Generation of orbital angular momentum hologram using a modified U-net

Orbital angular momentum(OAM)holography has become a promising technique in information encryption,data storage and opto-electronic computing,owing to the infinite topological charge of one single OAM mode and the orthogonality of different OAM modes.In this paper,we propose a novel OAM hologram generation method based on a densely connected U-net(DCU),where the densely connected convolution blocks(DCB)replace the convolution blocks of the U-net.Importantly,the reconstruction process of the OAM hologram is integrated into DCU as its output layer,so as to eliminate the requirement to prepare training data for the OAM hologram,which is required by conventional neural networks through an iterative algorithm.The experimental and simulation results show that the OAM hologram can rapidly be generated with the well-trained DCU,and the reconstructed image's quality from the generated OAM hologram is significantly improved in comparison with those from the Gerchberg-Saxton generation method,the Gerchberg-Saxton based generation method and the U-net method.In addition,a 10-bit OAM multiplexing hologram scheme is numerically demonstrated to have a high capacity with OAM hologram.

Bessel–Gaussian beam-based orbital angular momentum holography

Orbital angular momentum(OAM), as a new degree of freedom, has recently been applied in holography technology.Due to the infinite helical mode index of OAM mode, a large number of holographic images can be reconstructed from an OAM-multiplexing hologram. However, the traditional design of an OAM hologram is constrained by the helical mode index of the selected OAM mode, for a larger helical mode index OAM mode has a bigger sampling distance, and the crosstalk is produced for different sampling distances for different OAM modes. In this paper, we present the design of the OAM hologram based on a Bessel–Gaussian beam, which is non-diffractive and has a self-healing property during its propagation. The Fourier transform of the Bessel–Gaussian beam is the perfect vortex mode that has the fixed ring radius for different OAM modes. The results of simulation and experiment have demonstrated the feasibility of the generation of the OAM hologram with the Bessel–Gaussian beam. The quality of the reconstructed holographic image is increased, and the security is enhanced. Additionally, the anti-interference property is improved owing to its self-healing property of the Bessel-OAM holography.

Robust measurement of orbital angular momentum of a partially coherent vortex beam under amplitude and phase perturbations

The ability to overcome the negative effects,induced by obstacles and turbulent atmosphere,is a core challenge of long-distance information transmission,and it is of great significance in free-space optical communication.The spatial-coherence structure,that characterizes partially coherent fields,provides a new degree of freedom for carrying information.However,due to the influence of the complex transmission environment,the spatial-coherence structure is severely damaged during the propagation path,which undoubtedly limits its ability to transmit information.Here,we realize the robust far-field orbital angular momentum(OAM)transmission and detection by modulating the spatial-coherence structure of a partially coherent vortex beam with the help of the cross-phase.The cross-phase enables the OAM information,quantified by the topological charge,hidden in the spatial-coherence structure can be stably transmitted to the far field and can resist the influence of obstructions and turbulence within the communication link.This is due to the self-reconstruction property of the spatial-coherence structure embedded with the cross-phase.We demonstrate experimentally that the topological charge information can be recognized well by measuring the spatial-coherence structure in the far field,exhibiting a set of distinct and separated dark rings even under amplitude and phase perturbations.Our findings open a door for robust optical signal transmission through the complex environment and may find application in optical communication through a turbulent atmosphere.

Asymmetrical spiral spectra and orbital angular momentum density of non-uniformly polarized vortex beams in uniaxial crystals

To explore the effect of non-uniform polarization on orbital angular momentum(OAM) in anisotropic medium, in this work investigated are the evolution of the spiral spectra and OAM densities of non-uniformly polarized vortex(NUPV)beams in uniaxial crystals propagating orthogonal to the optical axis, and also the case of uniformly polarized vortex(UPV)beams with left-handed elliptical polarization. In the input plane, the NUPV beams present their spiral spectra of m-mode concentrated at m = l ± 1 modes rather than m = l mode, and reveal the relation among topological charge l, mode of spiral spectra m and the power weight value Rmexpressed by l=∑^(∞)_(m)=-∞Rm. is still satisfied for UPV beams in uniaxially anisotropic crystals, whereas for NUPV beams their relations are no longer valid owing to non-uniform polarization. Furthermore, the analysis indicates that the asymmetrical distribution of power weight of spiral spectra and the non-zero value in the sum of longitudinal OAM densities originate from the initial non-uniform polarization and anisotropy in uniaxial crystals rather than topological charges. In addition, the relation between spiral spectrum and longitudinal OAM density is numerically discussed. This work may provide an avenue for OAM-based communications,optical metrology, and imaging by varying the initial non-uniform polarization.

Diffraction deep neural network based orbital angular momentum mode recognition scheme in oceanic turbulence

Orbital angular momentum(OAM)has the characteristics of mutual orthogonality between modes,and has been applied to underwater wireless optical communication(UWOC)systems to increase the channel capacity.In this work,we propose a diffractive deep neural network(DDNN)based OAM mode recognition scheme,where the DDNN is trained to capture the features of the intensity distribution of the OAM modes and output the corresponding azimuthal indices and radial indices.The results show that the proposed scheme can recognize the azimuthal indices and radial indices of the OAM modes accurately and quickly.In addition,the proposed scheme can resist weak oceanic turbulence(OT),and exhibit excellent ability to recognize OAM modes in a strong OT environment.The DDNN-based OAM mode recognition scheme has potential applications in UWOC systems.

The Development Trends and Research Fronts in Orbital Angular Momentum Technology:A Bibliometric Analysis

Orbital angular momentum(OAM)technology,refers to Laguerre-Gaussian(LG)beams,twisted beams,vector/vortex beams,acoustic vortex beams and fractional vortex beams.It is an emerging and promising technology to improve the communication capacity,spectral efficiency,and anti-jamming capability due to its helical phase fronts and infinite orthogonal states.Although the OAM research began in the 1990s,the developing trends,current status,issues and characteristics through a systematic observation have not yet been performed.This paper presents a knowledge-based evolution of OAM research published in the Web of Science(WoS)from 2011 to 2021 using bibliometric analysis in Citepspace.The results demonstrate that the bandwidth,efficiency,gain,divergence,phase quantization,bulky and complex feeding structures,misalignment,distortion,interferences atmospheric turbulence and diffraction were the key issues found in the OAM technology.The main research hotspots and categories,influential authors,leading journals,best institutions of OAM show a strong bias in favor of their functions and technology developments.The research on OAM was mainly performed by the counties that have developed the 5G and now moving towards 6G communications like China,USA and South Korea.This study would serve as an inclusive guide on the future research trends and status especially for the OAM researchers.

Calibration of quantitative rescattering model for simulating vortex high-order harmonic generation driven by Laguerre–Gaussian beam with nonzero orbital angular momentum

We calibrate the macroscopic vortex high-order harmonic generation(HHG)obtained by the quantitative rescattering(QRS)model to compute single-atom induced dipoles against that by solving the time-dependent Schr?dinger equation(TDSE).We show that the QRS perfectly agrees with the TDSE under the favorable phase-matching condition,and the QRS can accurately predict the main features in the spatial profiles of vortex HHG if the phase-matching condition is not good.We uncover that harmonic emissions from short and long trajectories are adjusted by the phase-matching condition through the time-frequency analysis and the QRS can simulate the vortex HHG accurately only when the interference between two trajectories is absent.This work confirms that it is an efficient way to employ the QRS model in the single-atom response for precisely simulating the macroscopic vortex HHG.

A new method of calculating the orbital angular momentum spectra of Laguerre-Gaussian beams in channels with atmospheric turbulence

Studying orbital angular momentum（OAM） spectra is important for analyzing crosstalk in free-space optical（FSO）communication systems. This work offers a new method of simplifying the expressions for the OAM spectra of Laguerre-Gaussian（LG） beams under both weak/medium and strong atmospheric turbulences. We propose fixing the radius to the extreme point of the intensity distribution, review the expression for the OAM spectrum under weak/medium turbulence,derive the OAM spectrum expression for an LG beam under strong turbulence, and simplify both of them to concise forms.Then, we investigate the accuracy of the simplified expressions through simulations. We find that the simplified expressions permit accurate calculation of the OAM spectrum for large transmitted OAM numbers under any type of turbulence. Finally,we use the simplified expressions to analytically address the broadening of the OAM spectrum caused by atmospheric turbulence. This work should contribute to the concise theoretical derivation of analytical expressions for OAM channel matrices for FSO-OAM communications and the analytical study of the laws governing OAM spectra.

Free-space measurement-device-independent quantum-key-distribution protocol using decoy states with orbital angular momentum

In this paper, we propose a measurement-device-independent quantum-key-distribution（MDI-QKD） protocol using orbital angular momentum（OAM） in free space links, named the OAM-MDI-QKD protocol. In the proposed protocol,the OAM states of photons, instead of polarization states, are used as the information carriers to avoid the reference frame alignment, the decoy-state is adopted to overcome the security loophole caused by the weak coherent pulse source, and the high efficient OAM-sorter is adopted as the measurement tool for Charlie to obtain the output OAM state. Here, Charlie may be an untrusted third party. The results show that the authorized users, Alice and Bob, could distill a secret key with Charlie＇s successful measurements, and the key generation performance is slightly better than that of the polarization-based MDI-QKD protocol in the two-dimensional OAM cases. Simultaneously, Alice and Bob can reduce the number of flipping the bits in the secure key distillation. It is indicated that a higher key generation rate performance could be obtained by a high dimensional OAM-MDI-QKD protocol because of the unlimited degree of freedom on OAM states. Moreover,the results show that the key generation rate and the transmission distance will decrease as the growth of the strength of atmospheric turbulence（AT） and the link attenuation. In addition, the decoy states used in the proposed protocol can get a considerable good performance without the need for an ideal source.

Light beams with orbital angular momentum for free space optics

The light＇s orbital angular momentum （OAM） is a consequence of the spiral flow of the electromagnetic energy. In this paper, an analysis of light beams with OAM used for free space optics （FSO） is conducted. The basic description and conception of light＇s OAM are reviewed. Both encoding information into OAM states of single light beam and encoding information into spatial structure of the mixed optical vortex with OAM are discussed, and feasibility to improve the FSO＇s performance of security and obstruction of line of sight is examined.

Demonstration of orbital angular momentum channel healing using a Fabry‐Pérot cavity

Orbital angular momentum （OAM） mode division provides a promising solution to push past the already exhausted available degrees of freedom available in conventional optical communications. Nevertheless, the practical deploymentof OAM within a free-space optical （FSO） communications system is still hampered by a major challenge, namely that OAM-based FSO links are vulnerable to disturbances. Though several techniques, such as using various non-diffraction beams and multiple transmit–receive apertures, are proposed to alleviate the influence of disturbances, these techniquessignificantly reduce the performance with regard to combating single fading for spatial blockages of the laser beam byobstructions. In this work, we initially demonstrate that a Fabry-Pérot resonant cavity has the ability to implement OAM mode healing, even for a blocking percentage of over 50%. Consequently, the proposed method will expand the use ofOAM in the FSO secure communications and quantum encryption fields.

Scheme for generating 1 nm X-ray beams carrying orbital angular momentum at the SXFEL

Optical vortices have the main features of helical wavefronts and spiral phase structures,and carry orbital angular momentum.This special structure of visible light has been produced and studied for various applications.These notable characteristics of photons were also tested in the extreme-ultraviolet and X-ray regimes.In this article,we simulate the use of a simple afterburner configuration by directly adding helical undulators after the SASE undulators with the Shanghai Soft X-ray FEL to generate high intensity X-ray vortices with wavelengths^1 nm.Compared to other methods,this approach is easier to implement,cost-effective,and more efficient.

Terahertz Orbital Angular Momentum: Generation, Detection and Communication

To accommodate the ever-increasing wireless capacity,the terahertz(THz)orbital angular momentum(OAM)beam that combines THz radiation and OAM technologies has attracted much attention recently,with contributing efforts to explore new dimensions in the THz region.In this paper,we provide an overview of the generation and detection techniques of THz-OAM beams,as well as their applications in communications.The principle and research status of typical generation and detection methods are surveyed,and the advantages and disadvantages of each method are summarized from a viewpoint of wireless communication.It is shown that developing novel THz components in generating,detecting and(de)multiplexing THz-OAM beams has become the key engine to drive this direction forward.Anyway,beneficial from the combination of infinite orthogonal modes and large bandwidth,THz-OAM beams will have great potential in delivering very large capacity in next generation wireless communications.

Hybrid vector beams with non-uniform orbital angular momentum density induced by designed azimuthal polarization gradient

Based on angular amplitude modulation of orthogonal base vectors in common-path interference method, we propose an interesting type of hybrid vector beams with unprecedented azimuthal polarization gradient and demonstrate in experiment. Geometrically, the configured azimuthal polarization gradient is indicated by intriguing mapping tracks of angular polarization states on Poincaré sphere, more than just conventional circles for previously reported vector beams. Moreover, via tailoring relevant parameters, more special polarization mapping tracks can be handily achieved. More noteworthily, the designed azimuthal polarization gradients are found to be able to induce azimuthally non-uniform orbital angular momentum density, while generally uniform for circle-track cases, immersing in homogenous intensity background whatever base states are. These peculiar features may open alternative routes for new optical effects and applications.

Turbulence mitigation scheme based on multiple-user detection in an orbital-angular-momentum multiplexed system

Atmospheric turbulence（AT） induced crosstalk can significantly impair the performance of a free-space optical（FSO）communication link using orbital angular momentum（OAM） multiplexing.In this paper,we propose a multiple-user detection（MUD） turbulence mitigation scheme in an OAM-multiplexed FSO communication link.First,we present a MUD equivalent communication model for an OAM-multiplexed FSO communication link under AT.In the equivalent model,each input bit stream represents one user＇s information.The deformed OAM spatial modes caused by AT,instead of the pure OAM spatial modes,are used as information carriers,and the overlapping between the deformed OAM spatial modes are computed as the correlation coefficients between the users.Then,we present a turbulence mitigation scheme based on MUD idea to enhance AT tolerance of the OAM-multiplexed FSO communication link.In the proposed scheme,the crosstalk caused by AT is used as a useful component to deduce users＇ information.The numerical results show that the performance of the OAM-multiplexed communication link has greatly improved by the proposed scheme.When the turbulence strength C_n^2 is 1 × 10^（-15） m^（-2/3）,the transmission distance is 1000 m and the channel signal-to-noise ratio（SNR）is 26 dB,the bit-error-rate（BER） performance of four spatial multiplexed OAM modes l_m = ＋ 1,＋2,＋3,＋4 are all close to 10-5,and there is a 2-3 fold increase in the BER performance in comparison with those results without the proposed scheme.In addition,the proposed scheme is more effective for an OAM-multiplexed FSO communication link with a larger OAM mode topological charge interval.The proposed scheme is a promising direction for compensating the interference caused by AT in the OAM-multiplexed FSO communication link.

Design of Photonic Crystal Fiber Capable of Carrying Multiple Orbital Angular Momentum Modes Transmission

For the traditional photonic crystal fibers with circular air holes, rectangular air holes are added to the fiber cladding. The periodic arrangement of the inner rectangular air holes allows the fiber structure to better match the annular mode field distribution of the vortex beam. The fiber structure was analyzed and calculated by COMSOL Multiphysics 5.4 finite element software, and the characteristics of fiber were analyzed, such as the dispersion, confinement loss, effective mode area and nonlinear coefficient. The results reveal that the photonic crystal fiber structure capable of carrying 50 orbital angular momentum (OAM) modes at the wavelength of 1.15 to 2.0 μm (850 nm). The effective refractive index difference Δneff between vector modes can reach 1 × 10-3, and larger difference can effectively separate the vector modes and improve the transmission performance of OAM modes. Moreover, the fiber has good performance, such as flat dispersion distribution of the low-order modes, low confinement loss below 10-9 dB·m-1, large effective mode field area and small nonlinear coefficient in the 850 nm wavelength range. Therefore, this fiber structure can be applied to the high-capacity communication system of fiber multiplexing OAM. In addition, the good characteristics of this fiber structure are of great significance for the transmission of vortex beam in fiber.

Optical spin-to-orbital angular momentum conversion in structured optical fields

We investigate the dynamic quantities:momentum,spin and orbital angular momenta(SAM and OAM),and their conversion relationship in the structured optical fields at subwavelength scales,where the spin–orbit interaction(SOI)plays a key role and determines the behaviors of light.Specifically,we examine a nanostructure of a Ag nanoparticle(Ag NP)attached on a cylindrical Ag nanowire(Ag NW)under illumination of elliptically polarized light.These dynamic quantities obey the Noether theorem,i.e.,for the Ag nanoparticle with spherical symmetry,the total angular momentum consisting of SAM and OAM conserves;for the Ag NW with translational symmetry,the orbital momentum conserves.Meanwhile,the spin-to-orbital angular momentum conversion is mediated by SOI arising from the spatial variation of the optical potential.In this nanostructure,the conservation of momentum imposes a strict restriction on the propagation direction of the surface plasmon polaritons along the Ag NW.Meanwhile,the orbital momentum is determined by the polarized properties of the excitation light and the topography of the Ag NP.Our work offers insights to comprehend the light behaviors in the structured optical fields in terms of the dynamic quantities and benefits to the design of optical nano-devices based on interactions between spin and orbital degrees of freedom.

Controlling acoustic orbital angular momentum with artificial structures:From physics to application

Acoustic orbital angular momentum(OAM)associated with helicoidal wavefront recently attracts rapidly-growing attentions,offering a new degree of freedom for acoustic manipulation.Due to the unique dynamical behavior and inherent mode orthogonality of acoustic OAM,its harnessing is of fundamental interests for wave physics,with great potential in a plethora of applications.The recent advance in materials physics further boosts efforts into controlling OAM-carrying acoustic vortices,especially acoustic metasurfaces with planar profile and subwavelength thickness.Thanks to their un-conventional acoustic properties beyond attainable in the nature,acoustic artificial structures provide a powerful platform for new research paradigm for efficient generation and diverse manipulation of OAM in ways not possible before,enabling novel applications in diverse scenarios ranging from underwater communication to object manipulation.In this article,we present a comprehensive view of this emerging field by delineating the fundamental physics of OAM-metasurface interac-tion and recent advances in the generation,manipulation,and application of acoustic OAM based on artificial structures,followed by an outlook for promising future directions and potential practical applications.

Radiation pattern analyses of circular aperture antenna to generate radio orbital angular momentum

Circular aperture antenna recently has been regarded as a nature source to generate high power radio orbital angular momentum （OAM） in millimeter （mm） wave; however, the radiation pattern was not investigated. Theoretical derivation of radiation pattern of circular aperture OAM antenna is conducted to evaluate the performance. Extensive simulations verify the validity of the theoretical result. Furthermore, performance of such antenna excited by orthogonal TE and TM modes is compared, which shows the potential application for TEgl mode to create pure OAM g-1 mode in a practical system, providing guidance for generation of twisted radio waves in mm-wave bands.

Brightγ-ray source with large orbital angular momentum from the laser near-criticalplasma interaction

We propose a new laser-plasma-based method to generate brightγ-rays carrying large orbital angular momentum by interacting a circularly polarized Laguerre–Gaussian laser pulse with a near-critical hydrogen plasma conflned in an over-dense solid tube.In the flrst stage of the interaction,it is found via fully relativistic three-dimensional particle-in-cell simulations that high-energy helical electron beams with large orbital angular momentum are generated.In the second stage,this electron beam interacts with the laser pulse reflected from the plasma disc behind the solid tube,and helicalγbeams are generated with the same topological structure as the electron beams.The results show that the electrons receive angular momentum from the drive laser,which can be further transferred to theγphotons during the interaction.Theγbeam orbital angular momentum is strongly dependent on the laser topological charge l and laser intensity a_(0),which scales as L_(γ)∝a_(0)~4.A short(duration of 5 fs)isolated helicalγbeam with an angular momentum of-3.3×10^(-14)kg m~2 s^(-1)is generated using the Laguerre–Gaussian laser pulse with l=2.The peak brightness of the helicalγbeam reaches 1.22×10^(24)photons s^(-1)mm^(-2)mrad^(-2)per 0.1%BW(at 10 Me V),and the laser-to-γ-ray angular momentum conversion rate is approximately 2.1%.