Integrated coherent beam combining system for orbital-angular-momentum shift-keying-based free-space optical links

Orbital-angular-momentum(OAM)multiplexing technology offers a significant dimension to enlarge communication capacity in free-space optical links.The coherent beam combining(CBC)system can simultaneously realize OAM multiplexing and achieve high-power laser output,providing substantial advantages for long-distance communication.Herein,we present an integrated CBC system for freespace optical links based on OAM multiplexing and demultiplexing technologies for the first time,to the best of our knowledge.A method to achieve flexible OAM multiplexing and efficient demultiplexing based on the CBC system is proposed and demonstrated both theoretically and experimentally.The experimental results exhibit a low bit error rate of 0.47%and a high recognition precision of 98.58%throughout the entire data transmission process.By employing such an ingenious strategy,this work holds promising prospects for enriching ultra-long-distance structured light communication in the future.

Secure optical interconnects using orbital angular momentum beams multiplexing/multicasting

Orbital angular momentum(OAM),described by an azimuthal phase term expej lθT,has unbound orthogonal states with different topological charges l.Therefore,with the explosive growth of global communication capacity,especially for short-distance optical interconnects,light-carrying OAM has proved its great potential to improve transmission capacity and spectral efficiency in the space-division multiplexing system due to its orthogonality,security,and compatibility with other techniques.Meanwhile,100-m freespace optical interconnects become an alternative solution for the“last mile”problem and provide interbuilding communication.We experimentally demonstrate a 260-m secure optical interconnect using OAM multiplexing and 16-ary quadrature amplitude modulation(16-QAM)signals.We study the beam wandering,power fluctuation,channel cross talk,bit-error-rate performance,and link security.Additionally,we also investigate the link performance for 1-to-9 multicasting at the range of 260 m.Considering that the power distribution may be affected by atmospheric turbulence,we introduce an offline feedback process to make it flexibly controllable.

Dynamic properties of the magnetic skyrmion driven by electromagnetic waves with spin angular momentum and orbital angular momentum

We theoretically studied the dynamic properties of the skyrmion driven by electromagnetic(EM)waves with spin angular momentum(SAM)and orbital angular momentum(OAM)using micromagnetic simulations.First,the guiding centers of the skyrmion driven by EM waves with SAM,i.e.,left-handed and right-handed circularly polarized EM waves,present circular trajectories,while present elliptical trajectories under linear EM waves driving due to the superposition of oppositely polarized wave components.Second,the trajectories of the skyrmion driven by EM waves with OAM demonstrate similar behavior to that driven by linearly polarized EM waves.Because the wave vector intensity varies with the phase for both linearly polarized EM waves and EM waves with OAM,the angular momentum is transferred to the skyrmion non-uniformly,while the angular momentum is transferred to the skyrmion uniformly for left-handed and right-handed circularly polarized EM driving.Third,the dynamic properties of the skyrmion driven by EM waves with both SAM and OAM are investigated.It is found that the dynamic trajectories exhibit more complex behavior due to the contributions or competition of SAM and OAM.We investigate the characteristics of intrinsic gyration modes and frequency-dependent trajectories.Our research may provide insight into the dynamic properties of skyrmion manipulated by EM waves with SAM or OAM and provide a method for controlling skyrmion in spintronic devices.

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.

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.

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.

A Theoretical Analysis of the Acceleration and the Angular Momentum of the Universe

The loss of Baryonic Matter through Black Holes from our spatial 3-D Universe into its 4th dimension as Dark Matter, is used along with the Conservation of Angular Momentum Principle to prove theoretically the accelerated expansion of the 3-D Universe, as has already been confirmed experimentally being awarded the 2011 Nobel Prize in Physics. Theoretical calculations can estimate further to indicate the true nature of the acceleration;that the outward acceleration is due to the rotation of the Universe caused by Dark Energy from the Void, that the acceleration is non-linear, initially increasing from zero for the short period of about a Million years at a constant rate, and then leveling off non-linearly over extended time before the outward acceleration begins to decrease in a non-linear fashion until it is matched by the gravitational attraction of the matter content of 4D Space and the virtual matter in 3-D Vacuum Space. m = m(4D) + m(Virtual). The rotation of our 3D Universe will become constant once all 3D matter has entered 4D space. As the 3-D Universe tries to expand further it will be pulled inward by its gravitational attraction and will then keep on oscillating about a final radius rf while it also keeps on oscillating at right angles to the radius rf around final angular velocity ωf, until it becomes part of the 4-D Universe. The constant value of the Angular Momentum of our Universe is L = .

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.

Intrinsic Spin Angular Momentum of Electron Relation to the Discrete Indivisible Quantum of Time Kshana or Moment

The frequency of any periodic event can be defined in terms of units of Time. Planck constructed a unit of time called the Plank time from other physical constants. Vyasa defined a natural unit of time, kshana, or moment based on the motion of a fundamental particle. It is the time taken by an elementary particle, to change its direction from east to north. According to Vyasa, kshana is discrete, exceedingly small, indivisible, and is a constant time quantum. When the intrinsic spin angular momentum of an electron was related to the angular momentum of a simple thin circular plate, spherical shell, and solid sphere model of an electron, we found that the value of kshana in seconds was equal to ten to a power of minus twenty-one second. The disc model for the spinning electron provides an accurate value of the number of kshanas per second as determined previously and compared with other spinning models of electrons. These results indicate that the disk-like model of spinning electrons is the correct model for electrons. Vyasa’s definition of kshana opens the possibility of a new foundation for the theory of physical time, and perspectives in theoretical and philosophical research.

Achieving high-security and massive-capacity optical communications based on orbital angular momentum configured chaotic laser

Secure and high-speed optical communications are of primary focus in information transmission.Although it is widely accepted that chaotic secure communication can provide superior physical layer security,it is challenging to meet the demand for high-speed increasing communication rate.We theoretically propose and experimentally demonstrate a conceptual paradigm for orbital angular momentum(OAM)configured chaotic laser(OAM-CCL)that allows access to high-security and massivecapacity optical communications.Combining 11 OAM modes and an all-optical feedback chaotic laser,we are able to theoretically empower a well-defined optical communication system with a total transmission capacity of 100 Gb∕s and a bit error rate below the forward error correction threshold 3.8×10^(-3).Furthermore,the OAM-CCL-based communication system is robust to 3D misalignment by resorting to appropriate mode spacing and beam waist.Finally,the conceptual paradigm of the OAM-CCL-based communication system is verified.In contrast to existing systems(traditional free-space optical communication or chaotic optical communication),the OAM-CCL-based communication system has threein-one characteristics of high security,massive capacity,and robustness.The findings demonstrate that this will promote the applicable settings of chaotic laser and provide an alternative promising route to guide high-security and massive-capacity optical communications.

Azimuthal beam shaping in orbital angular momentum basis

Shaping the light beam is always essential for laser technology and its applications.Among the shaping technologies,shaping the laser in its Fourier domain is a widely used and effective method,such as a pulse shaper,or a 4f system with a phase mask or an iris in between.Orbital angular momentum(OAM)modes spectrum,the Fourier transform of the light field in azimuth,provides a perspective for shaping the light.Here,we propose and experimentally demonstrate a shaping strategy for the azimuthal field by modulating the complex amplitude of the OAM mode spectrum.The scheme utilizes multi-plane light conversion technology and consists only of a spatial light modulator and a mirror.Multiple functions,including beam rotating,beam splitting/combining in azimuth,and OAM mode filtering,are demonstrated.Our work provides a compact and programmable solution for modulating the OAM mode spectrum and shaping beams in azimuth.

Ultra-low-loss all-fiber orbital angular momentum mode-division multiplexer based on cascaded fused-biconical mode selective couplers

Mode-division multiplexers(MDMUXs)play a pivotal role in enabling the manipulation of an arbitrary optical state within few-mode fibers,offering extensive utility in the fields of mode-division multiplexing and structured optical field engineering.The exploration of MDMUXs employing cascaded resonant couplers has garnered significant attention owing to their scalability,exceptional integration capabilities,and the anticipated low insertion loss.In this work,we present the successful realization of high-quality orbital angular momentum MDMUX corresponding to topological charges 0,±1,and±2,achieved through the utilization of cascaded fused-biconical tapered couplers.Notably,the measured insertion losses at 1550 nm exhibit remarkable minimal values:0.31,0.10,and 0.64 dB,respectively.Furthermore,the 80%efficiency bandwidths exceed 106,174,and 174 nm for these respective modes.The MDMUX is composed of precisionmanufactured high-quality mode selective couplers(MSCs).Utilizing a proposed supermode propagation method based on mode composition analysis,we precisely describe the operational characteristics of MSCs.Building upon this comprehensive understanding,we embark on a pioneering analysis elucidating the influence of MSC cascading order on the performance of MDMUXs.Our theoretical investigation substantiates that when constructing MDMUXs,MSCs should adhere to a specific cascading sequence.

Multidimensional multiplexing holography based on optical orbital angular momentum lattice multiplexing

The use of orbital angular momentum(OAM)as an independent dimension for information encryption has garnered considerable attention.However,the multiplexing capacity of OAM is limited,and there is a need for additional dimensions to enhance storage capabilities.We propose and implement orbital angular momentum lattice(OAML)multiplexed holography.The vortex lattice(VL)beam comprises three adjustable parameters:the rotation angle of the VL,the angle between the wave normal and the z axis,which determines the VL’s dimensions,and the topological charge.Both the rotation angle and the VL’s dimensions serve as supplementary encrypted dimensions,contributing azimuthally and radially,respectively.We investigate the mode selectivity of OAML and focus on the aforementioned parameters.Through experimental validation,we demonstrate the practical feasibility of OAML multiplexed holography across multiple dimensions.This groundbreaking development reveals new possibilities for the advancement of practical information encryption systems.

Solar System. Angular Momentum. Dark Matter Reactors

The developed Hypersphere World-Universe Model (WUM) is consistent with all Concepts of the World [1]. In WUM, we postulate the principal role of Angular Momentum and Dark Matter in Cosmological theories of the World. The most widely accepted model of Solar System formation, known as the Nebular hypothesis, does not solve the Angular Momentum problem—why is the orbital momentum of Jupiter larger than rotational momentum of the Sun? WUM is the only cosmological model in existence that is consistent with this Fundamental Law. The Nebular hypothesis does not solve Internal Heating and Diversity problems for all Planets and Moons in Solar system—why the actual mean surface temperature of them is higher than their effective temperature calculated based on the Sun’s heat for them and how could each one be so different if all of them came from the same nebula? The proposed concept of Dark Matter Reactors in Cores of all gravitationally-rounded Macroobjects successfully resolves these problems.

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.

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.

Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

We study quantum classical correspondence in terms of the coherent wave functions of a charged particle in two-dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than h is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 27r-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.

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.