Learning to decompose the modes in few-mode fibers with deep convolutional neural network

General error analysis of matrix-operation-mode decomposition technique in few-mode fiber laser

The mode decomposition based on matrix operation (MDMO) is one of the fastest mode decomposition (MD) techniques, which is important to the few-mode fiber laser characterization and its applications. In this paper, the general error of the MDMO technique was analyzed, where different influencing factors, such as position deviation of the optical imaging system, coordinate deviation of the image acquisition system, aberrations, and mode distortion were considered. It is found that the MDMO technique based on far-field intensity distribution is less affected by optical imaging system position deviation, coordinate deviation of the image acquisition system, and mode distortion than those based on direct near-field decomposition. But far-field decomposition is more affected by aberration than those based on near-field decomposition. In particular, the numerical results show that the deviation of the coordinate axis direction is an important factor limiting the accuracy of MD. In addition, replacing the ideal eigenmode basis with a distorted eigenmode basis can effectively suppress the decrease in mode decomposition accuracy caused by fiber bending. Moreover, based on detailed numerical analysis results, fitting formulas for estimating the accuracy of the MDMO technique with imperfections are also provided, which provides a comprehensive method for evaluating the accuracy of the MDMO technique in practical engineering operations.

Flexible design of chiroptical response of planar chiral metamaterials using deep learning

Optical chirality is highly demanded for biochemical sensing, spectral detection, and advanced imaging, however, conventional design schemes for chiral metamaterials require highly computational cost due to the trial-and-error strategy, and it is crucial to accelerate the design process particularly in comparably simple planar chiral metamaterials. Herein, we construct a bidirectional deep learning (BDL) network consists of spectra predicting network (SPN) and design predicting network (DPN) to accelerate the prediction of spectra and inverse design of chiroptical response of planar chiral metamaterials. It is shown that the proposed BDL network can accelerate the design process and exhibit high prediction accuracy. The average process of prediction only takes ∼15 ms, which is 1 in 40000 compared to finite-difference time-domain (FDTD). The mean-square error (MSE) loss of forward and inverse prediction reaches 0.0085 after 100 epochs. Over 95.2% of training samples have MSE ≤ 0.0042 and MSE ≤ 0.0044 for SPN and DPN, respectively; indicating that the BDL network is robust in the inverse deign without underfitting or overfitting for both SPN and DPN. Our founding shows great potentials in accelerating the on-demand design of planar chiral metamaterials.

Spatiotemporal mode-locking and dissipative solitons in multimode fiber lasers

Multimode fiber (MMF) lasers are emerging as a remarkable testbed to study nonlinear spatiotemporal physics with potential applications spanning from high energy pulse generation, precision measurement to nonlinear microscopy. The underlying mechanism for the generation of ultrashort pulses, which can be understood as a spatiotempoal dissipative soliton (STDS), in the nonlinear multimode resonators is the spatiotemporal mode-locking (STML) with simultaneous synchronization of temporal and spatial modes. In this review, we first introduce the general principles of STML, with an emphasize on the STML dynamics with large intermode dispersion. Then, we present the recent progress of STML, including measurement techniques for STML, exotic nonlinear dynamics of STDS, and mode field engineering in MMF lasers. We conclude by outlining some perspectives that may advance STML in the near future.

On similarity metrics evaluating the performance of mode decomposition in few-mode optical fibers

Mode decomposition refers to a set of techniques aimed to recover modal content in multimode optical fibers. In this Letter, we examine the appropriateness of the similarity metrics commonly used in experiments on mode decomposition in few-mode fibers. We show that the conventional Pearson correlation coefficient is often misleading and should not be used as the sole criterion for justifying decomposition performance in the experiment. We consider several alternatives to the correlation and propose another metric that most accurately reflects the discrepancy between complex mode coefficients, given received and recovered beam speckles. In addition, we show that such a metric enables transfer learning of deep neural networks on experimental data and tangibly ameliorates their performance.

Analysis of an image noise sensitivity mechanism for matrix-operation-mode-decomposition and a strong anti-noise method

Mode decomposition (MD) based on the matrix operation (MDMO) is one of the fastest mode decomposition methods in fiber laser which has great potential for optical communications, nonlinear optics and spatial characterization applications. However, we found that the image noise sensitivity is the main limit to the accuracy of the original MDMO method, but improving the decomposition accuracy by using conventional image filtering methods is almost ineffective. By using the norm theory of matrices, the analysis result shows that both the image noise and the coefficient matrix condition number determine the total upper-bound error of the original MDMO method. Besides, the greater the condition number, the more sensitive of MDMO method is to noise. In addition, it is found that the local error of each mode information solution in the original MDMO method is different, which depends on the L2-norm of each row vector of the inverse coefficient matrix. Moreover, a more noise-insensitive MD method is achieved by screening out the information corresponding to large L2-norm. In particular, selecting the higher accuracy among the original MDMO method and such noise-insensitive method as the result in a single MD process, a strong anti-noise MD method was proposed in this paper, which displays high MD accuracy in strong noise for both near-filed and far-filed MD cases.

Theoretical and experimental studies on intermodal nonlinear effects of a high-power near-single-mode CW Yb-doped fiber laser

An intermodal-nonlinearity-induced time-frequency evolution model of high-power near-single-mode continuous-wave fiber lasers (NSM-CWHPFLs) was proposed to simulate the evolution of spectral characteristics and beam quality under the combined action of intermodal and intramodal nonlinear effects. The influence of fiber laser parameters on intermodal nonlinearities was analyzed, and a suppression method involving fiber coiling and seed mode characteristic optimization was proposed. Verification experiments were conducted with 20/400, 25/400, and 30/600 fiber-based NSM-CWHPFLs. The results demonstrate the accuracy of the theoretical model, clarify the physical mechanisms of nonlinear spectral sidebands, and demonstrate the comprehensive optimization of intermodal-nonlinearity-induced spectral distortion and mode degradation.

Seeing the strong suppression of higher order modes in single trench fiber using the S2 technique

The single trench fiber (STF) is a promising fiber design for mode area scaling and higher order mode (HOM) suppression. In this Letter, we experimentally demonstrate the strong HOM-suppression in a homemade STF using the spatially and spectrally resolved imaging (S²) technique. This STF has a 20-µm core and its performance is compared to a conventional step-index fiber with almost the same parameter. Results show that the bending loss of the HOM in STF is 8-times larger than conventional fiber at a bend radius of 7 cm. In addition, when severe coupling mismatch is introduced at the input end of the fiber, the STF can keep the fundamental-mode output while the conventional fiber cannot. To the best of our knowledge, this is the first time to experimentally analyze the HOM content in an STF and compare its performance with that of a conventional fiber. Our results indicate the great potential of the STF for filtering the HOM in fiber laser applications.

Contribution to the Improvement of the Correlation Filter Method for Modal Analysis with a Spatial Light Modulator

Modal decomposition of light is essential to study its propagation properties in waveguides and photonic devices. Modal analysis can be carried out by implementing a computer-generated hologram acting as a match filter in a spatial light modulator. In this work, a series of aspects to be taken into account in order to get the most out of this method are presented, aiming to provide useful operational procedures. First of all, a method for filter size adjustment based on the standard fiber LP-mode symmetry is presented. The influence of the mode normalization in the complex amplitude encoding-inherent noise is then investigated. Finally, a robust method to measure the phase difference between modes is proposed. These procedures are tested by wavefront reconstruction in a conventional few-mode fiber.

Complete modal decomposition of a few-mode fiber based on ptychography technology

An exact modal decomposition method plays an important role in revealing the modal characteristics of a few-mode fiber, and it is widely used in various applications ranging from imaging to telecommunications. Here, ptychography technology is successfully used to achieve modal decomposition of a few-mode fiber. In our method, the complex amplitude information of the test fiber can be recovered by ptychography, and then the amplitude weight of each eigenmode and the relative phase between different eigenmodes can be easily calculated by modal orthogonal projection operations. In addition, we also propose a simple and effective method to realize coordinate alignment. Numerical simulations and optical experiments validate the reliability and feasibility of the approach.

High-performance mode decomposition using physics- and data-driven deep learning

A novel physics- and data-driven deep-learning (PDDL) method is proposed to execute complete mode decomposition (MD) for few-mode fibers (FMFs). The PDDL scheme underlies using the embedded beam propagation model of FMF to guide the neural network (NN) to learn the essential physical features and eliminate unexpected features that conflict with the physical laws. It can greatly enhance the NN's robustness, adaptability, and generalization ability in MD. In the case of obtaining the real modal weights (ρ2) and relative phases (θ), the PDDL method is investigated both in theory and experiment. Numerical results show that the PDDL scheme eliminates the generalization defect of traditional DL-based MD and the error fluctuation is alleviated. Compared with the DL-based MD, in the 8-mode case, the errors of ρ2 and θ can be reduced by 12 times and 100 times for beam patterns that differ greatly from the training dataset. Moreover, the PDDL maintains high accuracy even in the 8-mode MD case with a practical maximum noise factor of 0.12. In terms of adaptation, with a large variation of the core radius and NA of the FMF, the error keeps lower than 0.43% and 2.08% for ρ2 and θ, respectively without regenerating new dataset and retraining NN. The experimental configuration is set up and verifies the accuracy of the PDDL-based MD. Results show that the correlation factor of the real and reconstructed beam patterns is higher than 98%. The proposed MD-scheme shows much potential in the application of practical modal coupling characterization and laser beam quality analysis.

M2 factor estimation in few-mode fibers based on a shallow neural network

A high-accuracy, high-speed, and low-cost M² factor estimation method for few-mode fibers based on a shallow neural network is presented in this work. Benefiting from the dimensionality reduction technique, which transforms the two-dimension near-field image into a one-dimension vector, a neural network with only two hidden layers can estimate the M² factor directly. In the simulation, the mean estimation error is smaller than 3% even when the mode number increases to 10. The estimation time of 10000 simulation test samples is around 0.16s, which indicates a high potential for real-time applications. The experiment results of 50 samples from the 3-mode fiber have a mean estimation error of 0.86%. The strategies involved in this method can be easily extended to other applications related to laser characterization.

High-power cylindrical vector beam fiber laser based on an all-polarization-maintaining structure

We propose and demonstrate an all-polarization-maintaining (PM) high-power cylindrical vector beam (CVB) fiber laser based on the principle of mode superposition. The non-degenerated LPy 11a is generated from the oscillator with the maximum power of 11.9W, whose slope efficiency is 24.4%. Then the stable single TE₀₁ vector beam is achieved by the superposition of LPy 11a and LPx 11b in an all-PM architecture, its output power is 3.1W and mode purity of 91.2%. Due to the all-PM architecture, our configuration is free of adjusting polarization controller (PC) and reliable during long-term operation. This laser could be used as a high-power CVBs source for a wide range of applications towards scientific research and industrial field.

Modal decomposition of an incoherent combined laser beam based on the combination of residual networks and a stochastic parallel gradient descent algorithm

With the increase of the superimposed eigenmodes number, the traditional numerical modal decomposition (MD) technique will inevitably suffer from ambiguity and local minima problems and thus is typically unsuitable for conducting modal decomposition of an incoherent combined laser beam. In this paper, we propose a novel, to the best of our knowledge, MD algorithm, named ResNet-SPGD, which combines the advantages of residual networks (ResNet) and stochastic parallel gradient descent (SPGD) algorithm. Via setting the modal mode coefficients obtained from the CNN model as the initial value of the SPGD algorithm, such algorithm shows an attractive solution to mitigate the problem of modal ambiguity. The proposed algorithm is preliminarily applied to the modal decomposition of an incoherent combined laser beam, and the feasibility is demonstrated via numerical simulations. Complete MD is performed with high accuracy, and the only cost is the sacrifice of some real-time capacity.

Deep learning-based ballistocardiography reconstruction algorithm on the optical fiber sensor

Ballistocardiography (BCG) is a vibration signal related to cardiac activity, which can be obtained in a non-invasive way by optical fiber sensors. In this paper, we propose a modified generative adversarial network (GAN) to reconstruct BCG signals by solving signal fading problems in a Mach-Zehnder interferometer (MZI). Based on this algorithm, additional modulators and demodulators are not needed in the MZI, which reduces the cost and hardware complexity. The correlation between reconstructed BCG and reference BCG is 0.952 in test data. To further test the model performance, we collect special BCG signals including sinus arrhythmia data and post-exercise cardiac activities data, and analyze the reconstructed results. In conclusion, a BCG reconstruction algorithm is presented to solve the signal fading problem in the optical fiber interferometer innovatively, which greatly simplifies the BCG monitoring system.

Adjusted EfficientNet for the diagnostic of orbital angular momentum spectrum

Orbital angular momentum (OAM) is one of multiple dimensions of beams. A beam can carry multiple OAM components, and their intensity weights form the OAM spectrum. The OAM spectrum determines complex amplitude distributions of a beam and features unique characteristics. Thus, measuring the OAM spectrum is of great significance, especially for OAM-based applications. Here we employ a deep neural network combined with a phase-only diffraction optical element to measure the OAM spectrum. The diffraction optical element is designed to diffract incident beams into distinct patterns corresponding to OAM distributions. Then, the EfficientNet, a kind of deep neural network, is adjusted to adapt and analyze the diffraction pattern to calculate the OAM spectrum. The favorable experimental results show that our proposal can reconstruct the OAM spectra with high precision and speed, works well for different numbers of OAM channels, and is also robust to Gaussian noise and random zooming. This work opens a new, to the best of our knowledge, ability for OAM spectrum recognition and will find applications in a number of advanced domains including large capacity optical communications, quantum key distribution, optical trapping, rotation detection, and so on.

2D least-squares mode decomposition for mode division multiplexing

We investigate a fast and accurate technique for mode decomposition in multimode optical fibers. Initial decomposition task of near-field beam patterns is reformulated in terms of a system of linear equations, requires neither machine learning nor iterative routines. We apply the method to step and graded-index fibers and compare the decomposition performance. We determine corresponding application boundaries, propose an efficient algorithm for phase retrieval and carry out a specific preselective procedure that increases the number of decomposable modes and makes it possible to handle up to fifteen modes in presence of realistic noise levels.

Surveillance of few-mode fiber-communication channels with a single hidden layer neural network

Multi- and few-mode fibers (FMFs) promise to enhance the capacity of optical communication networks by orders of magnitude. The key for this evolution was the strong advancement of computational approaches that allowed inherent complex light transmission to be surpassed, learned, or controlled, reined in by modal crosstalk and mode-dependent losses. However, complex light transmission through FMFs can be learned by a single hidden layer neural network (NN). The emerging developments in NNs additionally allow the implementation of novel concepts for security enhancements in optical communication. Once the transmission characteristics of FMFs are learned, it is possible to survey the incoming and outgoing light fields via monitoring channels during data transmission. If an eavesdropper tries to gain unauthorized access to the FMF, its transmission properties are impaired through sensitive modal crosstalk. This process is registered by the NN and thus the eavesdropper is revealed. With our solution, the security of optical communication can be improved.

Modal decomposition of complex optical fields using convolutional neural networks

Recent studies have shown convolutional neural networks (CNNs) can be trained to perform modal decomposition using intensity images of optical fields. A fundamental limitation of these techniques is that the modal phases cannot be uniquely calculated using a single intensity image. The knowledge of modal phases is crucial for wavefront sensing, alignment, and mode matching applications. Heterodyne imaging techniques can provide images of the transverse complex amplitude and phase profiles of laser beams at high resolutions and frame rates. In this work, we train a CNN to perform modal decomposition using simulated heterodyne images, allowing the complete modal phases to be predicted. This is, to our knowledge, the first machine learning decomposition scheme to utilize complex phase information to perform modal decomposition. We compare our network with a traditional overlap integral and center-of-mass centering algorithm and show that it is both less sensitive to beam centering and on average more accurate in our simulated images.

Intensity-only-measurement mode decomposition in few-mode fibers

Recovery of optical phases using direct intensity detection methods is an ill-posed problem and some prior information is required to regularize it. In the case of multi-mode fibers, the known structure of eigenmodes is used to recover optical field and find mode decomposition by measuring intensity distribution. Here we demonstrate numerically and experimentally a mode decomposition technique that outperforms the fastest previously published method in terms of the number of modes while showing the same decomposition speed. This technique improves signal-to-noise ratio by 10 dB for a 3-mode fiber and by 7.5 dB for a 5-mode fiber.

Sub-sampled modal decomposition in few-mode fibers

Retrieving modal contents from a multimode beam profile can provide the most detailed information of a beam. Numerical modal decomposition is a method of retrieving modal contents, and it has gained significant attention owing to its simplicity. It only requires a measured beam profile and an algorithm. Therefore, a complicated setup is not necessary. In this study, we conceived that the modal decomposition can be notably improved by data-efficiently sub-sampling the beam image instead of using full pixels of a beam profiler. By investigating the window size, the number of pixels, and algorithm for sub-sampling, the calculation time for the algorithm was faster by approximately 100 times than the case of full pixel modal decomposition. Experiments with 3-mode and 6-mode beams, which originally span 201×201 and 251×251 pixels, respectively, confirmed the remarkable improvement of calculation speed while maintaining the error function at a level of ∼10^-3. This first demonstration of sub-sampling for modal decomposition is based on the modified stochastic parallel gradient descent algorithm. However, it can be applied to other numerical or artificial intelligence algorithms and can enhance real-time analysis or active control of beam characteristics.

CNN-based few-mode fiber modal decomposition method using digital holography

Modal decomposition (MD) has become an indispensable analysis approach for revealing the modal characteristics of optical fibers. A new MD approach based on the convolutional neural network (CNN) is presented to retrieve the exact superposition of eigenmodes of few-mode fibers. Using the near-field beam intensity and phase patterns obtained from digital holography, not only the amplitude of each eigenmode but also the exact phase difference between the higher-order modes and the fundamental mode can be predicted. Numerical simulations validate the reliability and feasibility of the approach. When ten modes in the few-mode fiber are considered, the similarities of the intensity and phase pattern between the reconstructed fields and the given fields can achieve to 97.0% and 85.6%, respectively.

Vortex soliton oscillation in a mode-locked laser based on broadband long-period fiber grating

Optical vortex beams (OVBs) have attracted much attention in diverse applications and spatiotemporal mode locking for optical soliton formation. In this Letter, a compact mode-locked (ML) vortex fiber laser is demonstrated based on a broadband long-period fiber grating near the dispersion turnaround point, where the group velocities between the core modes of ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ in a two-mode fiber are matched. The OVB pulses with first-order orbital angular momentum are oscillated through broadband mode conversion inside the cavity. The time-stretch dispersive Fourier transform method is also employed for the observation of vortex soliton buildup dynamics. The study of vortex soliton oscillation motivates the development towards controlling vortex modes in the ML fiber lasers.

Fast fiber mode decomposition with a lensless fiber-point-diffraction interferometer

Recently, the growing interest in few-mode fibers in telecommunications and high-power lasers has stimulated the demand for fiber mode decomposition (MD). Here we present a fast fiber MD method with a lensless fiber-point-diffraction interferometer. The complex amplitude at the fiber end is achieved by the polarization phase-shifting technique and the lensless imaging technique. Then, the eigenmode coefficients are determined by the mode orthogonal operations of the complex amplitude. In the experiment, the SMF-28e fiber containing 10 linear polarized modes at the wavelength of 632.8 nm is studied for MD. The decomposition of the 50 * 50 pixels interferograms takes only 0.0168 s. The similarity of the intensity patterns of the testing light is larger than 97% before and after the MD. This new, to the best of our knowledge, method can achieve fast and accurate 10-mode MD without using any imaging systems.

Experimental investigation of quasi-static mode degradation in a high power large mode area fiber amplifier

In this work, quasi-static mode degradation in high power fiber amplifiers has been investigated experimentally. An increase of M² from 1.3 to 2.6 with distortion of the beam profile is observed, which results in the signal spectra and backward light characterization departing from the traditional phenomena. The amplifier has been operated at the same input pump power of 705 W for nearly 2.2 hours to investigate the relationship between quasi-static mode degradation and photodarkening. The evolution of M² factor/beam profile, mode correlation coefficient and output laser power at different working times indicate that the quasi-static mode degradation in the high power fiber amplifiers is dependent on photodarkening and evolves on the scale of tens of minutes. A visible green light has been injected to photobleach the gain fiber for 19 hours, which reveals that the quasi-static mode degradation has been suppressed simultaneously. To the best of our knowledge, this is the first detail report of photodarkening-induced quasi-static degradation in high power fiber amplifiers.

Comparing Performance of Deep Convolution Networks in Reconstructing Soliton Molecules Dynamics from Real-Time Spectral Interference

Deep neural networks have enabled the reconstruction of optical soliton molecules with more complex structures using the real-time spectral interferences obtained by photonic time-stretch dispersive Fourier transformation (TS-DFT) technology. In this paper, we propose to use three kinds of deep convolution networks (DCNs), including VGG, ResNets, and DenseNets, for revealing internal dynamics evolution of soliton molecules based on the real-time spectral interferences. When analyzing soliton molecules with equidistant composite structures, all three models are effective. The DenseNets with layers of 48 perform the best for extracting the dynamic information of complex five-soliton molecules from TS-DFT data. The mean Pearson correlation coefficient (MPCC) between the predicted results and the real results is about 0.9975. Further, the ResNets in which the MPCC achieves 0.9906 also has the better ability of phase extraction than VGG which the MPCC is about 0.9739. The general applicability is demonstrated for extracting internal information from complex soliton molecule structures with high accuracy. The presented DCNs-based techniques can be employed to explore undiscovered mechanisms underlying the distribution and evolution of large numbers of solitons in dissipative systems in experimental research.

Dynamic vortex mode-switchable erbium-doped Brillouin laser pumped by high-order mode

We experimentally demonstrated that the transversal vortex modes of an all-fiber erbium-doped Brillouin laser can be dynamically switched by using the high-order mode (HOM) of Brillouin pump (BP), which is used to achieve the oscillation of HOM inside the ring cavity. Core-mode conversion in a few-mode fiber (FMF) between the fundamental mode and HOM is obtained by cascading an acoustically induced fiber grating (AIFG) and a mode selection coupler (MSC) operating at the same wavelength region. Through frequency shift keying (FSK) modulation of the AIFG signal, the output transversal modes can be switched dynamically between LP₀₁ and vortex modes, and the measured purities of output HOM are more than 82%. Moreover, the output Brillouin wavelength can also be tuned via altering the input wavelength of BP and the resonant response of AIFG. We have achieved HOM Brillouin-shifted laser output within the wavelength band from 1545-1560 nm. The output linewidth of the proposed Brillouin laser is less than 4 kHz.

Fast mode decomposition in few-mode fibers

Retrieval of the optical phase information from measurement of intensity is of a high interest because this would facilitate simple and cost-efficient techniques and devices. In scientific and industrial applications that exploit multi-mode fibers, a prior knowledge of spatial mode structure of the fiber, in principle, makes it possible to recover phases using measured intensity distribution. However, current mode decomposition algorithms based on the analysis of the intensity distribution at the output of a few-mode fiber, such as optimization methods or neural networks, still have high computational costs and high latency that is a serious impediment for applications, such as telecommunications. Speed of signal processing is one of the key challenges in this approach. We present a high-performance mode decomposition algorithm with a processing time of tens of microseconds. The proposed mathematical algorithm that does not use any machine learning techniques, is several orders of magnitude faster than the state-of-the-art deep-learning-based methods. We anticipate that our results can stimulate further research on algorithms beyond popular machine learning methods and they can lead to the development of low-cost phase retrieval receivers for various applications of few-mode fibers ranging from imaging to telecommunications.

Characterizing the modes at the output of a multimode fiber is time consuming due to computational cost. Here the authors present an algorithm for few-mode-fiber mode decomposition with a fast processing time and using only intensity measurements.

Accurate stacked-sheet counting method based on deep learning

The accurate counting of laminated sheets, such as packing or printing sheets in industry, is extremely important because it greatly affects the economic cost. However, the different thicknesses, adhesion properties, and breakage points and the low contrast of sheets remain challenges to traditional counting methods based on image processing. This paper proposes a new stacked-sheet counting method with a deep learning approach using the U-Net architecture. A specific dataset according to the characteristics of stack side images is collected. The stripe of the center line of each sheet is used for semantic segmentation, and the complete side images of the slices are segmented via training with small image patches and testing with original large images. With this model, each pixel is classified by multi-layer convolution and deconvolution to determine whether it is the target object to be detected. After the model is trained, the test set is used to test the model, and a center region segmentation map based on the pixel points is obtained. By calculating the statistical median value of centerline points across different sections in these segmented images, the number of sheets can be obtained. Compared with traditional image algorithms in real product counting experiments, the proposed method can achieve better performance with higher accuracy and a lower error rate.

Optical circular dichroism engineering in chiral metamaterials utilizing a deep learning network

Here, a deep learning (DL) algorithm based on deep neural networks is proposed and employed to predict the chiroptical response of two-dimensional (2D) chiral metamaterials. Specifically, these 2D metamaterials contain nine types of left-handed nanostructure arrays, including U-like, T-like, and I-like shapes. Both the traditional rigorous coupled wave analysis (RCWA) method and DL approach are utilized to study the circular dichroism (CD) in higher-order diffraction beams. One common feature of these chiral metamaterials is that they all exhibit the weakest intensity but the strongest CD response in the third-order diffracted beams. Our work suggests that the DL model can predict CD performance of a 2D chiral nanostructure with a computational speed that is four orders of magnitude faster than RCWA but preserves high accuracy. The DL model introduced in this work shows great potentials in exploring various chiroptical interactions in metamaterials and accelerating the design of hypersensitive photonic devices.

Fast modal analysis for Hermite-Gaussian beams via deep learning

The eigenmodes of Hermite-Gaussian (HG) beams emitting from solid-state lasers make up a complete and orthonormal basis, and they have gained increasing interest in recent years. Here, we demonstrate a deep learning-based mode decomposition (MD) scheme of HG beams for the first time, to the best of our knowledge. We utilize large amounts of simulated samples to train a convolutional neural network (CNN) and then use this trained CNN to perform MD. The results of simulated testing samples have shown that our scheme can achieve an averaged prediction error of 0.013 when six eigenmodes are involved. The scheme takes only about 23 ms to perform MD for one beam pattern, indicating promising real-time MD ability. When larger numbers of eigenmodes are involved, the method can also succeed with slightly larger prediction error. The robustness of the scheme is also investigated by adding noise to the input beam patterns, and the prediction error is smaller than 0.037 for heavily noisy patterns. This method offers a fast, economic, and robust way to acquire both the mode amplitude and phase information through a single-shot intensity image of HG beams, which will be beneficial to the beam shaping, beam quality evaluation, studies of resonator perturbations, and adaptive optics for resonators of solid-state lasers.

Deep Learning for Computational Mode Decomposition in Optical Fibers

Multimode fibers are regarded as the key technology for the steady increase in data rates in optical communication. However, light propagation in multimode fibers is complex and can lead to distortions in the transmission of information. Therefore, strategies to control the propagation of light should be developed. These strategies include the measurement of the amplitude and phase of the light field after propagation through the fiber. This is usually done with holographic approaches. In this paper, we discuss the use of a deep neural network to determine the amplitude and phase information from simple intensity-only camera images. A new type of training was developed, which is much more robust and precise than conventional training data designs. We show that the performance of the deep neural network is comparable to digital holography, but requires significantly smaller efforts. The fast characterization of multimode fibers is particularly suitable for high-performance applications like cyberphysical systems in the internet of things.

Deep learning enabled superfast and accurate M2 evaluation for fiber beams

We introduce deep learning technique to predict the beam propagation factor M² of the laser beams emitting from few-mode fiber for the first time, to the best of our knowledge. The deep convolutional neural network (CNN) is trained with paired data of simulated near-field beam patterns and their calculated M² value, aiming at learning a fast and accurate mapping from the former to the latter. The trained deep CNN can then be utilized to evaluate M² of the fiber beams from single beam patterns. The results of simulated testing samples have shown that our scheme can achieve an averaged prediction error smaller than 2% even when up to 10 eigenmodes are involved in the fiber. The error becomes slightly larger when heavy noises are added into the input beam patterns but still smaller than 2.5%, which further proves the accuracy and robustness of our method. Furthermore, the M² estimation takes only about 5 ms for a prepared beam pattern with one forward pass, which can be adopted for real-time M² determination with only one supporting Charge-Coupled Device (CCD). The experimental results further prove the feasibility of our scheme. Moreover, the method we proposed can be confidently extended to other kinds of beams provided that adequate training samples are accessible. Deep learning paves the way to superfast and accurate M² evaluation with very low experimental efforts.

Adaptive phase correction of dynamic multimode beam based on modal decomposition

We propose and demonstrate a method for the adaptive phase correction of dynamic multimode fiber beams. The phase of incident beam is reconstructed in real-time based on the complete modal information, which obtained by using the modal decomposition of correlation filter method. For the proof of principle, both of the modal decomposition and the phase correction are implemented using the same computer-generated hologram, which was encoded into a phase-only spatial light modulator. We demonstrate the phase correction of dynamic multimode beam at a rate of 5 Hz and achieve a 1.73-fold improvement on the average power-in-the-bucket. The experimental results indicate the feasibility of the real-time phase correction for the large mode area fiber laser by adaptive optics.