Experimental demonstration of free-space multi-state orbital angular momentum shift keying

Spatiotemporal vortex strings

Light carrying orbital angular momentum (OAM) holds unique properties and boosts myriad applications in diverse fields. However, the generation of an ultrafast wave packet carrying numerous vortices with various transverse OAM modes, i.e., vortex string, remains challenging, and the corresponding detection method is lacking. Here, we demonstrate that a vortex string with 28 spatiotemporal optical vortices (STOVs) with customizable topological charge (TC) arrangements can be generated in one wave packet. The diffraction rules of STOV strings are revealed theoretically and experimentally. Following these rules, the TC values and positions of all STOVs in a vortex string can be simultaneously recognized from the diffraction pattern. Such STOV strings facilitate STOV-based optical communication. As a proof-of-principle demonstration, the transmission of an image is realized with 16-STOV strings. This work provides guidance for revealing the underlying properties of the transverse OAM light and opens up opportunities for applications of the structured light in optical communication, quantum information processing, etc.

Research Progress on Router Devices for the OAM Optical Communication

Vortex beams carrying orbital angular momentum (OAM) provide a new degree of freedom for light waves in addition to the traditional degrees of freedom, such as intensity, phase, frequency, time, and polarization. Due to the theoretically unlimited orthogonal states, the physical dimension of OAM is capable of addressing the problem of low information capacity. With the advancement of the OAM optical communication technology, OAM router devices (OAM-RDs) have played a key role in significantly improving the flexibility and practicability of communication systems. In this review, major breakthroughs in the OAM-RDs are summarized, and the latest technological standing is examined. Additionally, a detailed account of the recent works published on techniques related to the OAM-RDs has been categorized into five areas: channel multicasting, channel switching, channel filtering, channel hopping, and channel adding/extracting. Meanwhile, the principles, research methods, advantages, and disadvantages are discussed and summarized in depth while analyzing the future development trends and prospects of the OAM-RDs.

Deep-learning assisted fast orbital angular momentum complex spectrum analysis

Analyzing the orbital angular momentum (OAM) distribution of a vortex beam is critical for OAM-based applications. Here, we propose a deep residual network (DRN) to model the relationship between characteristics of the multiplexed OAM beam and their complex spectrum. The favorable experimental results show that our proposal can obtain both the intensity and phase terms of multiplexed OAM beams, dubbed complex spectrum, with a wide range of OAM modes, varying in intensity, phase ratio, and mode intervals at high accuracy and real-time speed. Specifically, the root mean square error (RMSE) of intensity and phase spectrum is evaluated as 0.002 and 0.016, respectively, with a response time of only 0.020 s. To the best of our knowledge, this work opens a new sight for fast OAM complex spectrum analysis and paves the way for numerous advanced domains that need real-time OAM complex spectrum diagnostic like ultrahigh-dimensional OAM tailoring.

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.

Color image information transmission based on elliptic optical vortex array encoding/decoding

A multichannel high-dimensional data encoding/decoding scheme based on composite elliptic optical vortex (EOV) arrays is proposed. By exploiting the rotation angle of the EOV, a 4 × 4 composite EOV array is used for high-dimensional data encoding. The conjugate symmetric extension Fourier computer-generated holography algorithm with controllable reconstruction focus is used to assign different reconstruction focus to the data of the three channels (R, G, and B) of the color image. Then, the data of the three channels is transmitted simultaneously by a single hologram to further improve the transmission efficiency. At the receiver, the initial information sequence is decoded by directly identifying the captured intensity patterns with a deep learning-based convolutional neural network. In the experiment, a 128 × 128-pixel color image is successfully transmitted, which confirms the feasibility of our proposed encoding/decoding scheme. This method has great potential for future high-capacity optical communications.

1024-ary composite OAM shift keying for free-space optical communication system decoded by a two-step neural network

The demand for high-dimensional encoding techniques for communication systems is increasing. Vortex beams carrying orbital angular momentum (OAM) provide new degrees of freedom for optical communication. In this study, we propose an approach for increasing the channel capacity of free-space optical communication systems by integrating superimposed orbital angular momentum (OAM) states and deep learning techniques. We generate composite vortex beams with topological charges ranging from -4 to 8 and radial coefficients ranging from 0 to 3. A phase difference among each OAM state is introduced to significantly increase the number of available superimposed states, achieving up to 1024-ary codes with distinct features. To accurately decode the high-dimensional codes, we propose a two-step convolutional neural network (CNN). The first step is to make a coarse classification of the codes, while the second step is to finely identify the code and achieve decoding. Our proposed method demonstrates 100% accuracy achieved for the coarse classification after 7 epochs, 100% accuracy achieved for the fine identification after 12 epochs, and 99.84% accuracy achieved for testing, which is much faster and more accurate than one-step decoding. To demonstrate the feasibility of our method, we successfully transmitted a 24-bit true-color Peppers image once with a resolution of 64 × 64 in the laboratory, yielding a bit error rate of 0.

Multiplexed vortex state array toward high-dimensional data multicasting

Optical vortex array has drawn widespread attention since the boom of special applications such as molecular selecting and optical communication. Here, we propose an integrated phase-only scheme to generate multiple multiplexed vortex beams simultaneously, constituting a multiplexed vortex state array, where the spatial position, as well as the corresponding orbital angular momentum (OAM) spectrum, can be manipulated flexibly as desired. Proof-of-concept experiments are carried out and show a few different multiplexed vortex state arrays that fit well with the simulation. Moreover, regarding the array as a data-carrier, a one-to-many multicasting link through multi-state OAM shift keying, a high-dimensional data coding, is also available in free space. In the experiment, four various OAM states are employed and achieve four bits binary symbols, and finally distribute three different images to three separate receivers independently from the same transmitter, showing great potential in the future high-dimensional optical networks.

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.

Advances on Solid-State Vortex Laser

Vortex beams (VBs) are structured beams with helical wavefronts carrying orbital angular momentum (OAM) and they have been widely used in lots of domains, such as optical data-transmission, optical tweezer, quantum entanglement, and super-resolution imaging. The ability to generate vortex beams with favorable performance is of great significance for these advanced applications. Compared with extra-cavity schemes, such as spatial light modulation, mode conversion, and others which transform other modes into vortex modes, solid-state vortex lasers can output vortex beams directly and show advantages including a compact structure, high robustness, easy to integrate, and low cost. In this review, we summarize intra-cavity generation approaches to vortex beams in solid-state lasers. Our work on 1.6μm eye-safe vector vortex lasers is also introduced.

Free-Space Transmission and Detection of Variously Polarized Near-IR Beams Using Standard Communication Systems with Embedded Singular Phase Structures

We propose to achieve multichannel information transmission in free space by means of variously polarized beams. The interaction of vortex beams of various orders with the main polarization states is theoretically analyzed. The passage of beams with different polarization states through multi-order diffractive optical elements (DOEs) is simulated numerically. Using the simulation results, tables of code correspondence of diffraction order numbers to the presence of phase vortices in the analyzed beams are constructed, which allow one to determine diffraction orders that carry information about various polarization states. The performed experiment made it possible to study the recognition of the first order cylindrical polarization state formed by a Q-plate converter using a phase DOE. In the experiment, these elements were built into a commercial fiber-optic communication system operating at the near-IR frequencies. After detecting the beam polarization state, beams of the required diffraction orders are efficiently coupled into optical fiber using an additional phase element. The developed optical detection system also provides channel suppression of homogeneously polarized components, which are supposed to be used for transmission of other channels.

Adaptive demodulation by deep-learning-based identification of fractional orbital angular momentum modes with structural distortion due to atmospheric turbulence

Since the great success of optical communications utilizing orbital angular momentum (OAM), increasing the number of addressable spatial modes in the given physical resources has always been an important yet challenging problem. The recent improvement in measurement resolution through deep-learning techniques has demonstrated the possibility of high-capacity free-space optical communications based on fractional OAM modes. However, due to a tiny gap between adjacent modes, such systems are highly susceptible to external perturbations such as atmospheric turbulence (AT). Here, we propose an AT adaptive neural network (ATANN) and study high-resolution recognition of fractional OAM modes in the presence of turbulence. We perform simulations of fractional OAM beams propagating through a 1-km optical turbulence channel and analyze the effects of turbulence strength, OAM mode interval, and signal noise on the recognition performance of the ATANN. The recognition of multiplexed fractional modes is also investigated to demonstrate the feasibility of high-dimensional data transmission in the proposed deep-learning-based system. Our results show that the proposed model can predict transmitted modes with high accuracy and high resolution despite the collapse of structured fields due to AT and provide stable performance over a wide SNR range.

Experimental demonstration of multiple dimensional coding decoding for image transfer with controllable vortex arrays

Vortex beams carrying orbital angular momentum (OAM), which featuring helical phase front, have been regarded as an alternative spatial degree of freedom for optical mode coding and multiplexing. For most reported OAM-based mode coding schemes, data information is only encoded by different OAM mode states. In this paper, we introduce a novel design technique to construct vortex array phase grating (VAPGs) for the flexible generation of vortex arrays, and employ the proposed VAPGs to realize multi-dimensional space/mode/amplitude coding/decoding. By designing VAPGs with different parameters and loading them on to a single spatial light modulator (SLM), we successfully generate vortex array with different mode states and relative power in the experiments. Moreover, a 10-bit multi-dimensional space/mode/amplitude data coding/decoding scheme for image transfer in free-space link with a zero bit-error-rate is experimentally demonstrated, which confirm the feasibility of our proposed VAPG-based coding/decoding scheme.

Research on Hypergeometric-Gaussian Vortex Beam Propagating under Oceanic Turbulence by Theoretical Derivation and Numerical Simulation

In this paper, we use two methods to research the propagation characteristics of a Hypergeometric-Gaussian (HyGG) vortex beam under oceanic turbulence. One is numerical calculation based on the Rytov approximation theory, where the theoretical detection probability equation of the HyGG vortex beam propagating through oceanic turbulence is derived. The other is numerical simulation based on random phase screens model of oceanic turbulence, where the influences generated by oceanic turbulence on the phase and intensity of the propagation beam as well as the propagation of the beam through several independent phase screens, kept at the same distance, have the same effect. The effects of oceanic turbulence parameters and initial beam parameters on the detection probability of the HyGG vortex beam at the receiver are discussed. The results of theoretical derivation are well in agreement with those of numerical simulation, which demonstrated that the numerical simulation method could effectively simulate the complex theoretical derivation. Both results show that with higher dissipation rate of kinetic energy per unit mass of fluid, smaller dissipation rate of mean-squared temperature and lower temperature-salinity contribution ratio comes the better detection probability. Meanwhile, a HyGG vortex beam with smaller topological charge and longer wavelength has a superior turbulent resistance property. It provides a promising way to estimate the propagation characteristics of the optical beams in an underwater environment.

Tailoring a complex perfect optical vortex array with multiple selective degrees of freedom

Optical vortex arrays (OVAs) have successfully aroused substantial interest from researchers for their promising prospects ranging from classical to quantum physics. Previous reported OVAs still show a lack of controllable dimensions which may hamper their applications. Taking an isolated perfect optical vortex (POV) as an array element, whose diameter is independent of its topological charge (TC), this paper proposes combined phase-only holograms to produce sophisticated POV arrays. The contributed scheme enables dynamically controllable multi-ring, TC, eccentricity, size, and the number of optical vortices (OVs). Apart from traditional single ring POV element, we set up a β_g library to obtain optimized double ring POV element. With multiple selective degrees of freedom to be chosen, a series of POV arrays are generated which not only elucidate versatility of the method but also unravel analytical relationships between the set parameters and intensity patterns. More exotic structures are formed like the "Bear POV" to manifest the potential of this approach in tailoring customized structure beams. The experimental results show robust firmness with the theoretical simulations. As yet, these arrays make their public debut so far as we know, and will find miscellaneous applications especially in multi-microparticle trapping, large-capacity optical communications, novel pumping lasers and so on.

Deep-learning-based high-resolution recognition of fractional-spatial-mode-encoded data for free-space optical communications

Structured light with spatial degrees of freedom (DoF) is considered a potential solution to address the unprecedented demand for data traffic, but there is a limit to effectively improving the communication capacity by its integer quantization. We propose a data transmission system using fractional mode encoding and deep-learning decoding. Spatial modes of Bessel-Gaussian beams separated by fractional intervals are employed to represent 8-bit symbols. Data encoded by switching phase holograms is efficiently decoded by a deep-learning classifier that only requires the intensity profile of transmitted modes. Our results show that the trained model can simultaneously recognize two independent DoF without any mode sorter and precisely detect small differences between fractional modes. Moreover, the proposed scheme successfully achieves image transmission despite its densely packed mode space. This research will present a new approach to realizing higher data rates for advanced optical communication systems.

Quadrant Fourier transform and its application in decoding OAM signals

We present a new, to the best of our knowledge, concept of using quadrant Fourier transforms (QFTs) formed by microlens arrays (MLAs) to decode complex optical signals based on the optical intensity collected per quadrant area after the MLAs. From a computational optics viewpoint, we show the most promising use of the QFT in low-cost and passive decoding of laser signals carrying optical angular momenta (OAM) that are prevalent in research frontiers of optical communications, computation, and imaging. There are numerous ways of creating, adding, and combining OAM states in optical waves, while decoding or demultiplexing approaches often turn out to be complicated or expensive. The simple OAM decoder formed by a pair of identical MLAs, which are concatenated in the focal plane and transversely offset by half-pitch length, can accomplish the imaging task with four pixels per cell. By sorting the gradient curls of the optical wave into local quadrant cells, the decoder analyzes the intensity reallocation that is proportional to the gradients and computes the gradient curls accordingly. The low-cost, compactness, and simplicity of the proposed OAM sensor will further promote OAM-based applications, as well as many other applications that exploit the spatial complexity of optical signals.

Tailoring diffraction of light carrying orbital angular momenta

A unified approach to controlling the diffraction of light carrying orbital angular momenta (OAM) is developed and experimentally verified in this Letter. This approach allows one to specify not only the number of diffraction maxima, their spatial frequencies, and the intensity distribution between them, but also the OAM in each maximum. It is verified that the approach can be used for structuring both single and multiple beams carrying OAMs. Simulations reveal phase singularities in structured beams. In addition, the approach makes it possible to shape the light in regular and irregular two-dimensional arrays with addressing the OAMs at each site. This approach offers new opportunities for singular optics.