Twisted light transmission over 143 km

Spatiotemporal optical vortices with controllable radial and azimuthal quantum numbers

Optical spatiotemporal vortices with transverse photon orbital angular momentum (OAM) have recently become a focal point of research. In this work we theoretically and experimentally investigate optical spatiotemporal vortices with radial and azimuthal quantum numbers, known as spatiotemporal Laguerre-Gaussian (STLG) wavepackets. These 3D wavepackets exhibit phase singularities and cylinder-shaped edge dislocations, resulting in a multi-ring topology in its spatiotemporal profile. Unlike conventional ST optical vortices, STLG wavepackets with non-zero p and l values carry a composite transverse OAM consisting of two directionally opposite components. We further demonstrate mode conversion between an STLG wavepacket and an ST Hermite-Gaussian (STHG) wavepacket through the application of strong spatiotemporal astigmatism. The converted STHG wavepacket is de-coupled in intensity in space-time domain that can be utilized to implement the efficient and accurate recognition of ultrafast STLG wavepackets carried various p and l . This study may offer new insights into high-dimensional quantum information, photonic topology, and nonlinear optics, while promising potential applications in other wave phenomena such as acoustics and electron waves.

Machine learning-based classification of structured light modes under turbulence and eavesdropping effects

This paper considers the classification of multiplexed structured light modes, aiming to bolster communication reliability and data transfer rates, particularly in challenging scenarios marked by turbulence and potential eavesdropping. An experimental free-space optic (FSO) system is established to transmit 16 modes [8-ary Laguerre Gaussian (LG) and 8-ary superposition LG (Mux-LG) mode patterns] over a 3-m FSO channel, accounting for interception threats and turbulence effects. To the best of authors' knowledge, this paper is the first to consider both factors concurrently. We propose four machine/deep learning algorithms-artificial neural network, support vector machine, 1D convolutional neural network, and 2D convolutional neural network-for classification purposes. By fusing the outputs of these methods, we achieve promising classification results exceeding 92%, 81%, and 69% in cases of weak, moderate, and strong turbulence, respectively. Structured light modes exhibit significant potential for a variety of real-world applications where reliable and high-capacity data transmission is crucial.

Ultrafast all-optical second harmonic wavefront shaping

Optical communication can be revolutionized by encoding data into the orbital angular momentum of light beams. However, state-of-the-art approaches for dynamic control of complex optical wavefronts are mainly based on liquid crystal spatial light modulators or miniaturized mirrors, which suffer from intrinsically slow (µs-ms) response times. Here, we experimentally realize a hybrid meta-optical system that enables complex control of the wavefront of light with pulse-duration limited dynamics. Specifically, by combining ultrafast polarization switching in a WSe2 monolayer with a dielectric metasurface, we demonstrate second harmonic beam deflection and structuring of orbital angular momentum on the femtosecond timescale. Our results pave the way to robust encoding of information for free space optical links, while reaching response times compatible with real-world telecom applications.

Fundamental probing limit on the high-order orbital angular momentum of light

The orbital angular momentum (OAM) of light, possessing an infinite-dimensional degree of freedom, holds significant potential to enhance the capacity of optical communication and information processing in both classical and quantum regimes. Despite various methods developed to accurately measure OAM modes, the probing limit of the highest-order OAM remains an open question. Here, we report an accurate recognition of superhigh-order OAM using a convolutional neural network approach with an improved ResNeXt architecture, based on conjugated interference patterns. A type of hybrid beam carrying double OAM modes is utilized to provide more controllable degrees of freedom for greater recognition of the OAM modes. Our contribution advances the OAM recognition limit from manual counting to machine learning. Results demonstrate that, within our optical system, the maximum recognizable OAM modes exceed l = ±690 with an accuracy surpassing 99.93%, the highest achieved by spatial light modulator to date. Enlarging the active area of the CCD sensor extends the number of recognizable OAM modes to 1300, constrained only by the CCD resolution limit. Additionally, we explore the identification of fractional high-order OAM modes with a resolution of 0.1 from l = ±600.0 to l = ±600.9, achieving a high accuracy of 97.86%.

Universal Crosstalk of Twisted Light in Random Media

Structured light offers wider bandwidths and higher security for communication. However, propagation through complex random media, such as the Earth's atmosphere, typically induces intermodal crosstalk. We show numerically and experimentally that coupling of photonic orbital angular momentum modes is governed by a universal function of a single parameter: the ratio between the random medium's and the beam's transverse correlation lengths, even in the regime of pronounced intensity fluctuations.

Topological charge identification of superimposed orbital angular momentum beams under turbulence using an attention mechanism

Due to the unique features, orbital angular momentum (OAM) beams have been widely explored for different applications. Accurate determination of the topological charge (TC) of these beams is crucial for their optimal utilization. In this paper, we propose a method that combines adaptive image processing techniques with a simple, parameter-free attention module (SimAM) based convolutional neural network to accurately identify the TC of high-order superimposed OAM beams. Experimental results demonstrate that under the combined influence of non-extreme light intensity and turbulence, it can achieve >95% identification accuracy of TCs ranging from ±1 to ±40. Moreover, even under partial-pattern-missing conditions, our method maintains an accuracy rate of over 80%. Compared with traditional attention mechanisms, SimAM does not require additional network design, significantly reducing the computational costs. Our approach showcases remarkable efficiency, robustness, and cost-effectiveness, making it adaptable to challenging factors such as non-uniform lighting and partially occluded light paths. This research provides a new direction for recognizing OAM modes with valuable implications for the future of communication systems.

High-order orbital angular momentum mode-based phase shift-keying communication using phase difference modulation

Orbital angular momentum (OAM) mode offers a promising modulation dimension for high-order shift-keying (SK) communication due to its mode orthogonality. However, the expansion of modulation order through superposing OAM modes is constrained by the mode-field mismatch resulting from the rapidly increased divergence with mode orders. Herein, we address this problem by propose a phase-difference modulation strategy that breaks the limitation of modulation orders via introducing a phase-difference degree of freedom (DoF) beyond OAM modes. Phase-difference modulation exploits the sensitivity of mode interference to phase differences, thereby providing distinct tunable parameters. This enables the generation of a series of codable spatial modes with continuous variation within the same superposed OAM modes by manipulating the interference state. Due to the inherent independence between OAM mode and phase-difference DoF, the number of codable modes increases exponentially, which facilitates establishing ultra-high-order phase shift-keying by discretizing the continuous phase difference and establishing a one-to-one mapping between coding symbols and constructed modes. We show that a phase shift-keying communication link with a modulation order of up to 4 × 104 is achieved by employing only 3 OAM modes (+1, + 2 and +3), and the decode accuracy reaches 99.9%. Since the modulation order is exponentially correlated with the OAM modes and phase differences, the order can be greatly improved by further increasing the superimposed OAM modes, which may provide new insight for high-order OAM-based SK communication.

Significance of the longitudinal component of paraxial light in position-dependent selection rules for quadrupole atomic transitions

It is well established that the longitudinal component of paraxial optical vortices has a key role in specific atomic quadrupole transitions near the beam axis when the spin and orbital angular momenta are antiparallel. By deriving analytical expressions for the position-dependent selection rules, this work shows that the significant role of the longitudinal fields is not limited to this case, but rather is a more general feature for any paraxial light including, for example, optical vortices with parallel spin and orbital angular momenta as well as Guassian beams. Numerically, the transition strengths induced by the weaker longitudinal component can be twice as high as those by the stronger transverse component. We also show that there are transitions that can be induced exclusively by the longitudinal component for light carrying two quanta of orbital angular momentum.

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.

Vision transformers motivating superior OAM mode recognition in optical communications

Orbital angular momentum (OAM) has recently obtained tremendous research interest in free-space optical communications (FSO). During signal transmission within the free-space link, atmospheric turbulence (AT) poses a significant challenge as it diminishes the signal strength and introduce intermodal crosstalk, significantly reducing OAM mode detection accuracy. This issue directly impacts the performance of OAM-based communication systems and leads to a reduction in received information. To address this critical bottleneck of low mode recognition accuracy in OAM-based FSO-communications, a deep learning method based on vision transformers (ViT) is proposed for what we believe is for the first time. Designed carefully by numerous experts, the advanced self-attention mechanism of ViT captures more global information from the input image. To train the model, pretraining on a large dataset, named IMAGENET is conducted. Subsequently, we performed fine-tuning on our specific dataset, consisting of OAM beams that have undergone varying AT strengths. The computer simulation shows that based on ViT method, the multiple OAM modes can be recognized with a high accuracy (nearly 100%) under weak-to-moderate turbulence and with almost 98% accuracy even under long transmission distance with strong turbulence (C N2=1×10-14). Our findings highlight that leveraging ViT enables robust detection of complex OAM beams, mitigating the adverse effects caused by atmospheric turbulence.

An Efficient Recognition Method for Orbital Angular Momentum via Adaptive Deep ELM

For orbital angular momentum (OAM) recognition in atmosphere turbulence, how to design a self-adapted model is a challenging problem. To address this issue, an efficient deep learning framework that uses a derived extreme learning machine (ELM) has been put forward. Different from typical neural network methods, the provided analytical machine learning model can match the different OAM modes automatically. In the model selection phase, a multilayer ELM is adopted to quantify the laser spot characteristics. In the parameter optimization phase, a fast iterative shrinkage-thresholding algorithm makes the model present the analytic expression. After the feature extraction of the received intensity distributions, the proposed method develops a relationship between laser spot and OAM mode, thus building the steady neural network architecture for the new received vortex beam. The whole recognition process avoids the trial and error caused by user intervention, which makes the model suitable for a time-varying atmospheric environment. Numerical simulations are conducted on different experimental datasets. The results demonstrate that the proposed method has a better capacity for OAM recognition.

Generation of integer and fractional vortex beams based on liquid crystal electronically reconfigurable spiral phase plates

The manufacturing and characterization of a large-size 72-electrode liquid crystal-based reconfigurable spiral phase plate (SPP) is presented. The SPP is addressed by a custom-made driver with 72 independent channels, which allows for the generation of any arbitrary integer or fractional optical vortex beam with topological charges ranging from -24 to +24. The 25 mm diameter device is fabricated using direct laser writing, leading to a fill factor over 99%. The device performance and flexibility exceed previous transparent reconfigurable SPP in terms of size, tuning range, and fill factor. The device and the light path have been simulated using the angular spectrum propagation method, showing excellent correspondence.

Hybrid channel coding for OAM division multiplexing free space optical communication systems

An orbital angular momentum division multiplexing free space optical communication (OAM-DM FSO) system with channel coding can compensate atmospheric channel fading and improve system performance. An OAM-DM FSO system based on hybrid channel coding is proposed in this paper. The coding gain is improved by taking into account mode dependent channel fading difference caused by atmospheric turbulence. Simulation results show that compared with single channel coding, the coding gain is increased by 1.85 dB under Cn2=1E-14, BER=1E-5 with non-uniform LDPC code (0.7 code rate) for an OAM1/OAM3 multiplexing system. In addition, for four OAM modes (+1,+3,+5,+7) multiplexing systems, the coding gain is increased by more than 3.8 dB under Cn2=1E-14 and BER=1E-5.

Spatial multiplexing for robust optical vortex transmission with optical nonlinearity

Optical vortex beams, with phase singularity characterized by a topological charge (TC), introduces a new dimension for optical communication, quantum information, and optical light manipulation. However, the evaluation of TCs after beam propagation remains a substantial challenge, impeding practical applications. Here, we introduce vortices in lateral arrays (VOILA), a novel spatial multiplexing approach that enables simultaneous transmission of a lateral array of multiple vortices. Leveraging advanced learning techniques, VOILA effectively decodes TCs, even in the presence of strong optical nonlinearities simulated experimentally. Notably, our approach achieves substantial improvements in single-shot bandwidth, surpassing single-vortex scheme by several orders of magnitude. Furthermore, our system exhibits precise fractional TC recognition in both linear and nonlinear regimes, providing possibilities for high-bandwidth communication. The capabilities of VOILA promise transformative contributions to optical information processing and structured light research, with significant potential for advancements in diverse fields.

Same Wavelength Noise Filtering via Quantum Orbital Angular Momentum Emission

In laser active detection, detection performance is affected by optical noise, laser interference, and environmental background interference. Conventional methods to filter optical noise take advantage of the differences between signal and noise in wavelength and polarization. Due to the limitations of traditional methods in the physical dimension, noise cannot be completely filtered out. In this manuscript, a new method of noise filtering based on the spatial distribution difference between the quantum orbital angular momentum beam and the background noise is proposed. The use of beams containing quantum orbital angular momentum can make the signal light have a new physical dimension and enrich the information of emitted light. We conduct a complete theoretical analysis and provide a proof-of-principle experiment. The experimental results are in good agreement with the theoretical analysis results, and there is a signal-to-noise ratio improvement of more than five times in laser active detection. Our method meets the urgent needs of laser active detection and can be applied in the field of high-quality target detection.

Speckle-based structured light shift-keying for non-line-of-sight optical communication

We report an experimental proof of concept for speckle-based one-to-three non-line-of-sight (NLOS) free space optical (FSO) communication channels employing structured light shift-keying. A 3-bit gray image of resolution 100×100 pixels is encoded in Laguerre-Gaussian or Hermite-Gaussian beams and decoded using their respective intensity speckle patterns via trained 1D convolutional neural network. We have achieved an average classification accuracy of 96% and 93% using L G ml and H G pq beams, respectively, among all three channels. It demonstrates the directional independence and broadcasting capability of speckle-based decoding (SBD) in FSO communication using structured light. Further, we have extended the study from 2D to 1D SBD in one-to-three NLOS FSO communication channels to decrease the computational cost and to emphasize the importance of the 1D SBD approach.

Propagation of coherence-OAM matrix of an optical beam in vacuum and turbulence

Propagation of the coherence-orbital angular momentum (COAM) matrix of partially coherent beams in homogeneous and isotropic turbulence, e.g., atmosphere, is formulated using the extended Huygens-Fresnel principle. It is found that under the effect of turbulence the elements in the COAM matrix will generally be affected by other elements, resulting in certain OAM mode dispersion. We show that if turbulence is homogeneous and isotropic, there exists an analytic "selection rule" for governing such a dispersion mechanism, which states that only the elements having the same index difference, say l - m, may interact with each other, where l and m denote OAM mode indices. Further, we develop a wave-optics simulation method incorporating modal representation of random beams, multi-phase screen method and the coordinate transformation to simulate propagation of the COAM matrix of any partially coherent beam propagating in free space or in turbulent medium. The simulation method is thoroughly discussed. As examples, the propagation characteristics of the most representative COAM matrix elements of circular and elliptical Gaussian Schell-model beams in free space and in turbulent atmosphere are studied, and the selection rule is numerically demonstrated.

Radial-mode sensitive probe beam in the rotational Doppler effect

The rotational Doppler effect (RDE) attracts much attention in various research areas, from acoustics to optics. The observation of RDE mostly depends on the orbital angular momentum of the probe beam, while the impression of radial mode is ambiguous. To clarify the role of radial modes in RDE detection, we reveal the mechanism of interaction between probe beams and rotating objects based on complete Laguerre-Gaussian (LG) modes. It is theoretically and experimentally proved that radial LG modes play a crucial role in RDE observation because of topological spectroscopic orthogonality between probe beams and objects. We enhance the probe beam by employing multiple radial LG modes, which makes the RDE detection sensitive to objects containing complicated radial structures. In addition, a specific method to estimate the efficiency of various probe beams is proposed. This work has the potential to modify RDE detection method and take the related applications to a new platform.

Fragmental optical vortex for the detection of rotating object based on the rotational Doppler effect

Rotational Doppler effect (RDE), as a counterpart of the conventional linear Doppler effect in the rotating frame, has attracted increasing attention in recent years on rotational object detection. Many previous works have investigated the RDE based on the whole optical vortex field. In this work, we report on the RDE of the partially obstructed optical vortex and the corresponding rotational speed extraction method. Based on the orbital angular momentum (OAM) mode analysis theory, we establish the relationship between the OAM spectrum and the RDE frequency shift of fragmental optical vortex (FOV). The mechanism of the rotational speed extraction is analysed and validated by the numerical simulation and experiments. Further, a dual Fourier transformation method is proposed to accurately obtain the rotational speed which successfully overcomes the problem of the discrete distribution of the RDE signals. Our work may be useful for practical remote sensing based on the optical RDE metrology.

Deep-learning-assisted communication capacity enhancement by non-orthogonal state recognition of structured light

In light of pending capacity crunch in information era, orbital-angular-momenta-carrying vortex beams are gaining traction thanks to enlarged transmission capability. However, high-order beams are confronted with fundamental limits of nontrivial divergence or distortion, which consequently intensifies research on new optical states like low-order fractional vortex beams. Here, we experimentally demonstrate an alternative mean to increase the capacity by simultaneously utilizing multiple non-orthogonal states of structured light, challenging a prevailing view of using orthogonal states as information carriers. Specifically, six categories of beams are jointly recognized with accuracy of >99% by harnessing an adapted deep neural network, thus providing the targeted wide bandwidth. We then manifest the efficiency by sending/receiving a grayscale image in 256-ary mode encoding and shift keying schemes, respectively. Moreover, the well-trained model is able to realize high fidelity recognition (accuracy >0.8) onto structured beams under unknown turbulence and restricted receiver aperture size. To gain insights of the framework, we further interpret the network by revealing the contributions of intensity signals from different positions. This work holds potential in intelligence-assisted large-capacity and secure communications, meeting ever growing demand of daily information bandwidth.

Integrated orbital angular momentum mode sorters on vortex fibers

We design, fabricate, and characterize integrated mode sorters for multimode fibers that guide well-separated vortex modes. We use 3D direct laser printing to print a collimator and a Cartesian to a log-polar mode transformer on the tip of the fiber. This polarization insensitive device can send different modes into different exit angles and is therefore useful for space division multiplexed optical communication. Two types of fibers with two corresponding sorters are used, enabling the sorting of either four or eight different modes in a compact and robust manner. The integration of the vortex fiber and multiplexer opens the door for widespread exploitation of orbital angular momentum (OAM) for data multiplexing in fiber networks.

Towards higher-dimensional structured light

Structured light refers to the arbitrarily tailoring of optical fields in all their degrees of freedom (DoFs), from spatial to temporal. Although orbital angular momentum (OAM) is perhaps the most topical example, and celebrating 30 years since its connection to the spatial structure of light, control over other DoFs is slowly gaining traction, promising access to higher-dimensional forms of structured light. Nevertheless, harnessing these new DoFs in quantum and classical states remains challenging, with the toolkit still in its infancy. In this perspective, we discuss methods, challenges, and opportunities for the creation, detection, and control of multiple DoFs for higher-dimensional structured light. We present a roadmap for future development trends, from fundamental research to applications, concentrating on the potential for larger-capacity, higher-security information processing and communication, and beyond.

Divergence-degenerate spatial multiplexing towards future ultrahigh capacity, low error-rate optical communications

Spatial mode (de)multiplexing of orbital angular momentum (OAM) beams is a promising solution to address future bandwidth issues, but the rapidly increasing divergence with the mode order severely limits the practically addressable number of OAM modes. Here we present a set of multi-vortex geometric beams (MVGBs) as high-dimensional information carriers for free-space optical communication, by virtue of three independent degrees of freedom (DoFs) including central OAM, sub-beam OAM, and coherent-state phase. The novel modal basis set has high divergence degeneracy, and highly consistent propagation behaviors among all spatial modes, capable of increasing the addressable spatial channels by two orders of magnitude than OAM basis as predicted. We experimentally realize the tri-DoF MVGB mode (de)multiplexing and data transmission by the conjugated modulation method, demonstrating lower error rates caused by center offset and coherent background noise, compared with OAM basis. Our work provides a potentially useful basis for the next generation of large-scale dense data communication.

Towards fine recognition of orbital angular momentum modes through smoke

Light beams carrying orbital angular momentum (OAM) have been constantly developing in free-space optical (FSO) communications. However, perturbations in the free space link, such as rain, fog, and atmospheric turbulence, may affect the transmission efficiency of this technique. If the FSO communications procedure takes place in a smoke condition with low visibility, the communication efficiency also will be worse. Here, we use deep learning methods to recognize OAM eigenstates and superposition states in a thick smoke condition. In a smoke transmission link with visibility about 5 m to 6 m, the experimental recognition accuracy reaches 99.73% and 99.21% for OAM eigenstates and superposition states whose Bures distance is 0.05. Two 6 bit/pixel pictures were also successfully transmitted in the extreme smoke conditions. This work offers a robust and generalized proposal for FSO communications based on OAM modes and allows an increase of the communication capacity under the low visibility smoke conditions.

Speckle-based deep learning approach for classification of orbital angular momentum modes

We present a speckle-based deep learning approach for orbital angular momentum (OAM) mode classification. In this method, we have simulated the speckle fields of the Laguerre-Gauss (LG), Hermite-Gauss (HG), and superposition modes by multiplying these modes with a random phase function and then taking the Fourier transform. The intensity images of these speckle fields are fed to a convolutional neural network (CNN) for training a classification model that classifies modes with an accuracy >99%. We have trained and tested our method against the influence of atmospheric turbulence by training the models with perturbed LG, HG, and superposition modes and found that models are still able to classify modes with an accuracy >98%. We have also trained and tested our model with experimental speckle images of LG modes generated by three different ground glasses. We have achieved a maximum accuracy of 96% for the most robust case, where the model is trained with all simulated and experimental data. The novelty of the technique is that one can do the mode classification just by using a small portion of the speckle fields because speckle grains contain the information about the original mode, thus eliminating the need for capturing the whole modal field, which is modal dependent.

Shaping the topology of light with a moving Rabi-oscillating vortex

Quantum vortices are the analogue of classical vortices in optics, Bose-Einstein condensates, superfluids and superconductors, where they provide the elementary mode of rotation and orbital angular momentum. While they mediate important pair interactions and phase transitions in nonlinear fluids, their linear dynamics is useful for the shaping of complex light, as well as for topological entities in multi-component systems, such as full Bloch beams. Here, setting a quantum vortex into directional motion in an open-dissipative fluid of microcavity polaritons, we observe the self-splitting of the packet, leading to the trembling movement of its center of mass, whereas the vortex core undergoes ultrafast spiraling along diverging and converging circles, in a sub-picosecond precessing fashion. This singular dynamics is accompanied by vortex-antivortex pair creation and annihilation and a periodically changing topological charge. The spiraling and branching mechanics represent a direct manifestation of the underlying Bloch pseudospin space, whose mapping is shown to be rotating and splitting itself. Its reshaping is due to three simultaneous drives along the distinct directions of momentum and complex frequency, by means of the differential group velocities, Rabi frequency and dissipation rates, which are natural assets in coupled fields such as polaritons. This state, displaying linear momentum dressed with oscillating angular momentum, confirms the richness of multi-component and open quantum fluids and their innate potentiality to implement sophisticated and dynamical topological textures of light.

Phase correlation arc and universal decay of entangled orbital angular momentum qubit states in atmospheric turbulence

In this study, we introduce the phase correlation arc of an orbital angular momentum (OAM) beam to investigate the evolution of OAM entanglement. We reveal that the entanglement decay of all OAM states of Laguerre-Gaussian modes in atmospheric turbulence is universal via both numerical predictions and experimental data. A similar evolution law is also theoretically confirmed to exist in Bessel-Gaussian modes. Finally, by using the phase correlation arc, the precise formula of the decay distance dependence on the OAM number is derived, and it exhibits excellent agreement with previous experimental conclusions.

Multidimensional phase singularities in nanophotonics

[Figure: see text].

Capacity of the Weakly Absorbent Turbulent Ocean Channel with the Coaxial Double-Position Power Gaussian Vortex

Turbulence and absorption of seawater are two important factors affecting the signal transmission quality of underwater optical communication link. Here, we study the channel capacity and bit error rate of an underwater extinction communication link with a coaxial double-position power Gaussian vortex carrier based on Rytov approximation theory. The study finds that channel capacity and bit error rate are the nonlinear functions of the dimensionless structural parameter and reach maximum and minimum values at |α| = 1, respectively. The seawater absorption has a great influence on the channel capacity but not bit error rate. The communication link with large receiving aperture, small transmitting beam diameter, long wavelength of light source in a seawater window, and more OAM channels has high channel capacity.

Laser Beam Positioning by Using a Broken-Down Optical Vortex Marker

We propose the use of high-order optical vortices as markers in the positioning of a laser beam. The broken optical vortices are arranged in constellations. The center of gravity of these constellations makes it possible to position the beam carrying information encoded in the optical vortices. This paper describes three positioning methods using both intensity and phase maps. The methods described were tested in experiments performed in a laboratory and an open space.

Non-zero dispersion-shifted ring fiber for the orbital angular momentum mode

As the dimension of orbital angular momentum (OAM) is orthogonal to the other degrees of freedom for photon, such as wavelength, it can be utilized to further increase data capacity in the wavelength division multiplexing (WDM) systems. However, the non-zero dispersion-shifted fiber (NZDSF) for the OAM mode has not yet been investigated or even proposed. In this work, we propose and design a ring fiber with low chromatic dispersion for the HE_2,1 mode, which can serve as NZDSF for its corresponding OAM_1,1 mode. A low dispersion of 3.3 ps/(nm·km) at 1550 nm and <2.9 ps/(nm·km) dispersion variation from 1530 to 1565 nm for the OAM_1,1 mode is achieved in simulation, which satisfies the standard of the ITU-T G.655.C. The designed fiber with ring width from 1.5 µm to 3.5 µm can support the OAM_1,1 mode within the C-band, and a large effective area of about 646 µm² is obtained. We also note that the fiber with larger inner radius and ring width are more tolerant to the perturbations, such as fiber ellipticity and bending. In the fiber-based optical communication systems, the designed ring fiber could be used as a candidate for supporting OAM modes with low dispersion and reduced nonlinear effects.

768-ary Laguerre-Gaussian-mode shift keying free-space optical communication based on convolutional neural networks

Beyond orbital angular momentum of Laguerre-Gaussian (LG) modes, the radial index can also be exploited as information channel in free-space optical (FSO) communication to extend the communication capacity, resulting in the LG- shift keying (LG-SK) FSO communications. However, the recognition of radial index is critical and tough when the superposed high-order LG modes are disturbed by the atmospheric turbulences (ATs). In this paper, the convolutional neural network (CNN) is utilized to recognize both the azimuthal and radial index of superposed LG modes. We experimentally demonstrate the application of CNN model in a 10-meter 768-ary LG-SK FSO communication system at the AT of Cn2 = 1e-14 m^-2/3. Based on the high recognition accuracy of the CNN model (>95%) in the scheme, a colorful image can be transmitted and the peak signal-to-noise ratio of the received image can exceed 35 dB. We anticipate that our results can stimulate further researches on the utilization of the potential applications of LG modes with non-zero radial index based on the artificial-intelligence-enhanced optoelectronic systems.

Fractional Angular Momenta, Gouy and Berry Phases in Relativistic Bateman-Hillion-Gaussian Beams of Electrons

A new Bateman-Hillion solution to the Dirac equation for a relativistic Gaussian electron beam taking explicit account of the four-position of the beam waist is presented. This solution has a pure Gaussian form in the paraxial limit but beyond it contains higher order Laguerre-Gaussian components attributable to the tighter focusing. One implication of the mixed mode nature of strongly diffracting beams is that the expectation values for spin and orbital angular momenta are fractional and are interrelated to each other by intrinsic spin-orbit coupling. Our results for these properties align with earlier work on Bessel beams [Bliokh et al., Phys. Rev. Lett. 107, 174802 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.174802] and show that fractional angular momenta can be expressed by means of a Berry phase. The most significant difference arises, though, due to the fact that Laguerre-Gaussian beams naturally contain Gouy phase, while Bessel beams do not. We show that Gouy phase is also related to Berry phase and that Gouy phase fronts that are flat in the paraxial limit become curved beyond it.

Bright solid-state sources for single photons with orbital angular momentum

Photons that have a helical phase front, that is, twisted photons, can carry a discrete, in principle, unlimited, but quantized amount of orbital angular momentum (OAM). Hence, twisted single photons constitute a high-dimensional quantum system with information-processing abilities beyond those of two-level single-photon qubits. To date, the generation of single photons carrying OAM has relied on a non-linear process in bulk crystals, for example, spontaneous parametric down-conversion, which limits both the efficiency and the scalability of the source. Here, we present a bright solid-state source of single photons in an OAM superposition state with a single-photon purity of g⁽²⁾(0) = 0.115(1) and a collection efficiency of 23(4)%. The mode purity of the single-photon OAM states is further examined via projection measurements. Future developments of integrated quantum photonic devices with pure OAM states as an additional degree of freedom may enable high-dimensional quantum information processing.

Classical characterization of quantum waves: comparison between the caustic and the zeros of the Madelung-Bohm potential

From a geometric perspective, the caustic is the most classical description of a wave function since its evolution is governed by the Hamilton-Jacobi equation. On the other hand, according to the Madelung-de Broglie-Bohm equations, the most classical description of a solution to the Schrödinger equation is given by the zeros of the Madelung-Bohm potential. In this work, we compare these descriptions, and, by analyzing how the rays are organized over the caustic, we find that the wave functions with fold caustic are the most classical beams because the zeros of the Madelung-Bohm potential coincide with the caustic. For another type of beam, the Madelung-Bohm potential is in general distinct to zero over the caustic. We have verified these results for the one-dimensional Airy and Pearcey beams, which, according to the catastrophe theory, have stable caustics. Similarly, we introduce the optical Madelung-Bohm potential, and we show that if the optical beam has a caustic of the fold type, then its zeros coincide with the caustic. We have verified this fact for the Bessel beams of nonzero order. Finally, we remark that for certain cases, the zeros of the Madelung-Bohm potential are linked with the superoscillation phenomenon.

Entanglement protection of Ince-Gauss modes in atmospheric turbulence using adaptive optics

In this paper, we describe the study of the faithful propagation of entangled orbital angular momentum states of light under atmospheric turbulence. The spatial mode is encoded in the Ince-Gauss modes that constitute a complete family of exact and orthogonal solutions of the paraxial wave equation in an elliptic coordinate system. Adaptive optics is employed to protect the entanglement from degradation, in which the threshold of turbulence strength could be enhanced for a reliable entanglement distribution. We find that the evolution of entanglements relies on ellipticity and shows the opposite trend when adopting adaptive optics. The turbulence strengths, at which the concurrences of various entangled states become zero, are different without adaptive optics but almost the same with adaptive optics. The trace of the density matrix is independent of the different ellipticity with or without adaptive optics. We believe that this investigation is useful for long-distance quantum communications and quantum networks using orbital angular momentum as information carriers.

Propagation of structured light through tissue-mimicking phantoms

Optical interrogation of tissues is broadly considered in biomedical applications. Nevertheless, light scattering by tissue limits the resolution and accuracy achieved when investigating sub-surface tissue features. Light carrying optical angular momentum or complex polarization profiles, offers different propagation characteristics through scattering media compared to light with unstructured beam profiles. Here we discuss the behaviour of structured light scattered by tissue-mimicking phantoms. We study the spatial and the polarization profile of the scattered modes as a function of a range of optical parameters of the phantoms, with varying scattering and absorption coefficients and of different lengths. These results show the non-trivial trade-off between the advantages of structured light profiles and mode broadening, stimulating further investigations in this direction.

Two-step system for image receiving in OAM-SK-FSO link

Turbulence resistance is a significant research area for orbital angular momentum shift keying-based free space optical communication (OAM-SK-FSO). We put forward a two-step combinational system to receive high fidelity image data from the atmospheric turbulence (AT) channels. Firstly, the AT-detector-based multi-CNN (ATDM-CNN) demodulator is proposed which is very different from the traditional single-CNN (S-CNN) demodulator. The AT detector detects the AT strength and then an AT-determined CNN-based demodulator is activated to recognize the incident OAM modes. Sufficient numeral simulations compare the recognition rates of ATDM-CNN and S-CNN. The results indicate a tremendous improvement owing to the ATDM-CNN demodulator. Base on the ATDM-CNN's significant advantage in OAM recognition, the significant optimization of image data quality is possible in the further correction. As an option, the residual information errors are corrected by jointly using the rank-order adaptive median filter (RAMF) and the very-deep super-resolution (VDSR) network with minor information loss in severe ATs. The data increase resulting from RAMF-VDSR is tested. In conclusion, the proposed two-step system can provide a much higher quality of receiving image data in the OAM-SK-FSO link.

Radial diffraction of light in the radial momentum state space

While linear or angular position and momentum can be linked by a continuous or discrete Fourier transform, there are some subtle problems in the analogous Fourier relationship between radial position and radial momentum in history. Here we exploit radial position and newly introduced radial momentum variables to report a radial version of light's diffraction. The mask with single or multiple radial slits confines the light to a radial transmission function. As a result, in the radial momentum state space, we can observe the diffraction sidebands generated on the transmitted light due to a transverse restriction of the radial range. Our experimental results clearly reveal the intriguing diffraction behaviors between radial position and radial momentum variables at the single-photon level, making them another candidate for fundamental tests of quantum mechanics and for a variety of quantum information applications.

Real-time shaping of entangled photons by classical control and feedback

Quantum technologies hold great promise for revolutionizing photonic applications such as cryptography. Yet, their implementation in real-world scenarios is challenging, mostly because of sensitivity of quantum correlations to scattering. Recent developments in optimizing the shape of single photons introduce new ways to control entangled photons. Nevertheless, shaping single photons in real time remains a challenge due to the weak associated signals, which are too noisy for optimization processes. Here, we overcome this challenge and control scattering of entangled photons by shaping the classical laser beam that stimulates their creation. We discover that because the classical beam and the entangled photons follow the same path, the strong classical signal can be used for optimizing the weak quantum signal. We show that this approach can increase the length of free-space turbulent quantum links by up to two orders of magnitude, opening the door for using wavefront shaping for quantum communications.

Experimental demonstration of structural robustness of spatially partially coherent fields in turbulence

Structured fields that are spatially completely coherent have been extensively studied in the context of long-distance optical communication, as the structure in the intensity profile of such fields is used for encoding information. This method of doing optical communication works very well in the absence of turbulence. However, in the presence of turbulence, the intensity structures of such fields start to degrade because of the complete spatial coherence of the field, and this structural degradation increases with the increase in turbulence strength. On the other hand, several theoretical studies have now shown that the structured fields that are spatially only partially coherent are less affected by turbulence. However, to the best of our knowledge, no such experimental demonstration has been reported until now. In this Letter, we experimentally demonstrate the structural robustness of partially coherent fields in the presence of turbulence, and we show that for a given turbulence strength, the structural robustness of a partially coherent field increases as the spatial coherence length of the field is decreased.

High-dimensional states of light with full control of OAM and transverse linear momentum

We present a compact scheme for the generation of high-dimensional states of light encoded in the transverse linear momentum of photons that carry orbital angular momentum (OAM). We use a programmable spatial light modulator in phase configuration to create correlations between these two spatial degrees of freedom. With our setup, we are able to control, independently, the relative phases and amplitudes of the spatial superposition in addition to the topological charge of the OAM. Moreover, we engineer correlations that emulate bipartite quantum states of dimensions d×m. Experimental results from the characterization of different generated states of dimensions up to 9×5 are in excellent agreement with the numerical simulations. Fidelity with the target state is, for all cases, above 95%.

Doing Spin Physics with Unpolarized Particles

Twisted, or vortex, particles refer to freely propagating non-plane-wave states with helicoidal wave fronts. In this state, the particle possesses a nonzero orbital angular momentum with respect to its average propagation direction. Twisted photons and electrons have been experimentally demonstrated, and creation of other particles in twisted states can be anticipated. If brought in collisions, twisted states offer a new degree of freedom to particle physics, and it is timely to analyze what new insights may follow. Here, we theoretically investigate resonance production in twisted photon collisions and twisted e^{+}e^{-} annihilation and show that these processes emerge as a completely novel probe of spin and parity-sensitive observables in fully inclusive cross sections with unpolarized initial particles. This is possible because the initial state with a nonzero angular momentum explicitly breaks the left-right symmetry even when averaging over helicities. In particular, we show how one can produce almost 100% polarized vector mesons in unpolarized twisted e^{+}e^{-} annihilation and how to control its polarization state.

Machine Learning-Based Classification of Vector Vortex Beams

Structured light is attracting significant attention for its diverse applications in both classical and quantum optics. The so-called vector vortex beams display peculiar properties in both contexts due to the nontrivial correlations between optical polarization and orbital angular momentum. Here we demonstrate a new, flexible experimental approach to the classification of vortex vector beams. We first describe a platform for generating arbitrary complex vector vortex beams inspired to photonic quantum walks. We then exploit recent machine learning methods-namely, convolutional neural networks and principal component analysis-to recognize and classify specific polarization patterns. Our study demonstrates the significant advantages resulting from the use of machine learning-based protocols for the construction and characterization of high-dimensional resources for quantum protocols.

Phenomenology of complex structured light in turbulent air

The study of light propagation has been a cornerstone of progress in physics and technology. Recently, advances in control and shaping of light have created significant interest in the propagation of complex structures of light - particularly under realistic terrestrial conditions. While theoretical understanding of this research question has significantly grown over the last two decades, outdoor experiments with complex light structures are rare, and comparisons with theory have been nearly lacking. Such situations show a significant gap between theoretical models of atmospheric light behaviour and current experimental effort. Here, in an attempt to reduce this gap, we describe an interesting result of atmospheric models that are feasible for empirical observation. We analyze in detail light propagation in different spatial bases and present results of the theory that the influence of atmospheric turbulence is basis-dependent. Concretely, light propagating as eigenstate in one complete basis is more strongly influenced by atmosphere than light propagating in a different, complete basis. We obtain these results by exploiting a family of the continuously adjustable, complete basis of spatial modes-the Ince-Gauss modes. Our concrete numerical results will hopefully inspire experimental efforts and bring the theoretical and empirical study of complex light patterns in realistic scenarios closer together.

Identifying structured light modes in a desert environment using machine learning algorithms

The unique orthogonal shapes of structured light beams have attracted researchers to use as information carriers. Structured light-based free space optical communication is subject to atmospheric propagation effects such as rain, fog, and rain, which complicate the mode demultiplexing process using conventional technology. In this context, we experimentally investigate the detection of Laguerre Gaussian and Hermite Gaussian beams under dust storm conditions using machine learning algorithms. Different algorithms are employed to detect various structured light encoding schemes including the use of a convolutional neural network (CNN), support vector machine, and k-nearest neighbor. We report an identification accuracy of 99% under a visibility level of 9 m. The CNN approach is further used to estimate the visibility range of a dusty communication channel.

Optical vortex rotation and propagation from a spiral phase plate resonator with surface reflective coating

A spiral phase plate resonator (SPPR) is created by depositing a reflective coating on the surfaces of a single conventional spiral phase plate (SPP) for the first time to the best of our knowledge. Optical transmission through the SPPR on the output plane of the device is measured to give sharp Fabry-Perot resonances as a function of beam roll angle. Similar measurements are performed for the reflected light emerging from the input plane of the SPPR device. Varying the light frequency going into the SPPR changes the orientation of the angular pattern (Fabry-Perot resonances) to give the rotational constant of the device, in agreement with theory. The optical mode profile is measured after the beam has propagated beyond the plane of the SPPR device while remaining in the diffraction near field, thus revealing new features in the transmitted optical beam. These new results have important implications for developing the SPPR for microscopy, imaging, angle measurement, rotational scanning, and LiDAR.

Frequency induced rotation of high-contrast angular intensity fringes from an uncoated SPP device

High-contrast angular intensity fringes are generated by reflecting laser light from an uncoated spiral phase plate (SPP) device for the first time, to the best of our knowledge. As the laser frequency going into the device is tuned, the fringes rotate. Measured transverse fringe patterns match their theoretical predicted values. They have unity contrast, and their measured intensity varies with laser frequency in a fashion similar to a Fabry-Perot etalon. This effect can be used to enable new miniature devices for angle metrology, imaging, and microscopy.

Orbital angular momentum radiator multiplexing electromagnetic waves in free space

Orbital angular momentum (OAM) modes of electromagnetic (EM) waves have been extensively studied to obtain more than two independent channels at a single frequency. Thus far, however, multiple radiators have been used to achieve this goal in wireless communications. For the first time, a single radiator was designed to simultaneously transmit three OAM waves in free space at the same frequency. Our design makes use of the radiating resonant modes of a dielectric resonator antenna (DRA). For demonstration, a wireless communication system consisting of a pair of transmitting and receiving OAM DRAs was setup and measured. Three EM waves carrying three different signals were transmitted and received successfully, increasing the system throughput without requiring any complex signal processing algorithms. It confirms that a single radiator can wirelessly transmit more than two independent EM waves at a single frequency by using multi-OAM modes. The work is useful for the future high-speed wireless communication systems.

Computer-Aided Laser-Fiber Output Beam 3D Spatial and Angular Design

Multiple laser beams and single-mode optical fibers output can be approximated by assuming that the emitted light has a symmetrical Gaussian intensity profile, which corresponds to the transverse electromagnetic mode (TEM00), which is designated as a Gaussian beam. Current free-accessible design tools are limited to the spatial analysis of the beams, in general, and to the intensity, in particular, and to the graphical visualization in 2D with very limited options. In this work, a novel a computer-aided laser-fiber output beam TEM00 designer, CATEM00, is presented based on the 3D representations typically provided by camera beam profilers, and on the fundamentals of the wave theory of light, including diverse flexibility capabilities for graphical manipulation and parameter comprehension both in terms of spatial behavior and in angular confinement. It must be highlighted that not only is the spatial limitation design of light impact relevant in TEM00 applications but, also, the angle with which the light reaches the target. Hence, the availability of capabilities of phase design in TEM00 following the paraxial limitations is highly convenient. Results and discussion in terms of intensity, power, divergence and wave fronts are presented considering a set of study cases, showing its coherence with Gaussian beam theory.