discussed. Our results are confirmed by the multi-phase screen numerical simulations and are consistent with the experimental results reported in Phys. Rev. A105, 053513 (2022)10.1103/PhysRevA.105.053513 and Opt. Lett.38, 4062 (2013)10.1364/OL.38.004062.

Generation of spatial combs digitized by orbital angular momentum

Shaping the transverse spatial domain of light has been experiencing recent growth in attention for its applications in optical tweezing, microscopy, communications, and quantum information sciences. The orbital angular momentum (OAM) of light is a transverse physical property that functions as a viable basis for many of such applications. While fields containing a single OAM mode order have extensively been used, fields containing a broad, discrete, and equally spaced OAM spectrum—an OAM comb—has largely been unexplored due to a lack of viable creation methods. Much like how frequency combs enabled myriad applications, it is conceivable that OAM combs would likewise enable further opportunities or expand upon single-OAM applications. For instance, an OAM comb may pave the way for more sophisticated particle manipulation, object detection, and pump shaping for high-dimensional spatial-mode entanglement. Here, we create four OAM combs with rectangular, sinusoidal, sinc, and Gaussian OAM spectral distributions using multiplane light conversion, which only involves phase modulations (hence is inherently lossless) and allows for improved tailoring of the spatial shape. The verification of such combs is done qualitatively by analyzing their propagation evolutions and quantitatively by employing a mode sorting technique—both exhibiting good agreement with user specifications and simulations. The scattering losses of all four combs were measured to be minimal, ranging from 0.66 to 1.04 dB.

Popper’s conjecture with angular slits and twisted light

Uncertainty relations are core to both classical and quantum physics, and lend themselves to tests across many degrees of freedom, with structured light emerging as a vibrant tool to harness these degrees of freedom. Here, we test Popper’s conjecture by replacing the traditional spatial and momentum states with angular position and orbital angular momentum (OAM) states of photons, showing that the OAM spectrum for an entangled photon passing through a virtual slit differs from that of a photon passing through a physical slit. To achieve this, we produce two OAM entangled photons, one of which is sent to a slit encoded as a digital hologram, thereby localising its angular position, all the while measuring the OAM of the other. We show that the measured OAM spectrum is limited to that of the initial SPDC photons, independent of the OAM encoded into the slit, consistent with Popper’s viewpoint. Our approach allows us to overcome prior limitations imposed by physical slits and linear momentum, and offers a versatile toolbox for further probes of quantum systems.

Generation of dual-polarization orbital angular momentum vortex beams with reflection-type metasurface

Orbital angular momentum (OAM) vortex beams can provide a new degree of freedom for information modulation at a physical level, which has great prospects to expand channel capacity in the fields of wireless microwave and optical communication. In this paper, a reflection-type anisotropic metasurface is proposed to transform the incident plane wave into reflected vortex beams by modulating the phase of wavefront. Single vortex beam, multi-beam vortex beams with different mode beams are demonstrated. Under the incidence of orthogonal linearly polarized waves, independent vortex beams can be generated at 15 GHz for polarization multiplexing. Besides, the OAM spectrum decomposition is performed to analyze the purity of the OAM modes based on a Fourier transformation. The results presented in the paper demonstrate the feasibility of generating vortex beams on metasurface within a subwavelength thickness, which may promote the development of electromagnetic/optical integration devices with polarization multiplexing techniques.

Detection accuracy of target accelerations based on vortex electromagnetic wave in keyhole space

The influence of the longitudinal acceleration and the angular acceleration of detecting target based on vortex electromagnetic waves in keyhole space are analyzed. The spectrum spreads of different orbital angular momentum (OAM) modes in different non-line-of-sight situations are simulated. The errors of target accelerations in detection are calculated and compared based on the OAM spectra spreading by using two combinations of composite OAM modes in the keyhole space. According to the research, the effects about spectrum spreads of higher OAM modes are more obvious. The error in detection is mainly affected by OAM spectrum spreading, which can be reduced by reasonably using different combinations of OAM modes in different practical situations. The above results provide a reference idea for investigating keyhole effect when vortex electromagnetic wave is used to detect accelerations.

Tailoring OAM spectrum of high-order harmonic generation driven by two mixed Laguerre–Gaussian beams with nonzero radial nodes

The extreme ultraviolet (XUV) light beam carrying orbital angular momentum (OAM) can be produced via high-order harmonic generation (HHG) due to the interaction of an intense vortex infrared laser and a gas medium. Here we show that the OAM spectrum of vortex HHG can be readily tailored by varying the radial node (from 0 to 2) in the driving laser consisting of two mixed Laguerre–Gaussian (LG) beams. We find that due to the change in spatial profile of HHG, the distribution range of the OAM spectrum can be broadened and its shape can be modified by increasing the radial node. We also show that the OAM mode range becomes much wider and its distribution shape becomes more symmetric when the harmonic order is increased from the plateau to the cutoff when the driving laser has the nonzero radial nodes. Through the map of coherence length and the evolution of harmonic field in the medium, we reveal that the favorable off-axis phase-matching conditions are greatly modified due to the change of intensity and phase distributions of driving laser with the radial node. We anticipate this work to stimulate some interests in generating the XUV vortex beam with tunable OAM spectrum through the gaseous HHG process achieved by manipulating the mode properties of the driving laser beam.

Propagation of radial phase modulated vortex beams in atmospheric turbulence

In practical free-space optical (FSO) communications, mitigating turbulence effects is crucial. This paper introduces radial phase modulation as a method to protect the signal's orbital angular momentum (OAM) in turbulent FSO. The results demonstrate that selecting appropriate modulation parameters can improve communication quality, particularly in stronger turbulence. However, a drawback is that radial phase modulation also increases crosstalk near the signal mode in strong turbulence. We further investigate the effects of radial phase modulation in two OAM multiplexing cases: mode broadcasting and intensity superposition. The results demonstrate that by employing radial phase modulation, both intensity and phase divergence, as well as beam wander, can be effectively reduced. In addition, the peaks in the OAM spectra enable easy identification of the signal modes. Moreover, even with a limited aperture in the detector, both channel capacity and transmission distance can be enhanced. These findings have potential applications in practical FSO communication in atmospheric turbulence.

Modulating and identifying an arbitrary curvilinear phased optical vortex array of high-order orbital angular momentum

Vortex beams can be used in optical communication, imaging, and processing applications. In this study, we generate a phased optical vortex array with high-order orbital angular momentum (OAM) based on a phased Gaussian optical array and high-order phase multiplication. We then analyze the OAM mode distribution using the OAM spectrum expansion, and the number of high-order phase singularities in the array verified in interference experiments. Our results substantiate the feasibility of generating a high-order optical vortex array using this method. At the same time, because the phase Gaussian optics array that forms the phased optical vortex array is discrete and separable, we can use the phase Gaussian optics array with different phase differences to generate the phased optical vortex array with different phase gradients. The shape of the generated optical vortex array can be arranged along any curve. The phase singularity and OAM distributions at high orders are also detailedly analyzed. The ability to control the high-order OAM and phase structure has possible applications in particle manipulation and free-space optical communication.

The Rotational Doppler Effect of Twisted Photons in Scattered Fields

AbstractAlong with broad applications of the linear Doppler effect, the rotational Doppler effect (RDE) of a structured light source carrying orbital angular momentum (OAM) has attracted significant attention for applications ranging from optical sensors to Doppler cooling. However, the high‐purity structured source's low energy efficiency and unknown optimal OAM parameters have significantly degraded the RDE's performance in previous work. Here, instead of utilizing an optical vortex source, the Doppler features are analyzed in scattered twisted photons carrying OAM with a common light source, and it is demonstrated that the RDE induced by a typical rotator can be extracted using a spiral phase spatial filter (SPSF) at the receiver. This model reveals that a rotating rough surface scatters abundant twisted photons carrying varied OAM values, and the OAM spectrum distribution is modulated by its angular coherence of spatial signature. Furthermore, common surfaces with different autocorrelation structures on received signals using the SPSF method are analyzed theoretically and experimentally. Such a scheme facilitates rotator detection with a generalized nonvortex simple source and dozen–fold improved efficiency with robustness against noncoaxial problems. These demonstrations open a path for studying and applying scattered twisted photons during light detection.

Single-shot Kramers–Kronig complex orbital angular momentum spectrum retrieval

Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverse OAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve the amplitude and phase information of complex OAM spectra in a few shots. Yet, its single-shot retrieval remains elusive, due to the signal–signal beat interference inherent in the measurement. Here, we introduce the concept of Kramers–Kronig (KK) receiver in coherent communications to the OAM domain, enabling rigorous, single-shot OAM spectrum measurement. We explain in detail the working principle and the requirement of the KK method and then apply the technique to precisely measure various characteristic OAM states. In addition, we discuss the effects of the carrier-to-signal power ratio and the number of sampling points essential for rigorous retrieval and evaluate the performance on a large set of random OAM spectra and high-dimensional spaces. Single-shot KK interferometry shows enormous potential for characterizing complex OAM states in real time.

Complex field manipulation based on OAM spectrum analysis with an arbitrarily distributed antenna array

In the next generation multiple-input multiple-output (MIMO) communication system, a higher effective degree of freedom (EDoF) is desired to increase the channel capacity. Hence, complex field manipulation, which enriches the diversity of the amplitude and phase distribution, is necessary for an antenna array. In this paper, the complex field manipulation (CFM) scheme based on an arbitrarily distributed antenna array is proposed, which takes the orbital angular momentum (OAM) spectrum analysis as the bridge. Whether the antenna element transformation states are fixed or flexible, the CFM can be achieved with different schemes. This work may promote the application of OAM spectrum analysis and the development of complex field manipulation in the high-EDoF MIMO communication system.