Deep learning based atmospheric turbulence compensation for orbital angular momentum beam distortion and communication

Time-varying propagation model and dynamic-feedback-phase correction for multiplexed orbital angular momentum beams in atmospheric turbulence

Freespace optical (FSO) communication in an outdoor setting is complicated by atmospheric turbulence (AT). A time-varying (TV) multiplexed orbital angular momentum (OAM) propagation model to consider AT under transverse-wind conditions is formulated for the first time, and optimized dynamic correction periods for various TV AT situations are found to improve the transmission efficiency. The TV nature of AT has until now been neglected from modeling of OAM propagation models, but it is shown to be important. First, according to the Taylor frozen-turbulence hypothesis, a series of AT phase screens influenced by transverse wind are introduced into the conventional angular-spectrum propagation analysis method to model both the temporal and spatial propagation characteristics of multiplexed OAM beams. Our model shows that while in weak TV AT, the power standard deviation of lower-order modes is usually smaller than that of higher-order modes, the phenomena in strong TV AT are qualitatively different. Moreover, after analyzing the effective time of each OAM phase correction, optimized dynamic correction periods for a dynamic feedback communication link are obtained. An optimized result shows that, under the moderate TV AT, both a system BER within the forward-error-correction limit and a low iterative computation volume with 6% of the real-time correction could be achieved with a correction period of 0.18 s. The research emphasizes the significance of establishing a TV propagation model for exploring the effect of TV AT on multiplexed OAM beams and proposing an optimized phase-correction mechanism to mitigate performance degradation caused by TV AT, ultimately enhancing overall transmission efficiency.

Conditional convolutional GAN-based adaptive demodulator for OAM-SK-FSO communication

The perturbation of atmosphere turbulence is a significant challenge in orbital angular momentum shift keying-based free space optical communication (OAM-SK-FSO). In this study, we propose an adaptive optical demodulation system based on deep learning techniques. A conditional convolutional GAN (ccGAN) network is applied to recover the distorted intensity pattern and assign it to its specified class. Compared to existing methods based on convolutional neural networks (CNNs), our network demonstrates powerful capability in recovering the distorted light beam, resulting in a higher recognition accuracy rate under the same conditions. The average recognition accuracy rates are 0.9928, 0.9795 and 0.9490 when the atmospheric refractive index structure constant $C_n^2$ is set at 3 × 10-13, 4.45 × 10-13, 6 × 10-13m-2/3, respectively. The ccGAN network provides a promising potential tool for free space optical communication.

Underwater entanglement propagation of auto-focusing Airy beams

In underwater wireless optical communication, orbital angular momentum (OAM) states suffer from turbulence distortions. This study aims to investigate the effectiveness of auto-focusing and OAM entanglement of the beams in reducing the turbulence effects. We implement the single-phase approximation and the extended Huygens-Fresnel principle to derive the detection probability of the entangled Airy beams under unstable oceanic turbulence. The results show that auto-focusing can protect the signal OAM mode and suppress modal crosstalks, while entangled OAM states can further enhance the resistance against oceanic turbulence around the focus position. The numerical analysis demonstrates that after the auto-focusing position, the beams evolve in completely opposite directions, indicating that the focal length should be modulated according to the length of a practical link to enhance received signals. These findings suggest that entangled auto-focusing vortex beams may be a desirable light source in underwater communication systems.

ASF-Transformer: neutralizing the impact of atmospheric turbulence on optical imaging through alternating learning in the spatial and frequency domains

Atmospheric turbulence, a pervasive and complex physical phenomenon, challenges optical imaging across various applications. This paper presents the Alternating Spatial-Frequency (ASF)-Transformer, a learning-based method for neutralizing the impact of atmospheric turbulence on optical imaging. Drawing inspiration from split-step propagation and correlated imaging principles, we propose the Alternating Learning in Spatial and Frequency domains (LASF) mechanism. This mechanism utilizes two specially designed transformer blocks that alternate between the spatial and Fourier domains. Assisted by the proposed patch FFT loss, our model can enhance the recovery of intricate textures without the need for generative adversarial networks (GANs). Evaluated across diverse test mediums, our model demonstrated state-of-the-art performance in comparison to recent methods. The ASF-Transformer diverges from mainstream GAN-based solutions, offering a new strategy to combat image degradation introduced by atmospheric turbulence. Additionally, this work provides insights into neural network architecture by integrating principles from optical theory, paving the way for innovative neural network designs in the future.

Direct prediction and compensation of atmospheric turbulence for free-space integer and fractional order OAM multiplexed transmission links

Atmospheric turbulence has an adverse impact on orbital angular momentum (OAM) beam transmission, resulting in power fluctuations and mode crosstalk. These challenges are particularly pronounced in OAM multiplexing links. In this paper, we propose and demonstrate a novel network architecture that integrates convolutional layers and residual structures to address the issue of turbulence phase compensation. By harnessing the local feature learning capability of convolutional layers and the information-preserving function of residual structures, we aim to mitigate the adverse effects of network depth on information loss. By employing the proposed network, we compensate the turbulence phase directly using the received intensity distributions for free space multiplexed integer and fractional order OAM links, respectively. The obtained results show that the received optical power can be improved for more than 10 dB for integer order OAM multiplexed FSO links under weak to strong turbulence conditions, while 9 dB for fractional-order OAM multiplexed FSO links. Moreover, mode crosstalk can be reduced for about 10 dB under 4 OAM modes multiplexed links under turbulence strength D/r0=5. The proposed deep learning based atmospheric turbulence compensation method can predict phase screens rapidly and accurately, thus enhancing the dependability of future OAM multiplexing technology.

Predictive correction method based on deep learning for a phase compensation system with frozen flow turbulence

We propose a deep learning method that includes convolution neural network (CNN) and convolutional long short-term memory (ConvLSTM) models to realize atmospheric turbulence compensation and correction of distorted beams. The trained CNN model can automatically obtain the equivalent turbulent compensation phase screen based on the Gaussian beams affected by turbulence and without turbulence. To solve the time delay problem, we use the ConvLSTM model to predict the atmospheric turbulence evolution and acquire a more accurate compensation phase under the Taylor frozen hypothesis. The experimental results show that the distorted Gaussian and vortex beams are effectively and accurately compensated.

Adaptive optics compensation of orbital angular momentum beams using a hybrid input-output algorithm with complementary binary masks

For orbital angular momentum (OAM) beams, we show that the twin-image problem in the single-intensity-measurement hybrid input-output algorithm (HIOA) severely impairs the phase retrieval performance and propose a very simple method to overcome this problem. First, we introduce the principle of the single-intensity-measurement HIOA together with the underlying reason for the twin-image problem and propose a new scheme of the HIOA using a pair of complementary binary masks (CBMs) to overcome the twin-image problem. To verify the usefulness of the proposed CBM-HIOA in the OAM free-space optical system, a wave-optics simulation is used to produce relatively realistic atmospheric turbulence, and the turbulence-induced distorted phase of the probe Gaussian beam is retrieved to compensate for the phase distortion of OAM beams. The suppression of the bidirectional and stagnant convergence caused by the twin-image problem, the compensation of the turbulence-induced distorted phase of the OAM beams, and the influence of different CBM shapes are studied in detail by numerical simulations. The corresponding numerical results show the feasibility and efficacy of the CBM-HIOA used for the adaptive optics compensation of OAM beams.

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.

Distorted wavefront detection of orbital angular momentum beams based on a Shack-Hartmann wavefront sensor

The vortex beams carried Orbital Angular Momentum (OAM) have recently generated considerable interest due to their potential used in communication systems to increase transmission capacity and spectral efficiency. In this paper, the distorted wavefront detection based on Shack-Hartmann wavefront sensor (HWS) for the vortex beams is investigated. The detection slope of the helical phase sub-spot pattern is used as the calibrated slope zero point, and then the distortion phase of the vortex beam is detected by the HWS. Simulation and experimental results demonstrate that this method can detect the distortion phase of vortex beam with high precision and high frame rate, which is expected to accelerate the application of optical communication systems with vortex beams.

Orbital angular momentum mode diversity gain in optical communication

Vortex beams carrying orbital angular momentum (OAM) modes show superior multiplexing abilities in enhancing communication capacity. However, the signal fading induced by turbulence noise severely degrades the communication performance and even leads to communication interruption. Herein, we propose a diversity gain strategy to mitigate signal fading in OAM multiplexing communication and investigate the gain combination and channel assignment to optimize the diversity efficiency and communication capacity. Endowing signals with distinct channel matrices and superposing them with designed channel weights, we perform the diversity gain with an optimal gain efficiency, and the signal fading is mitigated by equalizing the turbulence noise. For the tradeoff between turbulence noise tolerance and communication capacity, multiplexed channels are algorithm-free assigned for diversity and multiplexing according to bit-error-rate and outage probability. As a proof of concept, we demonstrate a 6-channel multiplexing communication, where 3 OAM modes are assigned for diversity gain and 24 Gbit/s QPSK-OFDM signals are transmitted. After diversity gain, the bit-error-rate decreases from 1.41 × 10^-2 to 1.63 × 10^-4 at -14 dBm, and the outage probability of 86.7% is almost completely suppressed.

Polarized deep diffractive neural network for sorting, generation, multiplexing, and de-multiplexing of orbital angular momentum modes

The multiplexing and de-multiplexing of orbital angular momentum (OAM) beams are critical issues in optical communication. Optical diffractive neural networks have been introduced to perform sorting, generation, multiplexing, and de-multiplexing of OAM beams. However, conventional diffractive neural networks cannot handle OAM modes with a varying spatial distribution of polarization directions. Herein, we propose a polarized optical deep diffractive neural network that is designed based on the concept of dielectric rectangular micro-structure meta-material. Our proposed polarized optical diffractive neural network is optimized to sort, generate, multiplex, and de-multiplex polarized OAM beams. The simulation results show that our network framework can successfully sort 14 kinds of orthogonally polarized vortex beams and de-multiplex the hybrid OAM beams into Gauss beams at two, three, and four spatial positions, respectively. Six polarized OAM beams with identical total intensity and eight cylinder vector beams with different topology charges have also been sorted effectively. Additionally, results reveal that the network can generate hybrid OAM beams with high quality and multiplex two polarized linear beams into eight kinds of cylinder vector beams.

Complex amplitude field reconstruction in atmospheric turbulence based on deep learning

In this paper, we use deep neural networks (DNNs) to simultaneously reconstruct the amplitude and phase information of the complex light field transmitted in atmospheric turbulence based on deep learning. The results of amplitude and phase reconstruction by four different training methods are compared comprehensively. The obtained results indicate that the training method that can more accurately reconstruct the complex amplitude field is to input the amplitude and phase pattern pairs into the neural network as two channels to train the model.

Engineering pupil function for optical adversarial attacks

Adversarial attacks inject imperceptible noise to images to deteriorate the performance of deep image classification models. However, most of the existing studies consider attacks in the digital (pixel) domain where an image acquired by an image sensor with sampling and quantization is recorded. This paper, for the first time, introduces a scheme for optical adversarial attack, which physically alters the light field information arriving at the image sensor so that the classification model yields misclassification. We modulate the phase of the light in the Fourier domain using a spatial light modulator placed in the photographic system. The operative parameters of the modulator for adversarial attack are obtained by gradient-based optimization to maximize cross-entropy and minimize distortion. Experiments based on both simulation and a real optical system demonstrate the feasibility of the proposed optical attack. We show that our attack can conceal perturbations in the image more effectively than the existing pixel-domain attack. It is also verified that the proposed attack is completely different from common optical aberrations such as spherical aberration, defocus, and astigmatism in terms of both perturbation patterns and classification results.

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.

Optical diffractive deep neural network-based orbital angular momentum mode add-drop multiplexer

Vortex beams have application potential in multiplexing communication because of their orthogonal orbital angular momentum (OAM) modes. OAM add-drop multiplexing remains a challenge owing to the lack of mode selective coupling and separation technologies. We proposed an OAM add-drop multiplexer (OADM) using an optical diffractive deep neural network (ODNN). By exploiting the effective data-fitting capability of deep neural networks and the complex light-field manipulation ability of multilayer diffraction screens, we constructed a five-layer ODNN to manipulate the spatial location of vortex beams, which can selectively couple and separate OAM modes. Both the diffraction efficiency and mode purity exceeded 95% in simulations and four OAM channels carrying 16-quadrature-amplitude-modulation signals were successfully downloaded and uploaded with optical signal-to-noise ratio penalties of ∼1 dB at a bit error rate of 3.8 × 10^-3. This method can break through the constraints of conventional OADM, such as single function and poor flexibility, which may create new opportunities for OAM multiplexing and all-optical interconnection.

Free-space optical communication with quasi-ring Airy vortex beam under limited-size receiving aperture and atmospheric turbulence

Vortex beams carrying orbital angular momentum (OAM), which feature helical wavefronts, have been regarded as an alternative degree of freedom for free-space optical (FSO) communication systems. However, in practical applications, atmospheric turbulence and limited-size receiving aperture effects will cause OAM modal degradation and seriously reduce the received power. In this paper, by controlling the radial phase distribution of conventional OAM beams, quasi-ring Airy vortex beams (QRAVBs) are successfully generated in the experiments to increase the received power under the limited-size receiving aperture conditions. By employing 72-Gbit/s 16-ary quadrature amplitude modulation (16-QAM) discrete multi-tone (DMT) signals, we successfully demonstrate free-space data transmission with QRAVBs in the experiments. Moreover, the transmission performance of QRAVBs under atmospheric turbulence is also evaluated. Comparing with conventional OAM beam and Bessel beam, the obtained results show that QRAVBs can achieve higher received power and better BER performance under limited-size receiving aperture and atmospheric turbulence conditions.

Intra-symbol frequency-domain averaging for turbulence mitigation in optical orbital angular momentum multiplexing

Optical vortex beams (VBs) possessing helical phase-front have attracted considerable attention in multiplexing communication for their orthogonal orbital angular momentum (OAM) modes. However, the mode-crosstalk and signal jitter caused by turbulence fluctuation are two main challenges in OAM multiplexing communication. Here, we introduce an intra-symbol frequency-domain averaging technology (ISFA) for turbulence mitigation. By equalizing the distorted multiplexing signals, ISFA mitigates the amplitude and phase jitter of received signals without adding system complexity and information redundancy. The experimental results show that VBs are successfully demultiplexed, and the transmission rate reaches 48 Gbit/s. After ISFA, the bit-error-rate of QPSK-OFDM signals is reduced from 1.10 × 10^-3 to 6.31 × 10^-4, and the error-vector-magnitude (EVM) is reduced from 31.69% to 26.29% under the turbulence strength of Cn2 = 1×10^-13m^-2/3 and equivalent transmission distance of 200 m. By combining ISFA with MIMO diversity gain, the EVM can be further reduced from 46.70% to 26.70%. These indicate that ISFA is available for turbulence mitigation and compatible with MIMO technology, which may have perspective potential in improving the performance of OAM multiplexing communication.

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.

Using Machine Learning Algorithms for Accurate Received Optical Power Prediction of an FSO Link over a Maritime Environment

The performance prediction of an optical communications link over maritime environments has been extensively researched over the last two decades. The various atmospheric phenomena and turbulence effects have been thoroughly explored, and long-term measurements have allowed for the construction of simple empirical models. The aim of this work is to demonstrate the prediction accuracy of various machine learning (ML) algorithms for a free-space optical communication (FSO) link performance, with respect to real time, non-linear atmospheric conditions. A large data set of received signal strength indicators (RSSI) for a laser communications link has been collected and analyzed against seven local atmospheric parameters (i.e., wind speed, pressure, temperature, humidity, dew point, solar flux and air-sea temperature difference). The k-nearest-neighbors (KNN), tree-based methods-decision trees, random forest and gradient boosting- and artificial neural networks (ANN) have been employed and compared among each other using the root mean square error (RMSE) and the coefficient of determination (R2) of each model as the primary performance indices. The regression analysis revealed an excellent fit for all ML models, indicative of their ability to offer a significant improvement in FSO performance modeling as compared to traditional regression models. The best-performing R2 model found to be the ANN approach (0.94867), while random forests achieved the most optimal RMSE result (7.37).

Free space optic channel monitoring using machine learning

Free space optic (FSO) is a type of optical communication where the signal is transmitted in free space instead of fiber cables. Because of this, the signal is subject to different types of impairments that affect its quality. Predicting these impairments help in automatic system diagnosis and building adaptive optical networks. Using machine learning for predicting the signal impairments in optical networks has been extensively covered during the past few years. However, for FSO links, the work is still in its infancy. In this paper, we consider predicting three channel parameters in FSO links that are related to amplified spontaneous emission (ASE) noise, turbulence, and pointing errors. To the best of authors knowledge, this work is the first to consider predicting FSO channel parameters under the effect of more than one impairment. First, we report the performance of predicting the FSO parameters using asynchronous amplitude histogram (AAH) and asynchronous delay-tap sampling (ADTS) histogram features. The results show that ADTS histogram features provide better prediction accuracy. Second, we compare the performance of support vector machine (SVM) regressor and convolutional neural network (CNN) regressor using ADTS histogram features. The results show that CNN regressor outperforms SVM regressor for some cases, while for other cases they have similar performance. Finally, we investigate the capability of CNN regressor for predicting the channel parameters for three different transmission speeds. The results show that the CNN regressor has good performance for predicting the OSNR parameter regardless of the value of transmission speed. However, for the turbulence and pointing errors, the prediction under low speed transmission is more accurate than under high speed transmission.

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.

Single-pixel pattern recognition with coherent nonlinear optics

In this Letter, we propose and experimentally demonstrate a nonlinear-optics approach to pattern recognition with single-pixel imaging and a deep neural network. It employs mode-selective image up-conversion to project a raw image onto a set of coherent spatial modes, whereby its signature features are extracted optically in a nonlinear manner. With 40 projection modes, the classification accuracy reaches a high value of 99.49% for the modified national institute of standards and technology handwritten digit images, and up to 95.32%, even when they are mixed with strong noise. Our experiment harnesses rich coherent processes in nonlinear optics for efficient machine learning, with potential applications in online classification of large-size images, fast lidar data analyses, complex pattern recognition, and so on.

Jointly recognizing OAM mode and compensating wavefront distortion using one convolutional neural network

In this work, a new recognition method of orbital angular momentum (OAM) is proposed. The method combines mode recognition and the wavefront sensor-less (WFS-less) adaptive optics (AO) by utilizing a jointly trained convolutional neural network (CNN) with the shared model backbone. The CNN-based AO method is implicitly applied in the system by providing additional mode information in the offline training process and accordingly the system structure is rather concise with no extra AO components needed. The numerical simulation result shows that the proposed method can improve the recognition accuracy significantly in different conditions of turbulence and can achieve similar performance compared with AO-combined methods.

Assisting target recognition through strong turbulence with the help of neural networks

Imaging and target recognition through strong turbulence is regarded as one of the most challenging problems in modern turbulence research. As the aggregated turbulence distortion inevitably degrades remote targets and makes them less recognizable, both adaptive optics approaches and image correction methods will become less effective in retrieving correct attributes of the target. Meanwhile, machine learning (ML)-based algorithms have been proposed and studied using both hardware and software approaches to alleviate turbulence effects. In this work, we propose a straightforward approach that treats images with turbulence distortion as a data augmentation in the training set, and investigate the effectiveness of the ML-assisted recognition outcomes under different turbulence strengths. Retrospectively, we also apply the recognition outcomes to evaluate the turbulence strength through regression techniques. As a result, our study helps to build a deep connection between turbulence distortion and imaging effects through a standard perceptron neural network (NN), where mutual inference between turbulence levels and target recognition rates can be achieved.

Free-space 16-ary orbital angular momentum coded optical communication system based on chaotic interleaving and convolutional neural networks

Recently, orbital angular momentum (OAM) rays passing through free space have attracted the attention of researchers in the field of free-space optical communication systems. Throughout free space, the OAM states are subject to atmospheric turbulence (AT) distortion leading to crosstalk and power discrepancies between states. In this paper, a novel chaotic interleaver is used with low-density parity-check coded OAM-shift keying through an AT channel. Moreover, a convolutional neural network (CNN) is used as an adaptive demodulator to enhance the performance of the wireless optical communication system. The detection process with the conjugate light field method in the presence of chaotic interleaving has a better performance compared to that without chaotic interleaving for different values of propagation distance. Also, the viability of the proposed system is verified by conveying a digital image in the presence of distinctive turbulence conditions with different error correction codes. The impacts of turbulence strength, transmission distance, signal-to-noise ratio (SNR), and CNN parameters and hyperparameters are investigated and taken into consideration. The proposed CNN is chosen with the optimal parameter and hyperparameter values that yield the highest accuracy, utmost mean average precision (MAP), and the largest value of area under curve (AUC) for the different optimizers. The simulation results affirm that the proposed system can achieve better peak SNR values and lower mean square error values in the presence of different AT conditions. By computing accuracy, MAP, and AUC of the proposed system, we realize that the stochastic gradient descent with momentum and the adaptive moment estimation optimizers have better performance compared to the root mean square propagation optimizer.

Turbulence aberration correction for vector vortex beams using deep neural networks on experimental data

The vector vortex beams (VVB) possessing non-separable states of light, in which polarization and orbital angular momentum (OAM) are coupled, have attracted more and more attentions in science and technology, due to the unique nature of the light field. However, atmospheric transmission distortion is a recurring challenge hampering the practical application, such as communication and imaging. In this work, we built a deep learning based adaptive optics system to compensate the turbulence aberrations of the vector vortex mode in terms of phase distribution and mode purity. A turbulence aberration correction convolutional neural network (TACCNN) model, which can learn the mapping relationship of intensity profile of the distorted vector vortex modes and the turbulence phase generated by first 20 Zernike modes, is well designed. After supervised learning plentiful experimental samples, the TACCNN model compensates turbulence aberration for VVB quickly and accurately. For the first time, experimental results show that through correction, the mode purity of the distorted VVB improves from 19% to 70% under the turbulence strength of D/r0 = 5.28 with correction time 100 ms. Furthermore, both spatial modes and the light intensity distribution can be well compensated in different atmospheric turbulence.

Mode Selective Up-conversion Detection with Turbulence

We experimentally study a nonlinear optical approach to selective manipulation and detection of structured images mixed with turbulent noise. Unlike any existing adaptive-optics method by applying compensating modulation directly on the images, here we account for the turbulence indirectly, by modulating only the pump driving the nonlinear process but not the images themselves. This indirect approach eliminates any signal modulation loss or noise, while allowing more flexible and capable operations. Using specifically sum frequency generation in a lithium niobate crystal, we demonstrate selective upconversion of Laguerre-Gaussian spatial modes mixed with turbulent noise. The extinction reaches ~40 dB without turbulence, and maintains ~20 dB in the presence of strong turbulence. This technique could find utilities in classical and quantum communications, compressive imaging, pattern recognition, and so on.

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

Orbital angular momentum (OAM), a new dimension of photons, has potentials in lots of domains as high-dimensional data coding/decoding. Here we experimentally demonstrate a free-space data transmission system based on 8 bits multi-state OAM shift keying, where multiplexed optical vortices containing 8 various OAM states are employed to constitute 8 bits binary symbols. In the transmitter, the data coding of OAM shift keying is realized by switching a series of special-designed holograms. And in the receiver, the decoding is done by a single Dammann vortex grating along with image processing. We experimentally transmit data, including a gray-scale image, in free-space for 10 meters, showing zero bit-error-rate. The demonstrated results indicate a wide prospect for the future high-dimensional large data rate optical security communications.