Orbital Angular Momentum Modes Research Articles

Selection of OAM signal constellations for atmospheric channels using optimal transport theory

We describe a method for determining optimal selections of orbital angular momentum (OAM) superpositions for OAM signal modulation in free-space optical communications using a measure of distance in the context of the Optimal Transport theory. Within the range of topological charges ℓ = −20 to ℓ = 20 we design OAM constellations using 16 to 128 symbols consisting of solos, duets, trios, and quartets of OAM modes. We propose a classification strategy requiring relatively low complexity to evaluate the performance of these constellations, achieving a classification error smaller than 1/1000 in weak to strong turbulence conditions for the 16-OAM constellation. We have found that the optimal set shows some dependence on the receiver’s architecture, so we offer results for optical detectors based on the conjugate projection, the mode sorter, and the Shack-Hartmann sensor.

All-optical image transmission through a dynamically perturbed multimode fiber and a ring-core fiber using diffractive deep neural networks.

In this study, we present an all-optical image reconstruction technique leveraging a diffractive deep neural network (D2NN) within a ring-core fiber (RCF) architecture. Orbital angular momentum (OAM) modes are employed to facilitate imaging transmission. We experimentally validate the efficacy of our approach for complex field diffractive image reconstruction through a multimode fiber (MMF) and RCF at a 1550 nm operating wavelength. The experimental results demonstrate the superior performance of the proposed method in mitigating RCF scattering-to-restoration transformation issues, significantly outperforming traditional MMF-based imaging correction techniques.

Ultra-security optical image encryption using speckles through a multi-mode fiber

To realize optical image encryption for long-distance transmission while considering its security performance, an optical image encryption scheme is proposed in this paper. In the scheme, the pixel information of the plaintext image is first encoded by orbital angular momentum (OAM) holograms; then, the information-coded OAM beam is transmitted through a 1 km multimode fiber to generate speckles as ciphertexts for encryption; and finally, a pre-trained deep learning model capable of learning the relationship between the output speckles and the input information-coded OAM modes is used for decryption. The proposed scheme is not only able to achieve high fidelity recovered image but also a remarkable level of security. The high security stems from the combined use of three keys: the order key, the model key, and the coder key, during optical encryption. The image can therefore only be decrypted by authorized users who simultaneously know the three keys. We have experimentally demonstrated the high fidelity and high security encryption/decryption capabilities. Our work can provide a promising avenue for further research into long-distance optical image transmission and encryption with ultra-high security.

Silicon–based integrated orbital angular momentum parity sorter

Abstract A silicon–based integrated orbital angular momentum (OAM) parity sorter using two-dimensional multimode interference (2D MMI) waveguides is designed and numerically analyzed. An OAM parity sorter, which sorts OAM modes according to their parity (even or odd) is an elegant device in a broad range of OAM states processing applications including quantum gates, quantum key distribution, generation of high dimensional quantum gates, quantum information, and teleportation. The presented three–part integrated parity sorter is realized based on the self–imaging and field–splitting properties of MMI structures. Its total length is 11 444 µm. The proposed device works for OAM modes with |l| ⩽ 5. The performance of OAM sorting is investigated with the results confirming the high purity (up to 98.33% and 94.45% at even and odd ports, respectively) for the telecommunication wavelength λ 0 = 1550 nm.

Off-axis dispersion-managed metasurface for routing orbital angular momentum mode and wavelength multiplexing channels

Off-axis dispersion-managed metasurface for routing orbital angular momentum mode and wavelength multiplexing channels

Optimal violation of a Bell inequality in two-dimensional state spaces for an asymmetric orbital angular momentum system

The symmetric orbital angular momentum (OAM) entanglement in the subspace of { ± ℓ} has been extensively exploited in quantum information science. Here we investigate instead the Bell inequalities for the two-dimensional subspace spanned by asymmetric OAM modes of ℓ1 and ℓ2, usually corresponding to the quantum property of nonmaximal entanglement. We demonstrate, both theoretically and experimentally, the optimal violation of a suitable Clauser-Horne-Shimony-Holt Bell inequality for the asymmetric OAM modes, thus manifesting the entanglement for asymmetric OAM states space.

Online Recursive Independent Component Analysis based equalization for Orbital Angular Momentum Mode Division Multiplexed Transmission

Online Recursive Independent Component Analysis based equalization for Orbital Angular Momentum Mode Division Multiplexed Transmission

A position-based method for detecting orbital angular momentum modes

Abstract Due to the inherent limitations of current Orbital Angular Momentum (OAM) mode detection methods and constraints posed by the physical size of receiving antennas, accurately identifying higher-order OAM modes represents a significant challenge. Therefore, there is a pressing necessity to overcome these hurdles. This paper introduces a new approach to OAM mode detection that exploits positional information. Our methodology ascertains the OAM mode by examining the phase and position data of the electric field at any two randomly chosen points within the energy's spatial distribution radiated by vortex electromagnetic waves. This innovation promises not only to precisely detect higher-order OAM modes but also grants greater versatility in the placement of receiving antennas. Moreover, the study delves into the correlation between the electric field phase of vortex electromagnetic waves, the azimuth angle, and the receiving distance. The validity of our approach is confirmed through both simulation outcomes and experimental data derived from physical tests.

High gain distributed Raman amplifier for orbital angular momentum mode-division multiplexing and wavelength-division multiplexing in a 104-km ring-core fiber over the C + L band

Mode-division multiplexing (MDM) and wavelength-division multiplexing (WDM) are regarded as effective solutions for enhancing the communication capacity of fiber-optic transmission systems. To extend the transmission distance, a suitable amplification technique is required to amplify the signal light, with distributed Raman amplifier (DRA) offering a high-flat gain. In this paper, we experimentally demonstrate the transmission of 3 orbital angular momentum (OAM) mode-division multiplexing and 9 wavelength-division multiplexing ranging from 1530 nm to 1610 nm over a 104-km self-designed ring-core fiber (RCF) with the assistance of DRA. The homemade all-fiber mode selective couplers (MSCs) can (de)multiplex OAM modes (OAM01, OAM11, OAM21) efficiently in long-distance MDM + WDM fiber-optic transmission systems. The OAM-DRA provides high gain (with an on-off gain greater than 10 dB) as well as flat gain (with a differential wavelength gain of less than 0.88 dB and a differential mode gain of less than 0.28 dB) over the C + L band.

Coherence vortices by binary pinholes

Abstract Singularity in a two-point complex coherence function, known as coherence vortices, represents zero visibility with a helical phase structure. In this paper, we introduce a novel technique to generate the coherence vortices of different topological charges by incoherent source transmittance with exotic structured binary pinholes. The binary pinhole structures have been realized by lithography, followed by wet etching methods. We control the transmittance from the incoherent source plane using these exotic apertures, which finally results in a coherence vortex spectrum that features multiple and pure orbital angular momentum modes. The generation of the coherence vortices is achieved within the two-point complex spatial coherence function. The spatial coherence function exhibits the helical phase profile in its phase part, and its absolute part shows a doughnut-shaped structure. A theoretical basis is developed and validated with simulation, and experimental results. The coherence vortex spectra with OAM modes superposed with opposite topological charges, known as photonic gears, are also generated with the proposed theory.

Terahertz switchable vortex beam generator based on vanadium dioxide reflective metasurface

Vortex beams exhibit significant potential for applications in diverse fields, such as optical communications, particle manipulation, and quantum information, due to the orbital angular momentum (OAM) they carry. While substantial progress has been made in the generation of vortex beams and the control of their wavefronts, further optimization is necessary to enhance the variability of OAM modes and the modulation of focusing. This study presents three tunable vortex beam generators based on vanadium dioxide metasurfaces. By leveraging the insulator-metal phase transition of vanadium dioxide (VO2), these metasurfaces can convert incident left-circularly polarized (LCP) light into a deflected vortex beam with adjustable OAM modes, a switchable focused vortex beam, or a focused vortex beam with tunable OAM modes in the terahertz band. Specifically, by varying the angle of the incident light, a vortex beam carrying variable topological charges can be deflected over a range from -34° to 90°. Vortex beams with a topological charge of 1 enable reversible switching between near-focus (0.85 mm) and far-focus (3.2 mm), demonstrating highly effective tunable focusing capabilities. Additionally, focused vortex generators with switchable topological charges are proposed. Focused vortex beams with a topological charge of -1 are generated in the insulating state, while a topological charge of -2 is observed in the metallic state. These vortex beam generators allow for different phase gradient distributions in the phase transition states, enabling diverse OAM and variable focuses. This research has potential applications in areas such as dynamic imaging and optical communications.

Atmospheric turbulence-distorted OAM mode recognition via multi-scale dilated convolution with multi-level feature fusion

Vortex beams with orbital angular momentum (OAM) significantly enhance system capacity, and high-precision recognition of OAM mode through atmospheric turbulence (AT) channels can markedly improve the information transmission capability of free-space optical communication systems. In this paper, with a cylindrical lens-assisted distinguish between positive and negative OAM, a reliable neural network combining multi-scale dilated convolution (MSDC) unit and multi-level feature fusion (MLFF) module is proposed to detect high order AT-distorted OAM modes. The network fully exploits the features in light-intensity images to achieve a highest recognition accuracy of 99.4% for mode-orders from -20 to +20 in a hybrid ATs dataset (C n 2 = 5×10−16, 5×10−14, 5×10−12 m-2/3), and almost 96% even in strong turbulence. Experimental results on accuracy, efficiency, reliability, and robustness demonstrate that the proposed method excels and provides a trustworthy solution for complex AT-distorted OAM mode recognition.

Spatial momentum separation for optical vortex via phase-assembled metasurfaces

Expanding the spatial degrees of freedom is regarded to be the most innovative and effective solution for optical vortex encoding/decoding technology. A phase-assembled metasurface is proposed here to separate the momentum of the optical vortex into different spatial locations, and the incident high-order optical vortex is encoded in 18 channels. By combining both the propagation phase and the Pancharatnam-Berry (PB) phase, the fundamental Gaussian mode (solid spot) positions and other higher-order orbital angular momentum modes (hollow mode spots) positions at different channels are used to achieve the encryption of all-optical information. The scheme of grouping the mode spots on different channels into solid and hollow points greatly reduces the difficulty of encoding/decoding a high-order optical vortex. In this way, the combination of 2 incident high-order optical vortexes can represent 256 hexadecimal numbers from 00 to FF. We envision this work will open avenues for information encryption, multidimensional data storage, wavefront manipulation, and advanced orbital angular momentum detection technologies.

Orbital angular momentum superimposed mode recognition based on multi-label image classification

Orbital angular momentum (OAM) multiplexing technology has great potential in high capacity optical communication. OAM superimposed mode can extend communication channels and thus enhance the capacity, and accurate recognition of multi-OAM superimposed mode at the receiver is very crucial. However, traditional methods are inefficient and complex for the recognition task. Machine learning and deep learning can offer fast, accurate and adaptable recognition, but they also face challenges. At present, the OAM mode recognition mainly focus on single OAM mode and ±l superimposed dual-OAM mode, while few researches on multi-OAM superimposed mode, due to the limitations of single-object image classification techniques and the diversity of features to recognize. To this end, we develop a recognition method combined with multi-label image classification to accurately recognize multi-OAM superimposed mode vortex beams. Firstly, we create datasets of intensity distribution map of three-OAM and four-OAM superimposed mode vortex beams based on numerical simulations and experimental acqusitions. Then we design a progressive channel-spatial attention (PCSA) model, which incorporates a progressive training strategy and two weighted attention modules. For the numerical simulation datasets, our model achieves the highest average recognition accuracy of 94.9% and 91.2% for three-OAM and four-OAM superimposed mode vortex beams with different transmission distances and noise strengths respectively. The highest experimental average recognition accuracy for three-OAM superimposed mode achieves 92.7%, which agrees with the numerical result very well. Furthermore, our model significantly outperforms in most metrics compared with ConvNeXt, and all experiments are within the affordable range of computational cost.

Time Evolution of Orbital Angular Momentum Modes for Deep-Routing Multiplexing Channels

Optical orbital angular momentum (OAM) mode multiplexing has emerged as a promising technique for boosting communication capacity. However, most existing studies have concentrated on channel (de)multiplexing, overlooking the critical aspect of channel routing. This challenge involves the reallocation of multiplexed OAM modes across both spatial and temporal domains—a vital step for developing versatile communication networks. To address this gap, we introduce a novel approach based on the time evolution of OAM modes, utilizing the orthogonal conversion and diffractive modulation capabilities of unitary transformations. This approach facilitates high-dimensional orthogonal transformations of OAM mode vectors, altering both the propagation direction and the spatial location. Using Fresnel diffraction matrices as unitary operators, it manipulates the spatial locations of light beams during transmission, breaking the propagation invariance and enabling temporal evolution. As a demonstration, we have experimentally implemented the deep routing of four OAM modes within two distinct time sequences. Achieving an average diffraction efficiency above 78.31%, we have successfully deep-routed 4.69 Tbit·s−1 quadrature phase-shift keying (QPSK) signals carried by four multiplexed OAM channels, with a bit error rate below 10–6. These results underscore the efficacy of our routing strategy and its promising prospects for practical applications.

Modal gain characteristics of few-mode erbium-doped fiber amplifiers with pump mode beating

Using the linear polarization (LP) mode decomposition method, we theoretically analyze the beat effect between the same polarization components of the vector pump modes and propose a pump beat model of few-mode erbium-doped fiber amplifiers (FM-EDFAs). The relationship of the overlap factor with the signal gain in the beat model is verified by the amplification of LP01 and LP11 modes for the first time, that is, the differential modal gain (DMG) is dependent on the integral of the overlap factor difference over the EDF length. We also simulate the effect of pump mode beating on signal amplification: the modal gain varies periodically with the pump mode phase, and the beat length can affect the fluctuation period and amplitude of the DMG. The DMG can further be reduced by controlling the initial phases of the vector modes and properly designing the beat length of the FM-EDF. The similar process can expand to more signal modes, such as the simultaneous amplification of LP01x, LP11ex, LP11oy, LP21ex and LP21oy modes. The LP mode decomposition method is also applied to the beat effect between signal modes or the amplification of orbital angular momentum (OAM) modes. One can expect to implement an experiment on the FM-EDFA amplification with pump mode beating by optimally designing the FM-EDF structure, using a properly narrow linewidth pump laser and precisely controlling the pump mode coherence.

Fourier-transform spectroscopy based on the rotational Doppler effect

We propose a new Fourier-transform spectroscopy technique based on the rotational Doppler effect. The technique offers an application for optical vortex frequency combs, where each frequency component carries a unique amount of orbital angular momentum (OAM). Here, we emulate a vortex comb using a tunable single frequency laser and a collection of spiral phase plates, generating up to 11 distinct OAM modes. Unlike in traditional Fourier-transform spectroscopy based on the Michelson interferometer (linear Doppler effect), the spectral resolution of vortex-comb spectroscopy is not limited by the mechanical scan distance of the instrument, but the instrument can be operated continuously without interruptions, leading to fast mode-resolved measurements.

Wavelength-multiplexed orbital angular momentum meta-holography

AbstractThe field of high-bandwidth holography has been extensively studied over the past decade. Orbital angular momentum (OAM) holography, which utilizes vortex beams with theoretically unbounded OAM modes as information carriers, showcases the large capacitance of hologram storage. However, OAM holography has been limited to a single wavelength, restricting its potential for full-color holography and displays. In this study, we propose wavelength and OAM multiplexed holography that utilizes the multiple dimensions of light—wavelength and OAM—to provide a multi-color platform that expands the information capacity of holographic storage devices. The proposed wavelength-OAM multiplexed holography is physically realized by a metasurface, the state-of-the-art optical element consisting of an array of artificially engineered nanostructures. Hydrogenated silicon meta-atoms, the constituents of the metasurface, are engineered to possess wavelength selectivity by tailoring the dispersion of polarization conversion. These meta-atoms are used to encode the calculated OAM-preserved phase maps based on our design. The sampling grid of the phase map is rotated by 45°, which effectively suppress higher-order diffraction, providing a great strategy for achieving large field-of-view (FOV) holography. We successfully demonstrate six holographic images that are selectively reconstructed under the illumination of light with specific wavelengths (λ = 450, 635 nm) and topological charges (l = -2, 0, 2), without high-order diffraction. Our work suggests that ultrathin meta-holograms can potentially realize ultrahigh-bandwidth full-color holography and holographic video displays with large FOV.

Investigation on the transmission attenuation of Bessel-Gaussian beams in a dusty environment

This paper delves into the transmission dynamics of Bessel-Gaussian (BG) beams in three distinct dusty environments, leveraging the Generalized Lorenz-Mie Theory (GLMT) alongside a single scattering model for a comprehensive analysis. Through numerical simulations, the study explores the interaction between dust particle scattering and the attenuation and transmittance behaviors of BG beams, elucidating the influences of varying particle concentrations and visibility conditions typical of floating dust, blowing sand, and sandstorms. The findings reveal numerous determinants, including particle number concentration, optical visibility, wavelength, orbital angular momentum (OAM) modes, waist radius, cone angle, and polarization states, which significantly affect the transmission performance of BG beams in dusty conditions. Notably, the attenuation rate decreases with increasing wavelengths and higher OAM modes, thereby extending effective transmission distances. Furthermore, the strategic use of linear polarization emerges as an optimal approach for enhancing BG beam transmission efficiency in dust-rich environments. These insights are crucial for optimizing BG beam transmission in real-world applications, marking a significant advancement in the field.

End-to-end learning of joint noise shaping and probabilistic shaping for OAM mode division multiplexing transmission.

Intensity modulation direct detection (IM/DD) orbital angular momentum (OAM) mode division multiplexing (MDM) technology can greatly expand the capacity of a communication system, which is a promising solution for the next generation of high-speed passive optical networks (PONs). However, there are serious obstacles such as mode coupling, device nonlinear impairment, and quantization noise in an IM/DD OAM-MDM system with a low-resolution digital-to-analog converter (DAC). In this Letter, we propose a novel, to the best of our knowledge, end-to-end (E2E) learning scheme based on a double residual feature decoupling network (DRFDnet) emulator with joint probabilistic shaping (PS) and noise shaping (NS) for the OAM-MDM IM/DD transmission. Our DRFDnet emulator can accurately build a complex nonlinear model of an OAM-MDM system by separating the signal impairments into linear and nonlinear. Meanwhile, a DRFDnet-based E2E scheme for joint PS and NS is presented with the aim of compensating the signal impairment for the OAM-MDM IM/DD system. An experiment is carried out on a 200 Gbit/s PON system based on the OAM-MDM IM/DD transmission. The experimental results demonstrate that the proposed DRFDnet-based joint PS and NS scheme is a promising solution to effectively mitigate nonlinear distortions and outperforms the CGAN-based joint PS and NS scheme and traditional joint PS and NS scheme with receiver sensitivity improvements of 1.2 dBm and 2.5 dBm under hard-decision forward error correction (HD-FEC) thresholds, respectively. Our experimental results demonstrate that the proposed DRFDnet emulator-based E2E learning scheme is a viable candidate for future PON.