Phase-sensitive optical time-domain reflection (Φ-OTDR) has the advantages of high accuracy, fast response speed, long monitoring distance, and anti-electromagnetic interference and has been widely used in dynamic sensing fields such as perimeter security and railway and pipeline monitoring. For direct detection intensity-demodulation Φ-OTDR, the pulse power is limited by the nonlinear effect, which causes a weak signal-to-noise ratio of the end signal, and its sensing distance is usually less than 25 km. Because the optical phase signal is linearly related to the vibration signal imposed on the fiber and coherent detection can significantly improve the detection sensitivity, the long-distance Φ-OTDR system mainly uses coherent detection and phase demodulation technology. Most coherent detection phase-demodulation Φ-OTDR system model recognition algorithms use phase signal as the input, combined with time-frequency feature extraction methods, such as Fourier transform and wavelet transform. However, interference fading occurs in the coherent detection system, which causes serious deterioration of the intensity signal, resulting in phase demodulation errors and false alarms. Common methods to eliminate interference fading are the frequency diversity, chirped pulses, and other frequency domain regulation technologies, which lead to complex system hardware. Moreover, owing to the variety of the disturbance signals and long sensing distance that results in a low signal-to-noise ratio of the end signal, Φ-OTDR systems suffer from false alarms in practical applications. It is of great significance to further improve the accuracy of the vibration signal identification for the timely detection of abnormal events.

A pattern recognition method based on a coherent detection Φ-OTDR system with mixed intensity and phase signal inputs is proposed, which can effectively reduce the impact of interference fading on the accuracy of event alarms without increasing the hardware complexity. The proposed method uses a hybrid deep neural network (HDNN), which combines a one-dimensional convolutional neural network (1DCNN) and a multi-layer perceptron (MLP), as shown in Fig. 4. The phase and intensity signal vectors are recovered simultaneously using the Hilbert demodulation algorithm. The phase and intensity vectors within a second are simply normalized by the max-min and tanh functions separately and then fed into the model. The model uses MLP to extract the fading noise features of the intensity signal and uses the 1DCNN model as the basic model to extract the disturbance characteristics of the phase signal. After the fusion of two-dimensional features and a classification layer, the model outputs the final detection results.

A long-distance Φ-OTDR system of more than 25 km was built. An adjustable optical attenuator (VOA) was used to simulate disturbance events occurring at different locations along the fiber, with attenuation of the VOA ranging from 1 dB to 7 dB. Four types of events, such as human beatings, walking, jumping, and machine excavating, are imposed at the outdoor optical cable buried 0.5 m underground. A 1DCNN network with only phase signal input was used as the comparison model. After multiple rounds of training, the experimental results show that the proposed HDNN model with intensity and phase signal inputs can achieve an average accuracy of 98.8%, which is better than the 1DCNN model result of 96.1% with only the phase signal input. Furthermore, comparing the confusion matrix of the two models, the 1DCNN model had the worst recognition accuracy of 91.0% with background noise and human beat events. In contrast, the HDNN model significantly improves the recognition accuracy of the two events to 99.4%. This shows that the interference fading anomalies contained in the background noise can be identified by the HDNN model with additional intensity input. For the other three types of events, the accuracy results of the two models are very close, indicating that the phase signal has a better ability to recover the vibration events than the intensity signal, which is consistent with the previous analysis.

Aiming to further improve the event alarm accuracy of the long-distance coherent detection Φ-OTDR system, a pattern recognition method with a mixed input of intensity and phase signals was proposed. To verify the improvement of the proposed method, a 1DCNN network with only the phase signal input was used as the comparison model. A hybrid deep neural network, combining 1DCNN and MLP, was used for the intensity and phase signal mixed-input classification. The model used MLP to extract the fading noise features of the intensity signal and used 1DCNN to extract the disturbance features of the phase signal. The phase and intensity vectors within a second are simply normalized by the max-min and tanh functions separately and then fed into the model. The experimental results show that the proposed HDNN model can achieve an average accuracy of 98.8% for four types of events, including human beatings, walking, jumping, and machine excavation, which is better than the 1DCNN model detection result of 96.1% with only a phase signal input. The method using intensity signal-assisted phase signal detection can further improve the accuracy of Φ-OTDR pattern recognition.

With the development of unmanned aerial vehicle (UAV) and wireless laser communication technology, as well as the continuous maturity of related devices, UAV laser communication has emerged as the current research hot spot because of its unique advantages in scientific detection, emergency rescue, and military reconnaissance. In UAV laser communication, atmospheric effect (including atmospheric absorption, scattering, and atmospheric turbulence) and pointing error are the two main factors that cause deterioration of link performance. Therefore, establishing a suitable channel model is essential to completely understand the dynamic communication process of UAV laser communication. Existing studies assume that the pointing errors between the communication terminals are identically distributed in the azimuth and elevation directions although they cannot accurately describe the random jitter characteristics of the actual UAV platform. In this study, the pointing characteristics of the oscillating mirror type laser communication terminal are analyzed, whereby a more realistic Hoyt distribution pointing error model is established, to obtain an expression for the joint channel probability density function. The accuracy of the proposed model is verified by numerical simulations and experimental analysis.

To accurately analyze the link performance of laser communication between UAVs, a more realistic Hoyt distribution pointing error model is established. First, the probability distribution of the pointing error angle of the oscillating mirror type laser communication terminal was calculated by using the vector reflection law and the rotation transformation matrix. Furthermore, a joint channel probability density function expression was derived considering atmospheric attenuation, atmospheric turbulence, and pointing error. Subsequently, the effects of different turbulence intensities and different UAV jitter variances on link performance were analyzed. Finally, to verify the correctness of the proposed pointing error model, we tested the pointing error angle of the system using the multi-rotor UAV equipped with laser communication equipment.

The pointing error of the UAV laser communication terminal was tested outdoors. The experimental system consisted of a multi-rotor UAV platform and an oscillating mirror type laser communication terminal (Fig. 6). When the initial azimuth and elevation angles are both zero, the attitude measurement unit on the laser communication terminal, measures the azimuth and elevation angles of the terminal in real-time and obtains the probability distributions of the error angles for the azimuth, elevation, and combined pointing. The results show that the terminal azimuth error angle follows a normal distribution with mean of 0 and standard deviation of 0.4° (Fig. 7); the elevation error angle follows a normal distribution with mean of 0 and standard deviation of 0.05° (Fig. 8); the combined pointing error angle obeys the Hoyt distribution (Fig. 9). The above experimental results were substituted into formula (15), the simulation results are consistent with the experimental data fitting results, which proves the correctness of the pointing error model.

This study investigated the channel model of laser communication between UAVs and proposed a method for solving the pointing error of the oscillating mirror type laser communication terminal. A more realistic Hoyt distribution pointing error model was established to accommodate the different jitter variances of the UAV platform in the azimuth and elevation directions, thereby deriving the probability density function expression of the joint channel. Finally, the pointing error model was verified by numerical simulations and experiments. The experimental results show that the azimuth and elevation pointing error angles of UAV conform to the normal distribution, with mean 0 and standard deviations of 0.4° and 0.05°, respectively. The combined pointing error angle conforms to the Hoyt distribution. The experimental results match the simulation results well, validating the correctness of the pointing error model.

Underground mine environments are intricate and complex, and maintaining smooth and stable communication in addition to the real-time positioning of miners is beneficial for the safety of mining operations. Visible light communication has several advantages: no electromagnetic radiation, no radio interference, and low implementation cost. It can be employed in areas with strict requirements of electromagnetic radiation, such as mining. Additionally, it can provide high-speed communication and high-precision positioning underground. The majority of current research on visible light communication and localization is focused on the indoor environment; however, research on the mining environment is limited, especially in the aspect of simultaneous consideration of multiple influencing factors in the channel model, there is still a large research space. This study proposes a method for constructing a visible channel model based on point cloud data in mines by considering two factors, irregular stone walls and random tilt at the receiver end, in the channel model, and dividing the reflective surface elements based on wall point cloud data using the point-by-point insertion method to compensate for the lack of integration of the theoretical channel model with real data. The effectiveness of the proposed model is verified by combining the genetic algorithm with the optimized back-propagation (BP) neural network localization algorithm.

First, the normal vectors of the tilted receiver end and reflective surface elements on the irregular wall are represented, and the incident angle of the reflective surface elements, radiation angle, and incident angle of the receiver end are calculated using the normal vectors. The calculated angles are replaced by the corresponding angles in the conventional model to complete the theoretical modeling. Subsequently, the point cloud data collected by a binocular camera is converted to a coordinate system, and the normal vector is calculated by plane fitting using the least squares method to correct the plane of the point cloud image. Based on the processed point cloud data, the reflective surface elements are divided using the point-by-point insertion method. The coordinates of each triangular reflective surface element vertex are determined according to the reflective surface element topology, and the corresponding normal vector, area, and center of gravity of each surface element are calculated and replaced with the corresponding values in the theoretical model to combine the theoretical model and real data. Finally, based on the fingerprint localization method, the localization algorithm of BP neural network optimized by a genetic algorithm (GA) is used in the simulation space to complete the application of the proposed model.

The two real stone walls used for data acquisition are used as the two sides of the simulation space, which have a size of 5.0 m×4.0 m×3.5 m. In the case of the ideal wall, the average power of primary reflection is 0.1487 W, and the average contribution ratio is 15.22%. After considering the uneven wall, the average power of primary reflection increases to 0.1811 W, and the average contribution ratio becomes 30.37%. When considering both the uneven wall and the inclined receiver, the average power of primary reflection and the average contribution ratio are 0.1674 W and 29.48%, respectively. After considering the roughness of the real wall surface, the power distribution at the edge of the primary reflection power is affected by the irregular wall surface, showing unevenness, and the maximum power of the non-line of sight (NLOS) link is significantly increased, while the random tilt of the receiver end causes the uneven spatial distribution of the received power (Fig. 8). Using the model built in this study and GA-BP algorithm for positioning, the root mean square positioning errors when only considering direct light and considering primary reflection are 9.83 cm and 13.4 cm, respectively (Fig. 12). Because the model built in this study combines the real data of the wall, the relationship between the coordinates of each reference point and primary reflection power becomes more random. Therefore, the root mean square positioning error of the proposed model when considering primary reflection increases by 36.62% compared with that when only considering direct light, while the root mean square positioning error of the traditional channel model only increases by 0.8% (Table 4). In addition, this study also compares the localization effects of BP and GA-BP neural networks when using the model proposed in this study, and the root mean square localization error is 84.7 cm and 13.4 cm, respectively (Table 5). Compared with the BP neural network, the error of the GA-BP localization algorithm is reduced by 84.18%, which effectively improves the localization accuracy.

This study focuses on the effects of uneven walls and random tilting of the receiver end on the visible light communication (VLC) channel under a mine, proposes a method to construct a VLC channel model combining realistic data with 3D point cloud technology, and applies the established channel model to visible light localization using a GA-BP localization algorithm to explore the effects of primary reflection and tilted receiver end on the localization accuracy. In the simulated tunnel of 5.0 m×4.0 m×3.5 m, the average total received powers obtained by using the conventional and proposed channel models are 0.1487 W and 0.1674 W, respectively. The average contribution ratio of primary reflection is about twice that of the conventional model, suggesting that primary reflection and wall concavity must be considered when studying visible light communication and localization underground. However, the localization accuracy of the conventional channel model is 2.51 cm while that of the proposed channel model is 13.4 cm when using the GA-BP algorithm for the case with primary reflection. The channel model developed in this study provides an effective way to research visible light communication and localization in mines and has good application value.

In recent years, the popularity of artificial intelligence (AI) has provided a new incentive for advances in science and technology in the laser industry, further promoting its rapid development and wide application. To present a clear view of the empowering effect of AI on lasers and facilitate further development of this emerging field, it is important to identify the advancements, opportunities, and challenges of AI-enabled lasers. Therefore, this work begins with a review of the progress in this field, from component design to system optimization and from laser property characterization to laser application. Then, we provide a preliminary analysis and outlook on the opportunities, challenges, and two-way empowerment of the laser and AI disciplines.

By analyzing published research articles indexed in the Web of Science, AI-assisted laser development can be divided into five parts: optimal design of laser components, optimal design of laser systems, intelligent control and optimization of laser beams, accurate characterization and prediction of laser properties, and optimization of laser application effectiveness. Regarding the optimal design of laser components, AI-assisted device design not only improves design efficiency but also allows better parameter optimization, which can aid optimization of laser systems and can play an important role in laser generation, transmission, and application. In terms of the optimal design of laser systems, AI can avoid complex physical principles for modeling and establish mapping between the laser performance and structural parameters, which accelerates the optimum design of the laser system for improved performance. Regarding intelligent control and optimization of laser beams, one example is the coherent beam combination (CBC). The control bandwidth is a bottleneck that limits implementation of large-scale CBC systems. An AI-assisted CBC system can overcome this limitation, and methods for coherently combining more than 100 beams are proposed. For the accurate characterization and prediction of laser properties, AI-enabled characterization technology can secure fast, accurate, and robust characterization of the mode content, beam quality, and pulse duration of lasers and shows great potential for the characterization of other properties of laser beams. In terms of the optimization of laser application effectiveness, AI can ignore the complex, highly nonlinear physical problems of light-matter interactions that occur during the laser-machining process and can achieve high-quality laser cutting/welding/additive manufacturing by establishing a mapping between the laser parameters and the processing quality.

In summary, AI technology is widely applied in laser research and applications. However, the rapid development of laser technology may also have a catalytic effect on the field of AI, ultimately creating a positive incentive for ‘two-way empowerment.'

AI-assisted lasers are expected to promote innovation and development of laser technology at the material, device, and system levels. At the material level, AI can help analyze and select laser materials by facilitating in-depth exploration of traditional optical fibers, semiconductors, and other materials, and expand the boundaries of the use of existing materials by improving their performance. At the device level, AI can revolutionize the design and development of laser-related devices. Data-driven modeling can provide theoretical analysis tools for complex laser phenomena and reveal the deeper physical mechanisms. Highly accurate device models can serve for the reverse design of specific device characteristics and enable multidimensional and comprehensive device function customization. At the system level, AI can provide efficient tools for the integration of laser systems, allowing for the simulation of operations during the system development phase, timely identification of potential problems, and efficient shaping and implementation of large and complex laser systems. AI-driven scientific research is a new frontier of AI, which has already been effective in several disciplines and is expected to inspire further breakthroughs in the future.

AI-assisted lasers not only result in breakthroughs in laser-performance indicators but also lead to breakthroughs in laser concepts, which may gradually become an enabling technology that is "used every day without realizing it" and can make future laser systems more attractive.

Furthermore, the development of laser technology can contribute to further development of AI by advancing arithmetic power. The current electronic computing performance relies on semiconductor lithography processes, and laser light sources are important factors supporting the continuous progress of lithography processes. In the future, laser-enabled ultra-computing photonic computers will hopefully drive AI technology.

AI-driven scientific research is a new frontier in AI worldwide and is effective in several disciplines, and the next five years are a critical window for its breakthrough development. In addition to the cross-fertilization of different disciplines in the scientific research process, the development of interdisciplinary and highly qualified personnel during the process of scientific research and education is a long-term strategy for the future.

Looking ahead, there are both opportunities and challenges; however, evolving AI technologies will certainly continue to facilitate the development of disciplines, such as lasers, and gradually build a new paradigm of basic and cutting-edge research supported by AI.

With the advent of the information era, the development of artificial intelligence technology has undergone an unprecedented transformation, leading to a growing demand for computing resources and efficiency. However, conventional computers based on electronic transistors, constrained by von Neumann architectures, encounter performance bottlenecks in complex computing tasks such as deep neural networks and large-scale combinatorial optimizations. To circumvent the limitations of traditional computing hardware systems, researchers have begun exploiting the inherent properties of different physical systems for computation or computing acceleration, including quantum computing, DNA computing, neuromorphic computing, and optical computing.

Among the innovative computing approaches mentioned above, optical computing aims to construct all-optical or optoelectronic systems for information processing by leveraging the physical properties of light and the intricate interactions between light and matter. Optical computing excels in many complex computing tasks due to ultra-fast transmission speeds, high parallelism, and minimal energy consumption. Since the proposal of the optical correlator in the 1950s and 1960s, optical computing has consistently drawn the attention of researchers across various fields. With emerging concepts, such as on-chip optical neural networks, diffractive deep neural networks, optoelectronic reservoir computing, and photonic Ising machines, the application potential of photons in diverse complex computing tasks is becoming increasingly evident. It is not an exaggeration to state that photons are evolving into one of the foundations of next-generation computing.

Lasers, as high-performance light sources, play a crucial role in industrial manufacturing and scientific research. Generated by laser cavities, laser has been widely employed in fabrication, measurement, communication, medicine, and other fields. In recent years, researchers have discovered that lasers can also serve as powerful computational tools. Specifically, the randomness and nonlinearity of lasers in chaotic oscillations, relaxation oscillations, and other unsteady states can be harnessed to address complex calculation problems. Additionally, in the absence of external disturbances, physical processes, such as mode competition, can cause the light field in laser cavities to spontaneously evolve into a stable oscillation state with the lowest loss, which can be mapped to the solution of a complex computation problem. As optical computing continues to advance, and laser generation, control, and detection technologies mature, there is a growing interest in the computational capabilities of lasers. Therefore, it is essential to summarize the progress of optical computing based on laser cavities to guide the further integration of lasers and artificial intelligence technology, ultimately promoting the development of intelligent laser computing systems.

In this review, we comprehensively summarize the recent progress in optical computing based on laser cavities, primarily focusing on reinforcement learning using laser chaos, reservoir computing by lasers with optical delayed feedback, and spin models for solving combinatorial optimization problems simulated by laser networks.

Firstly, we introduce methods that utilize laser chaos signals generated by semiconductor lasers to perform reinforcement learning (RL). Naruse et al. initially demonstrated RL assisted by laser chaos, which served as random numbers, and proved that laser chaos signals outperform pseudorandom numbers generated by conventional electronic circuitry in this calculation task. Subsequent research aiming at scalability and parallelism improvement is also discussed (Fig. 2). To further exploit the properties of oscillations within laser cavities, RL based on mode switching in a ring laser, lag synchronization of coupled lasers and laser networks, and chaotic itinerancy in a multimode semiconductor laser have been proposed and demonstrated as well (Fig. 3).

Subsequently, we discuss optoelectronic reservoir computing (RC) based on lasers, mainly focusing on delay-based RC using lasers with optical delayed feedback. Since 2013, when Brunner et al. experimentally implemented reservoir computing using a semiconductor laser as the nonlinear node, numerous studies have been conducted to enhance performance. These include RC based on semiconductor ring lasers, microchip lasers, vertical cavity surface-emitting lasers, and photonic integrated circuits (Fig. 6, Fig. 7).

Finally, we review recent advances in simulating spin models using laser networks. Artificial spin models can be employed to solve NP-hard combinatorial optimization problems, as their ground states are associated with the solutions. Under certain circumstances, the steady oscillation state of a laser network system can be mapped to the ground state of the spin Hamiltonian, and thus, to the solution of the combinatorial optimization problem. Photonic Ising machines based on injection-locked laser networks (Fig. 8) and XY model simulators based on degenerate cavity lasers (Fig. 11) are outlined, respectively. Additionally, other types of challenging computational problems solved by degenerate cavity lasers are presented, including real-time wavefront shaping, phase retrieval, generation of arbitrary-shaped laser beams, and real-time full-field imaging through scattering media (Fig. 12).

In addition to the inherent advantages of optical computing, such as ultra-fast transmission speed, high parallelism, and negligible energy consumption, laser-based optical computing fully utilizes the unique physical processes occurring in laser cavities, as well as various mature laser technologies, to provide a wealth of solutions for complex computing tasks. In the future, the theoretical model of optical computing based on laser cavities needs further optimization to continuously expand its application in various intelligent computing fields and to improve calculation accuracy, scale, and dimension. Additionally, with the exploration and development of intelligent algorithms and optoelectronic devices that are better suited for optical computing, combined with rapidly advancing online training and in situ training schemes, intelligent laser computing is expected to gradually achieve all-optical, high-efficiency, and real-time performance. Furthermore, by utilizing novel laser cavity structures, advanced laser technologies, and photon integration technologies, along with metamaterial and metasurface technologies, it is anticipated that more compact on-chip intelligent laser computing systems will be developed. In summary, the establishment of high-speed and high-efficiency intelligent laser systems for information processing and computation is a significant and promising research direction that encompasses the simultaneous development of hardware, software, and algorithms.

Machine learning is a specialized study on computer simulation and learning human behavior for obtaining new knowledge and skills and on reorganizing existing knowledge structure and skill to continuously improve performance. It is the core of artificial intelligence and the fundamental way of making computers intelligent. Machine learning is a multi-disciplinary subject, involving probability theory, statistics, approximation theory, convex analysis, and algorithm complexity theory. Its algorithm is widely used in many fields of engineering and science, and has advantages in terms of classification, pattern recognition, prediction, system parameter optimization, and building complex dynamic models from observations.

Ultrafast optical systems are usually complex, nonlinear, and multidimensional, and their dynamics are extremely sensitive to internal parameters and external disturbances. The design and optimization of these systems are generally based on physical models, numerical simulation, and trial and error approach. Owing to the increase in system complexity, these methods have reached their limits. Thus far, the application of machine learning in ultra-fast optics is mostly based on genetic algorithms or feedforward architecture. Although these implementations have undoubtedly brought significant results, there are still some limitations that need to be resolved . The machine learning neural network technology can find relationships among the state variables of the systems, which provides a new way to explore nonlinear dynamic systems without solving complex mathematical and physical equations. The generated nonlinear model can also be used to design and control laser characteristics. Pulse optimization in ultrafast experiments may involve multiple parameters, which are interrelated in complex ways. This is a field where neural networks can significantly surpass other forms of manual or partial automatic control. In addition, it is extremely challenging to process the data generated by ultrafast optical experiments. Traditional data processing requires to filter out the influence of noise. Solving the time-dependent Schr?dinger equation or using iterative algorithm makes the process extremely cumbersome and time-consuming. The neural network is based on the mathematics, and provides a new method combined with physical principles for efficient analysis and processing of ultrafast experimental data. Therefore, neural network has a good application prospect in the field of optics.

This review highlights the application of neural networks in ultrafast optics. Neural network plays an active role in the self-tuning and coherent dynamics control of ultrafast fiber lasers. In the processing of ultrafast optical experimental data, neural networks are applied to the study of ultrafast laser propagation dynamics, measurement of ultrafast pulse information, calculation of complex systems, and data mining involving physical laws.

Neural network has high application potential in ultrafast optical systems. On the one hand, the computing power of computer hardware is improved, which can efficiently process massive data and support more complex neural networks. On the other hand, the improvement in algorithm enables neural networks deal with more complex problems. The combination of neural networks and genetic algorithms or different types of neural networks can jointly explore the potential of machine learning and make more progress in understanding and optimizing nonlinear systems. In addition, the ability of unsupervised learning to infer and reveal hidden internal structures from datasets without labels is extremely important for noise-sensitive experimental data processing. However, there are also challenges in the application of neural networks in ultrafast optics. First, as a mathematical computing tool, neural network lacks the physical meaning. Although there have been works to integrate physical laws into the algorithms, it is still a challenge to intuitively obtain physical laws from the converged training results. Second, the training results of neural networks depend heavily on the quantity and quality of training data. However, sometimes the experimental conditions are limited and only a small amount of data can be obtained. Although training data can be obtained through theoretical simulation, the lack of noise and disturbance in the experimental environment challenges the generalization and robustness of the algorithms.

In summary, in the past few years, machine learning neural network has made significant progress in its application in ultrafast optics, and related achievements have emerged endlessly. With the progress of neural network algorithms and the development of ultrafast optics technology, we can expect that ultrafast optics study becomes more intelligent, more convenient, more automatic, and more accurate to reveal physical laws.

Laser is an important strategic technology that has been widely used in the processing, communication, military, and medical fields. Lasers are also indispensable tools for observing complex, multi-dimensional optical phenomena, especially in physics, biology, materials science, and astronomy. Laser possesses various modulable orthogonal physical dimensions, including wavelength, pulse width, repetition rate, intensity, phase, and polarization, which are the main objectives of laser manipulation. To explore new phenomena with high dimensions, laser manipulation is no longer limited to a single dimension, and the joint manipulation of multiple dimensions of laser is imperative.

Multi-dimensional (multi-mode) laser is important for breaking the bottleneck of single-mode laser performance, and it provides new opportunities for multidisciplinary research. Different from traditional single-mode lasers, multi-dimensional lasers exhibit a complex optical field that can be controlled through delicate tuning of the numerous parameters, but this complicacy also results in challenging manipulation of the performance of the multi-dimensional laser. Recently, with the rapid development of artificial intelligence, intelligent control techniques, particularly machine learning, have been widely applied to improve the performance of complex optical systems, which promotes the fast iteration of intelligent optics and related fields, elucidating the intelligent control of multi-dimensional lasers.

Here, we provide a literature review on the research progress of intelligent control in the field of multi-dimension laser manipulation from the aspects of in-cavity and out-of-cavity manipulation. First, in-cavity manipulation can be used in self-optimizing mode-locked lasers (Fig. 4) and precise control of the specific state (Fig. 5). The application of intelligent algorithms in multi-dimensional manipulation can be further explored using spatiotemporal mode-locked fiber lasers based on in-cavity manipulation. Subsequently, the applications of out-of-cavity manipulation in parameter control of laser beam (Fig. 10), dynamics in fibers (Fig. 11), and multi-dimensional information reconstruction of the light field (Fig. 13) are elaborated. Finally, we discuss the potential of intelligently-controlled multi-dimensional laser technology in the fields of optical micromanipulation (Fig. 15), laser micromachining (Fig. 17), and laser communication (Fig. 19). Future developments of multi-dimensional laser technologies with intelligent manipulation are discussed, and the possible problems and challenges are also discussed.

Driven by frontier exploration, intelligent manipulation of multi-dimensional laser technologies based on machine learning tools has become an important foundation for the study of complex physical phenomena and cross-disciplinary problems. With the increasing complexity of multi-dimensional laser systems, new intelligent manipulation techniques shoulds be exploited.

Laser manufacturing is an important component of advanced manufacturing technology, which has the advantages of high processing accuracy, wide applicability of materials, flexible non-contact processing, no loss, minimal deformation, and ease of automation integration. It has played an important role in the fields including aerospace, national defense, military, new energy vehicles, and biomedicine. It conforms to the advanced manufacturing trends of both intelligent and green manufacturing. With the popularity of the Internet and the advancement of big data technology, artificial intelligence (AI) has flourished in the past decade, providing great convenience in people's lives and promoting the transformation of the manufacturing industry from traditional to intelligent manufacturing. Applying AI to product design, production, management, and other aspects can help improve resource utilization efficiency, production efficiency, product quality, and service levels for enterprises to create greater economic value for society. Laser manufacturing and AI is becoming increasingly intertwined, driven by the rise of AI and interdisciplinary integration. AI is being utilized in various aspects of laser manufacturing, including beam shaping, beam correction, laser welding, laser cutting, laser polishing, laser additive manufacturing, and micro-nano processing. The performance of laser manufacturing equipment plays a vital role in the quality of the final product, and the application of AI to equipment design and management can improve the reliability and performance of laser equipment. Additionally, the difference of processing parameters has important influence on product quality. By establishing the relationship between processing parameters and product quality with the help of AI, the production efficiency can be improved and the production cost can be reduced significantly.

High-performance equipment is an important hardware base for high-precision and high-quality laser manufacturing. The instability of laser parameters or beam transmitting devices can lead to beam quality degradation, and in turn, poor machining quality. AI can be used to predict the translation/rotation state, output energy, phase mode, beam propagation factor, and other parameters of the beam to generate a high-quality laser beam and ensure the stability of the manufacturing process (Fig. 1). To meet the requirements of high-precision, high-efficiency manufacturing, AI is applied to beam shaping to improve the flexibility and controllability of the manufacturing process (Fig. 2). Meanwhile, AI can aid in fault detection, real-time status monitoring, and diagnosing issues in laser equipment, which not only helps to maintain normal equipment operation, but also ensures reliability and availability of laser equipment and reduces the risks of downtime and maintenance costs (Fig. 3). With the development of AI technology, its applications in laser manufacturing technologies, such as laser cutting, laser drilling, laser surface treatment, laser additive manufacturing, and laser welding, are becoming increasingly widespread, effectively improving the efficiency and quality of laser manufacturing. In the field of laser cutting, AI can not only predict the results to improve cutting efficiency, but also establish the relationship between the process parameters and cutting quality to obtain the best process parameters, reducing cutting roughness and slit width (Fig. 4). In the field of laser polishing, AI can obtain the best process parameters quickly by predicting the polishing results and ensure the stability of the polishing process through online monitoring (Fig. 5). In the field of laser cutting/drilling bones, AI can be used to process image and acoustic signals during the drilling process to achieve real-time identification of biological tissue types. Furthermore, it can be used for process optimization to achieve high-quality processing of biological bone materials (Figs. 6 and 7). In the field of laser welding, AI is currently used to predict welding quality, detect welding defects, and optimize welding process parameters (Fig. 8). In the field of laser additive manufacturing, AI assists in designing material compositions for superior mechanical properties, predicting tissue evolution and properties, constructing relationships between process parameters, optimizing additive manufacturing process, and monitoring the additive process in real time (Fig. 9).

The progress of AI has led to great changes in the manufacturing industry, promoting its development towards automation and intelligence. Laser manufacturing technology is one of the most promising advanced manufacturing technologies in the current manufacturing industry. The wide application of AI in laser manufacturing technology promotes its continuous progress. In this paper, the research status of AI in the field of laser manufacturing equipment and laser manufacturing technology is summarized. The applications of AI in beam control, equipment management, laser cutting, laser bone drilling, laser polishing, laser welding, and laser additive manufacturing are introduced. Although AI has not been widely used in practical production because of the challenges in creating algorithms, data processing, and hardware foundation, AI algorithms and data processing technology will be continuously improved, and the intelligent equipment industry will become increasingly mature. At that time, the coverage of AI in laser manufacturing will be further expanded, and the intelligence of laser manufacturing will be promoted effectively.

The invention of laser technology has had a transformative impact on society. Mode-locked fiber lasers have been widely used in research and industry, and they play an important role in basic science as a convenient nonlinear system. A mode-locked fiber laser is a complex nonlinear dissipative system with a large number of internal nonlinear dynamical phenomena that, in addition to outputting stable femtosecond pulses, exhibits a series of complex mode-locked states, including the breather locked mode, strange waves, noise-like locked modes, soliton explosions, and self-organized modes arising from soliton interactions, such as soliton molecules, soliton crystals, soliton complexes, and supramolecular structures. Even chaotic states have recently been discovered in mode-locked lasers. The study of these mode-locked states helps to understand the nonlinear dynamical properties of femtosecond fiber lasers. Additionally, because the femtosecond fiber laser is a universal nonlinear dissipative system, studying its dynamics can clarify the complex dynamics in related fields, such as Bose-Einstein condensation, microcavities, and oceanography. The intrinsic dynamics of these systems and the mode-locked laser are described uniformly by the nonlinear Schr?dinger equation and thus have similarities.

Owing to the presence of numerous mode-locked regions in mode-locked lasers, it has long been a challenging problem to control the parameters of the laser and thus access specific mode-locked states. For example, the most commonly used femtosecond fiber laser based on the nonlinear polarization rotational mode-locking technique is mathematically a multidimensional parametric space and experimentally requires tuning of at least seven parameters (pump, loss, dispersion, nonlinearity, and angles of the three waveplates) to traverse the entire parametric space. Because of the lack of a definite functional relationship between the mode-locking state and these parameters, a long trial-and-error process is needed to obtain the desired mode-locking state. In addition, even if the target locked mode is obtained, its repeatability is a problem.

Recently, a major breakthrough was made in intelligent mode-locked lasers, which can resolve the difficulty of precise control of mode-locked states. In 2015, Prof. Grelu’s group in France applied a genetic algorithm to the intelligent control of mode-locked lasers for the first time and realized the intelligent control of soliton pulses and noise-like pulses. Subsequently, the development of intelligent mode-locked lasers has accelerated. Hence, it is necessary to summarize the existing studies to rationally guide subsequent research in this area.

The principle of the commonly used smart locking algorithms and recent scientific research results are summarized. First, the principles of the genetic algorithm, human-like algorithm, and artificial neural network are explained, and a schematic (Fig.1) and architecture diagram (Fig.2) are presented. Then, recent scientific achievements in smart mode-locked lasers are described, including the first implementation of a soliton-locked mode in smart lasers by Andral et al. at the Université de Bourgogne, France (Fig.3); the development of genetic algorithms for soliton-locked mode recovery by Winters et al. at Kapteyn-Murnane Laboratories, USA (Fig.4); the development of the first smart programmable mode-locked laser by Pu et al. at Shanghai Jiao Tong University (Fig.5); and the development of the first smart programmable mode-locked laser using deep learning for intelligent mode-locking recovery by Yan et al. at the National University of Defense Technology (Fig.6). Subsequently, the realization of programmable control of the spectral width and spectral shape by Pu et al. of Shanghai Jiao Tong University (Fig.7) and the intelligent control of spatiotemporal mode-locking by Wei et al. of South China University of Technology (Fig.8) are elaborated. The intelligent regulation of the breather ultrafast laser is summarized, starting with the design of an adaptation function based on the radiofrequency signal of the breather locked mode (Fig.9), in which the relaxation oscillation dynamics and noise-like pulse dynamics in the laser are excluded (Fig.10). Then, experimental results of the genetic algorithm (Fig.11) are discussed, along with the control of the breather breathing ratio, the breathing period, and the number of pulses (Figs.12-14). Finally, the work related to the intelligent control of fractal respiratory subsets is briefly described. The differences in the spectra and stability of frequency-locked and non-frequency-locked breathers are examined (Figs.15 and 16), the evolutionary dynamics of fractal breathers are specified (Fig.17), and the intelligent search for fractal breathers is implemented using a smart laser based on a liquid-crystal phase delay (Figs.18 and 19).

This paper reviews the application of intelligent-control technology in passively mode-locked fiber lasers. Using intelligent-control technology, the automatic generation and control of the mode-locked state can be realized without manual tuning, which reduces the tuning time of the laser and improves the tuning accuracy as well as the repeatability of the mode-locked state. This self-optimizing ultrashort pulse laser has promising applications in certain environments. Although the passive mode-locked fiber laser is a complex dynamical system, the successful achievement of accurate tuning of multiple mode-locked states by genetic algorithms indicates the universality of these algorithms. A series of intelligent algorithms, including genetic algorithms, are expected to be applied to the intelligent control of more complex mode-locked states. The current intelligent-control technology focuses on controlling lasers and achieving automatic laser tuning. Whether intelligent-control techniques can have an impact on laser physics remains an open question.

Metamaterial design and fiber beam control are two important topics in the study of optical field manipulation. Metamaterials are artificial materials with periodic structures and physical properties that do not exist naturally in the world. Suitable structural designs are crucial for achieving the potential of metamaterials. Numerical calculations and parameter optimization methods such as finite difference time domain (FDTD), finite element method (FEM), rigorous coupled wave analysis (RCWA), and genetic algorithms are commonly used in metamaterials design. However, these methods suffer from high computational costs and strong dependence on expert experience. Specifically, the high computational cost is due to the complexity of solving partial differential equations, while the reliance on expert experience stems from the fact that these numerical calculation methods depend on physical modeling. Additionally, parameter optimization algorithms also suffer from high computational costs due to the explosion of parameter combinations and repeated calls to numerical computation methods. Therefore, many researchers have turned to deep learning methods, attempting to use a data-driven approach to allow neural network models to learn the mapping relationship between metamaterial structure and optical response during the feature learning process, thus achieving accurate and efficient metamaterial design while shielding underlying physical details.

Fiber beam control refers to adjusting parameters such as amplitude, phase, and polarization of a fiber optic beam to obtain novel features or stable states. Traditional methods mainly include genetic algorithms, stochastic parallel gradient descent (SPGD) algorithm, PID, and other search methods, which are limited by their inability to effectively solve system control problems in complex environments, i.e., speed and accuracy issues. These optimization methods have simple strategies that are unable to generate good behavioral paths, resulting in too many steps to reach the target state. Moreover, they mechanically respond to environmental states, making them vulnerable to system noise interference and limiting the accuracy of system output. Deep reinforcement learning overcomes these limitations by introducing a learning mechanism that can actively respond to environmental stimuli, making up for the shortcomings of traditional methods. Fiber beam control is a dynamic process that can be abstracted into a state machine, which is naturally suitable for control methods based on deep reinforcement learning. Therefore, for such or even more complex systems, deep reinforcement learning-based methods have considerable application prospects.

Multi-layer perceptron (MLP) is a simple and basic neural network model widely used in various metamaterial design works. Peurifoy et al. used MLP to complete the inverse design of an 8-layer spherical shell nanostructure [Fig. 7(a)]. Liu et al. proposed a method that combines forward prediction networks for spectra and inverse design networks for devices [Fig. 7(b)]. Du et al. developed a scalable multi-task learning (SMTL) model for designing low-dimensional nanostructures [Fig. 7(c)]. Zhao et al. released a data-enhanced iterative few-sample (DEIFS) algorithm based on data augmentation [Fig. 7(d)]. In addition to MLP, convolutional neural network (CNN) and generative adversarial network (GAN) are also commonly used network models. Zhu et al. proposed a transfer learning-based method for predicting metamaterials accurately and quickly using the pre-trained Inception V3 model on image data, achieving good results for binary metamaterial prediction [Fig. 8(a)]. Jiang et al. used GAN for the topology design of complex nano-devices, effectively solving the problem of time-consuming iterative optimization methods for designing complex devices, reducing design time by about 80% [Fig. 8(b)]. Sajedian et al. efficiently determined the optimal parameters for three-layer metamaterial devices among 23 different material types and geometry parameters using the double deep Q network (DDQN), greatly improving the computational transmittance efficiency of metamaterials [Fig. 8(c)]. Zhao et al. integrated the idea of reinforcement learning into the model and designed a data-enhanced deep greedy optimization (DEDGO) algorithm [Fig. 8(d)]. Sajedian et al. combined CNN with recurrent neural network (RNN) to predict the absorption spectra of nano-devices, which played an auxiliary role in device design [Fig. 8(e)].

In fiber beam control, the J. N. Kutz team at the University of Washington proposed using deep reinforcement learning algorithms to achieve automatic mode locking control of lasers from a simulation perspective in 2020 [Fig. 11(a)]. In 2021, the team led by researcher Jiang Tian at the National University of Defense Technology designed an automatic mode locking control laser system based on the DDPG strategy and the DELAY reinforcement learning algorithm [Fig. 11(b)]. In mid-2022, Li Zhan et al. from the Chinese Academy of Sciences designed a feedback control algorithm based on deep reinforcement learning and long short-term memory (LSTM) network models to stabilize the state of mode-locked lasers [Fig. 11(c)]. In the latter half of 2022, Luo Saiyu et al. from Nanjing University of Science and Technology applied the TD3 algorithm from deep reinforcement learning to an ultrafast green Ho:ZBLAN laser [Fig. 11(d)]. In 2023, the research team led by Jiang Tian at the National University of Defense Technology once again designed DRCON using reinforcement learning to control the stability of coherent optical neuron systems (Fig. 13).

This article focuses on recent research on deep learning in metamaterial design and fiber beam control. The introduction of deep learning has greatly promoted the development of both fields. Traditional methods face the following problems when dealing with increasingly complex optical systems: (1) inability to effectively transfer expert experience; (2) inability to avoid numerical calculations; and (3) a limited solvable problem space. Compared with traditional methods, deep learning methods can help isolate the underlying physical details to some extent, reducing the difficulty of design and control.

High power laser is an important application field of adaptive optics, and controlling a high-power laser system to achieve high-beam-quality laser output is an important goal of laser adaptive optics technology. To achieve high beam quality throughout the transmission of high-power laser to the target, adaptive optics must simultaneously correct the aberration of the high-power laser source, thermal effect and optical element aberration in the transmission channel, and atmospheric turbulence. Currently, adaptive optics has enabled the output beam of multimode high-power lasers to achieve near-diffraction limit beam quality; for example, the beam quality of a 1-MW DF chemical laser reaches twice the diffraction limit, and the average beam quality of a 105-kW solid-state laser is about 2.9. However, when promoting the practical application of high-power lasers with different systems in different working scenarios, adaptive optics still faces the following problems: 1) The near-field intensity distribution of high-power lasers is uneven, and there are large gradient aberrations locally. 2) In the case of strong turbulence transmission, the wavefront aberration has high spatio-temporal frequency characteristics, and some information of the wavefront is dynamically missing. 3) The signal-to-noise ratio and spatial resolution of the wavefront detector will be low due to the weak light and strong noise background of the dim target. 4) Platform vibration, temperature change, and other environmental factors will cause variation of the system model parameters. To solve these problems, researchers have developed a laser adaptive optics technique based on machine learning. This paper reviews the current intelligent development of laser adaptive optics based on machine learning in wavefront restoration, wavefront prediction, phase inversion, and wavefront correction, and the potential and challenges of current research methods used in the field of high-power laser are discussed.

In this paper, the research progress of laser adaptive optics techniques based on machine learning are summarized from four aspects: wavefront reconstruction, wavefront prediction, phase inversion, and wavefront correction. Further, the potential and challenges of the current methods in the application of high-power laser are discussed. In terms of wavefront reconstruction of a Hartmann sensor, this paper introduces the improvement of a deep learning method based on the calculation process of wavefront reconstruction, such as centroid extraction, aberration coefficient calculated from wavefront slope, wavefront phase calculated from spot array image, and full aperture wavefront slope estimation calculated from partial wavefront slope information. Finally, high-precision centroid calculation under low signal-to-noise ratio is realized, as shown in Table 1. High spatial frequency aberration restoration under low spatial resolution is shown in Fig. 4. Full-aperture wavefront information presumption under light deficiency is shown in Fig. 5. In terms of wavefront prediction, a variety of wavefront prediction methods based on the improved long short term memory (LSTM) network are introduced to achieve high-precision wavefront prediction under different turbulence intensities and delay periods, as shown in Figs. 7 and 8, and the consistent prediction accuracy is still available when some parameters of the atmospheric turbulence model are changed, as shown in Fig. 6. In terms of phase inversion, deep learning-based phase inversion methods are introduced from two pairs of focal and defocusing far field images as well as a single frame image modulated from far-field images, which realizes the direct transformation of far field image information to wavefront information, as shown in Figs. 9 and 12; further, this avoids the iterative process in wavefront sensorless adaptive optics technology. In terms of wavefront correction, the dynamic description of the deep learning network for the local response relationship of the adaptive optical system and dynamic solution of the system control strategy based on reinforcement learning are introduced, as shown in Figs. 15 and 17, respectively, realizing the self-identification and self-adaptive adjustment of the adaptive optical system when the system input and model parameters are changed.

Machine learning has demonstrated excellent potential in solving multiple problems faced by high-power laser systems in laser adaptive optics technology. Its contributions can be summarized as follows: 1) Achieving high-precision wavefront detection under weak targets, strong light background, and strong turbulence effects. 2) Breaking the limitation of system delay on the control bandwidth of the adaptive optical system and improving the correction accuracy of the system for high spatio-temporal frequency aberrations. 3) Avoiding the iterative process and improving the control bandwidth of the wavefront sensorless adaptive optics system. 4) Eliminating the influence of high-power laser applied in different scenarios on the correction performance of the adaptive optical system and improving the adaptive ability of the optical system in different maneuvering platforms and working environments.

However, the practical application of current research methods in high-power laser systems still has the following problems to be studied: 1) Training sample collection. The output time of high-power lasers is limited, and its thermal effect aberration characteristics are different from atmospheric turbulence aberration characteristics. It is difficult to collect or generate training samples conforming to the characteristics of high-power laser thermal effect aberration, and under the condition of high-power laser output or strong background noise, its corresponding real wavefront aberration is difficult to obtain. 2) Training environment and duration. Compared with the astronomical observation, it is difficult for high-power laser to provide the interactive environment required by machine learning. Therefore, an interactive environment that can simulate the states of high-power laser systems should be established with the reference light. In addition, the laser beacon irradiation time is limited, and characteristics of atmospheric turbulence aberration change with time, so it is urgent for machine learning methods to have a short training time. 3) Multi-method fusion. There are many problems in the application of high-power laser, such as strong background noise, dynamic light deficiency, and high spatio-temporal aberration. Taking wavefront reconstruction as an example, in order to realize the restoration of high spatial frequency aberration under complex conditions while ensuring the accuracy and speed of wavefront restoration, the existing network methods need to be integrated and optimized.

Adaptive optics (AO) technology enhances imaging quality by measuring and compensating for wavefront errors. It has been widely used in ground-based telescopes, biological imaging, ocular aberration correction, and laser communication,and so on.

Current AO systems can be categorized into two groups depending on the presence or absence of a wavefront sensor (WFS). Wavefront sensorless (WFSless) AO technology acquires the pupil phase via a retrieval algorithm based on the light intensity distribution. This type of technology can be divided into two kinds: single-image-based and phase-diversity-based technology. Single image-based technology measures the wavefront errors through a single intensity image. However, the phase distribution obtained from a solitary intensity image follows a one-to-many mapping relationship, resulting in limited accuracy. On the other hand, the phase-diversity-based AO technique can determine the phase distribution of the optical field on the input plane by collecting image information of the focal plane and the defocusing plane, resulting in a higher detection accuracy. However, a large number of iterations and measurements are required to obtain optimal results using traditional WFSless AO technology, making it unsuitable for high-speed and real-time scenarios. WFS AO technology employs a WFS based on the interference principle or a traditional geometric optics principle to measure the wavefront. Examples of WFSs used include phase-shifting interference WFSs, Shack-Hartmann WFSs (SHWFSs), and pyramid WFSs (PyWFSs). A high measurement accuracy is achieved using the traditional phase-shifting interference WFS method, but its real-time performance is suboptimal and is susceptible to environmental disturbances. The SHWFS is widely used in AO systems due to its simple structure and ease of operation. However, as a result of its pupil segmentation mechanism, the spatial resolution of the image is low and the dynamic range is small. While the PyWFS can detect weaker light than SHWFS AO technology, it is expensive and has a small linear range in the unmodulated mode.

Recently, the rapid development of artificial intelligence has accelerated development in various fields. Deep learning technology, a significant branch of artificial intelligence, has exhibited remarkable capabilities in search, data mining, machine translation, and speech recognition. Deep learning algorithms are founded on artificial neural networks, which optimize weights and biases based on the given sets of samples. The neural network, after being trained with vast amounts of data, can accurately establish the input-output relationship. Despite the prolonged training time, results can be inferred quickly, making it useful in a multitude of technical domains. The combination of AO and deep learning technology is expected to overcome the issues encountered in conventional AO techniques. It is hypothesized that deep learning can lead to faster and more precise wavefront correction, thereby enhancing the performance of AO technology.

This review introduces several popular artificial neural networks (Fig. 1) used in deep learning. The ways in which deep learning has been combined with AO technology are classified into two categories: techniques with and techniques without WFS. The WFSless category is subdivided into single-image-based (Figs. 3-4) and phase-diversity-based (Figs. 5-6) technologies, while the WFS category includes examples of SHWFSs (Figs. 7-9) and other WFS technologies combined with deep learning. Moreover, the review introduces a new diffraction neural network (Fig. 10), building on the traditional neural network, and provides examples of how this diffraction neural network has been combined with AO technology. The review notes that, over the past five years, examples of deep learning combined with AO technology have focused on improving the real-time performance and accuracy of traditional AO techniques. Finally, the review discusses the future development directions for deep learning-based AO technology.

Utilizing deep learning with WFSless AO technology provides several favorable advantages, such as its simple structure and low cost. While the single-image-based method only uses one image to correct the aberration, the corresponding phase of the intensity image reveals a one-to-many mapping, ultimately resulting in inaccurate calculations. On the other hand, the phase-diversity-based method uses two images with known phase differences to determine the size of the aberrations, yielding more accurate results than via the single-image-based method. Within the WFS AO technology field, numerous SHWFS-based methods exist. With a focus on improving the accuracies of centroid position and wavefront reconstruction, the application of deep learning networks has accelerated and further improved accuracy. Wavefront measurement methods based on sensors other than the SHWFS have gradually been integrated with deep-learning technology.

In the future, deep learning algorithms will be combined with other technologies, including reinforcement learning, and applied to other types of sensors such as the PyWFS to further enhance AO performance. Furthermore, AO will likely be integrated with a novel optical neural network to optimize its performance. Despite the growing body of literature on deep-learning based AO, most studies have been limited to simulation data; thus, it is imperative to evaluate deep-learning based AO using real-world scenarios. Moreover, while current AO technology focuses on the correction of point-source wavefront errors, the detection of extended-source wavefront errors should also be explored in future developments.

Phase control is a key factor in achieving coherent beam combining. Recently, the number of coherent combining paths has been continuously expanding, and the achieved combining power has been continuously increasing. However, when the power of a single combining light source exceeds kilowatts or even several kilowatts, the residual of the phase-locked control system significantly increases with the complexity of the application environment. With the rapid development of artificial intelligence technology, exploring new phase control methods based on machine learning has become a new development trend.

In 2019, Tünnermann et al. introduced reinforcement learning into coherent combining systems, achieving the prediction and compensation of phase noise below kHz (Fig. 1). In 2021, the team validated the feasibility of applying the reinforcement learning phase-locked control method to tiled-aperture coherent combining systems in a simulation environment and explored the ability of the control method to achieve combining light field shaping (Fig. 2). To overcome the limitations of reinforcement learning in expanding the number of coherent combining units, in 2021, Shpakovych et al. proposed a two-dimensional phase dynamic control scheme based on neural networks. This scheme uses a quasi-reinforcement learning method based on neural networks, and the phase-locked residual can reach up to λ/30 (Fig. 3). In 2022, Shpakovych et al. implemented the phase control of a seven-channel fiber amplifier array using a quasi-reinforcement learning algorithm (Fig. 4).

To test the feasibility of phase locking using deep learning in energy-type fiber laser coherent combining systems, in 2019, Hou et al. introduced deep learning into coherent combining systems for the first time and achieved phase locking (Fig. 6). Subsequently, the Chinese Academy of Sciences in China, the Berkeley National Laboratory in the United States, and the University of Southampton in the United Kingdom conducted the concept or experimental verification of phase-locking based on deep learning.

In addition to energy-based applications, the large array element characteristics and ability to quickly adjust the sub-beam phase of coherent combining systems provide a novel technical approach for the generation and customization of special light fields with high power and high mode switching speed. To solve the failure of light field control caused by phase conjugation, Hou et al. proposed the concept of phase-locked control evaluation function based on non-focal plane extraction. Further, they extended the evaluation function of power in the bucket widely used in the study of energy concentrated spot generated by conventional coherent combining to a generalized evaluation function suitable for complex light field customization, achieving decoupling control of the laser array conjugation phase. The feasibility of generating complex light fields such as orbital angular momentum beams was demonstrated. In 2020, Chang et al. proposed the problem of phase conjugation decoupling in the generation of coherent array special light fields using scatterers. With the application of artificial intelligence algorithms in energy-based coherent combining systems, introducing them into the array light field control of special beams to address complex phase control problems has become a new research approach.

In 2020, Hou et al. introduced deep learning algorithms into fiber laser arrays to achieve optical field regulation through a two-step phase control (Fig. 11). To further investigate the optical field information, in 2022, Hou et al. customized orbital angular momentum (OAM) beams from an angle domain perspective and introduced deep learning algorithms to learn the mapping of the relative phase from intensity information to array unit beams (Fig. 12). The purity of the OAM mode in the later stages of phase control using angular domain information has been improved, verifying that angular domain light field information is helpful to control the phase accurately.

Currently, significant results have been achieved in the design and preliminary verification of improving the phase control capability of fiber laser arrays based on machine learning. The number of control paths has exceeded 100, and it demonstrates better performance than traditional optimization algorithms in terms of control speed and control accuracy. However, issues still exist to be addressed in performance verification under high-power medium/strong noise conditions, and the system verification of larger array elements is urgently required. With the development of artificial intelligence technology, the comprehensive improvement in the sample training speed, capacity, accuracy, and mining accuracy is expected to promote machine learning to play a greater potential role in array laser phase regulation.

Nonlinear ultrashort laser pulse propagation in optical fibers, which is the physical principle of fiber-based optical devices, optical signal transmission, and processing, comprises a series of complex nonlinear dynamics. It finds extensive application in the fields of fiber lasers, fiber amplifiers, and fiber communications. Generally, nonlinear ultrashort pulse propagation is governed by the nonlinear Schr?dinger equation (NLSE) and can be solved using model-driven methods such as the split-step Fourier (SSF) and finite-difference methods. However, NLSE-based systems are sensitive to both the initial pulse and fiber parameters, making it difficult for traditional numerical methods to control the complex nonlinear pulse evolution in a time-efficient manner.

As a powerful tool for system parameter optimization and the construction of models of complex dynamics from observed data, deep learning (DL) algorithms have recently been applied to ultrafast photonics, optical communications, optical networks, optical imaging, and the modeling and control of nonlinear pulse propagation to reap the benefits of purely data-driven methods without any underlying governing equations. In this paper, the current key technologies and applications of the DL method for predicting nonlinear pulse dynamics in fiber optics, reconstructing ultrashort pulses, and evaluating critical pulse characteristics are summarized, and the development trends are predicted.

First, a brief introduction to the DL method and practical DNN is presented. Second, the applications of DL for predicting nonlinear ultrashort pulse propagation are listed. Several types of neural networks, i.e., LSTM, CNN, and FNN, have been applied to predict nonlinear pulse evolution, i.e., predicting the effects of GVD and SPM on ultrashort pulse propagation, higher-order soliton compression, and supercontinuum generation, in both the temporal and spectral domains with high prediction precision. Moreover, DL methods are used for modeling optical fiber channels, resulting in a significant reduction in computation demand. Further, the PINN is verified in multiple nonlinear pulse propagations governed by the NLSE, which considers the physical and boundary constraints of the physics model. Subsequently, the optimized PINN, i.e., subnet structure and adapted loss function, is applied to solve the NLSE and predict the nonlinear soliton dynamics with higher prediction accuracy and generalizability.

Third, the DL applications for solving the inverse problems of nonlinear propagation of ultrashort pulses are discussed. Therefore, FNNs and CNNs are utilized to reconstruct the ultrashort pulse and counteract the effects of nonlinearity without prior knowledge. The ultrashort pulse profiles are precisely recovered using SPM and four-wave mixing effects. Furthermore, CNNs have been applied as alternatives to the DBP algorithm to compensate for the nonlinear distortions in the ?ber-optic transmission systems. In addition, DNNs are used extensively in parameter estimation and optimization of optical fiber systems, including the optimal design of the pump power and pump wavelength in the FOPA (fiber optical parametric amplifier) system, predicting the collision between a single soliton and soliton molecule, realizing the extraction of important soliton characteristics, evaluating soliton properties in a quantum noise environment, and estimating the M² factor in few-mode fibers.

The DL methods have become a development frontier and research hotspot in the field of predicting, modeling, controlling, and designing nonlinear pulse propagation in optical fibers. Compared to the conventional SSF method, lightweight neural networks can significantly improve computing efficiency and reduce computing demand, making it simple and convenient to study nonlinear pulse dynamics and optimize fiber-based optical systems. In addition, DL methods have the following potential advantages: (1) They can conduct pure data-driven modeling for complex propagation scenarios that lack accurate mathematical theories or physical models. (2) They can achieve flexible end-to-end modeling for typical nonlinear dynamics or transmission systems, avoiding a nested function structure and repeated iterations, which effectively reduces the complexity of the simulation system.

However, the generalization of neural networks is a critical issue that restricts the prediction of precision and accuracy. Several methods have been developed to improve the generalization of neural networks, such as adding physical constraints to the loss function, coupling a physical model to a neural network, and embedding physical parameters into the neural network input. Further, scientific training methods such as transfer learning and reinforcement learning are conducive to enhancing the scalability of the network in an actual system and reducing the time and data cost of network training. As alternatives to the traditional numerical method, the application of DL methods could aid in the understanding of nonlinear ultrashort pulse propagations as well as the design and optimization of ultrashort pulse-based optical systems.

In the past decade, demand for deep learning-based technologies has exploded, gradually penetrating multiple optical technology fields and driving the development of many corresponding technologies. Meanwhile, optical industries such as aerospace observation, AR/VR consumer electronics, mobile phone photography, and ultrashort-throw projectors are booming. This introduces complex design requirements for optical systems. The performance requirements of these optical systems have increased, and optical elements have become more complex. Free-form surfaces and metasurfaces have far more freedom than traditional spherical and low-order aspheric surfaces. This allows for further optimization of the independent variable parameters. Therefore, free-form surfaces and metasurfaces provide more freedom for optical system design. Moreover, free-form surfaces and metasurfaces can reduce the number of required optical components.

However, traditional optical design, manufacturing, and testing methods are not competitive for free-form surfaces and metasurfaces. In a traditional spherical optical system design, the degrees of freedom and the power orders of the independent variables are low. Therefore, iterative optimization and optical design methods are based on linear equations. In addition, solving the inverse partial differential equations can improve the completion of optical design tasks. With the demand for high-performance optical systems, the numbers of free-form surfaces and metasurfaces have significantly increased, providing a larger design space for optical systems. For free-form surfaces and metasurfaces, early iterative optimization and direct-solution optical design methods face many difficulties and challenges. The introduction of artificial intelligence (AI) technology has facilitated the development of many technologies, such as optical imaging and optical physical field regulation. System design methods have now entered a new era: the “AI optical design era”.

Deep-learning-based technologies have powerful computing, data evolution, and nonlinear inverse solving capabilities, which provide new ideas and methods for more complex optical system designs. From a mathematical perspective, AI deep learning methods are used to solve the mathematical equation of the relationship between the optical surface shape and optical aberration. AI optical design methods are not only a breakthrough at the algorithm level, but also make full use of the new hardware “computer power” in the AI era. Although most traditional inverse solutions rely on iterative optimization, AI optical design methods are based on data-driven and physical-model-driven approaches. The iterative optimization process is performed in advance during the training process without the need for real-time iterative optimization to achieve the initial optical system design quickly and accurately.

The classical optical electromagnetic theory can be used to guide the construction of neural networks for deep learning. Physical models such as aberration theory and wave aberration can be used to design loss functions that match real optical engineering problems. This loss function design significantly improves the degree of matching between deep learning networks and actual engineering problems. The rapid and accurate characteristics of AI deep learning are based on the successful training of neural networks. Additionally, deep learning-based methods are optimized through training and learning data, resulting in an intelligent and optimized design process that benefits from the data used for training in each training session.

From traditional iterative optimization to AI deep-learning optimization, optical system design methods are not completely independent or separate. This review discusses the internal path connection and development logic of the optical system design method, and looks forward to future and potential development directions. First, the development trends of optical system design requirements and optical surface shape complexity are introduced. Second, the concepts of traditional optical design methods are introduced and problems are analyzed. Subsequently, optical design optimization algorithms based on AI deep learning are introduced, which are divided and categorized according to surface types. These include spherical and low-order aspherical surfaces, free-form surfaces, diffractive elements, metasurfaces, and the co-design of optical systems and computational imaging. The principles and time consumption of traditional design algorithms and AI deep-learning algorithms are compared for different surface types (Table 1). Finally, we look forward to the future direction of development in the “AI optical design era”.

From traditional iterative optimization to AI, optical system design methods cannot be analyzed and discussed separately. In traditional convex optimization algorithms, the partial differential solution consumes extremely large CPU threads. Moreover, the interference and diffraction models involving physical optics not only consume CPU threads, but also require the real-time memory space of the computer to perform multidimensional matrix operations. AI deep learning optical design technology provides new ideas on the algorithm as well as new means for computing the hardware of a GPU or TPU. Many optical algorithms have significantly improved both the algorithms (software) and parallel computing (hardware), demonstrating that AI optical design is superior to the traditional optical system design method based on convex optimization planning, in both algorithm and hardware ‘computing power.’ An AI optical design can be used to quickly obtain the initial structure of an optical system. It can be developed in conjunction with a classic optical system design method based on convex optimization. The optical system design idea, based on an AI deep-learning architecture, is a very young breakthrough technical idea. A large number of optical technicians still need to combine practical engineering problems for further development.

Recently, high-power fiber lasers (HPFLs) have become a popular topic in laser science and technology. Rare earth-doped active fibers are key components of HPFL. In contrast to common active fibers, one or more auxiliary refractive index layers are added between the core and cladding of multi-layer active fibers. These types of fibers exhibit special mode properties; therefore, they are expected to further enhance the output power of HPFLs. Evaluating the mode properties of multilayer active fibers under different fiber structural parameters is important because the corresponding results reveal the relationship between the structural parameters and fiber properties, indicate which structural parameter has the best performance, and provide guidance for fiber design. Traditional methods, such as finite difference, finite element, and transfer matrix methods, have been adopted to evaluate the mode properties of such fibers. However, these traditional approaches typically require a long time to repeatedly solve Maxwell's equations under different structural parameters. Doubtlessly, a faster approach to evaluating multilayer active fibers would be vital. In this study, we used machine learning to predict the mode properties of multilayer active fibers for the first time. This new approach can achieve fast and accurate predictions without solving Maxwell's equations.

We introduce a shallow neural network (NN) to learn the mapping from input structural parameters to output mode properties. The structural parameters include the refractive index difference between the core and cladding, thickness of the auxiliary layers, and working wavelength. The mode properties included the effective index, mode field area, and power-filling factor of the fundamental mode (FM) and higher-order mode (HOM). The NN approach can be divided into three steps: data generation, network training, and rapid evaluation (Fig. 2). In the data generation step, 0.1% of the training samples in the defined data space (Table 1) were generated using the transfer matrix method. An NN with one hidden layer is trained using the mean square error (MSE) loss function between the label and output in the network training step. After training, the NN can quickly and accurately predict the mode properties of the multilayer active fibers.

We trained the shallow NN for 200 epochs, and the MSE was finally close to 2.5×10^-5. The total training time was approximately 18 s. To test the accuracy of the trained NN, 256 testing samples were randomly generated. Three typical samples with different mode field distributions (Fig. 5) were used to test the accuracy of the trained NN, and the predicted mode properties agreed well with the ground truths (Fig. 6). The predicted mode properties for all testing samples were then collected and compared to the corresponding ground truths (Fig. 7). The predicted values remained very close to the ground truths. In addition to the randomly generated testing samples, we successfully utilized an NN to predict the mode properties under different wavelengths (Fig. 8), aiming at a special multilayer active fiber with a fixed refractive index difference and auxiliary layer thickness. The accuracy and cost of the NN approach were analyzed statistically. The averaged prediction error of the mode properties was less than 0.6% (Table 2), indicating the high accuracy of this shallow NN. Besides, the total time required to evaluate 256 samples was approximately 177 s for the traditional method and 23 ms for the NN approach. That is, NN takes only 0.09 ms to complete the evaluation for one sample, which is 7000 times faster than traditional methods.

In this study, we used machine learning for the first time to achieve a fast and accurate prediction of the mode properties of multilayer active fibers. This method requires only 0.1% of the samples in the data space to learn the complex mapping between the fiber's structural parameters and mode properties. Thus, fast and accurate prediction can be achieved without solving Maxwell's equations. The average prediction error of this method is less than 0.6%, and the prediction speed is 7000 times higher than that of the traditional method, providing a new way to evaluate the mode properties of multilayer active fibers.

Real-time characterization of temporal behaviors of ultrafast lasers is an important and challenging task. Existing methods are typically limited to a few spatial modes or a two-dimensional (2D) space, which is insufficient for adequately portraying the propagation of ultrafast lasers in a medium when superluminal motion is involved. To accurately characterize the propagation of ultrafast lasers in the presence of superluminal motion, it is necessary to record the complete four-dimensional (4D) space-time (x, y, z, t) in which the laser pulse exists. However, most ultrafast cameras are incapable of three-dimensional (3D) imaging. Additionally, when 2D imaging is performed, the tradeoff between the light throughput and imaging depth of field can be a hindrance for capturing superluminal motions, which typically occurs when the light is propagating at a large angle with respect to the camera plane. The objectives of this study were to develop efficient 3D ultrafast imaging methods that can capture the complete 4D space-time with an extended depth of field and to record and analyze superluminal motions with a high spatiotemporal resolution.

Light field tomography (LIFT), which leverages intelligent algorithms and novel optics, is a new method capable of 3D imaging of ultrafast phenomena with a picosecond-scale temporal resolution. The core idea of LIFT is to reformulate image formation as a computed-tomography problem. In LIFT, the spherical lens is replaced with a cylindrical lens, allowing each pixel to record a line integral of the scene along the direction of the invariant axis of the lens (one without optical power). With a one-dimensional (1D) sensor placed at the focal plane of the cylindrical lens, a parallel beam projection of the scene can be obtained, similar to that in X-ray computed tomography. By using a linear array of such cylindrical lenses, each oriented at a distinct angle with respect to the 1D sensor, projection data along different angles can be simultaneously recorded for computationally reconstructing the scene. Meanwhile, the light field information of the scene is obtained by the cylindrical lens array, which allows 3D depth extraction at each time instant; thus, complete 4D imaging is achieved. With an intelligent optimization algorithm, we improved the 3D imaging quality and achieved a light field image resolution of 128×128×7 with a time sequence of 1016 points, allowing the imaging depth of field to be increased approximately sevenfold.

Using LIFT, we captured the reflection of a picosecond laser pulse upon incidence on a mirror in 3D space. As the laser pulse propagates away from the camera, the measured propagation speed of the laser pulse is lower than the actual speed of light, and the speed is further reduced after the laser is reflected by the mirror, which modifies the propagation angle of the laser pulse. Such superluminal motion is made even more evident by coupling the laser into a multimode light-diffusing-fiber and then winding the fiber in a round-trip fashion. In this case, the forward propagation of the laser has a speed of only approximately 36% of the actual speed of light in the fiber, whereas the reverse propagation appears to be significantly faster: the apparent velocity is 135% of the actual speed, which is far faster than the forward propagation. Interestingly, the light field capability of LIFT is found to be critical for clearly resolving the fiber structure, as conventional imaging of the entire fiber structure with a single focal plane induces significant defocus blur. Moreover, we examined the laser pulse broadening inside the multimode fiber. While pulse broadening is common in multimode fibers, doping the light-diffusing fiber core with nanostructures for scattering light accelerates the broadening: within a propagation time of 720 ps, the picosecond laser pulse width increases from 10 ps to 50, 72, and 88 ps at three different points on the fiber. This is similar to laser pulse broadening after propagation through a thin scattering medium.

Using the novel LIFT method, we demonstrated in this study that it is important to consider the 3D nature of light propagation when characterizing the spatiotemporal behaviors of ultrafast lasers. Without accurate 3D information of the laser pulses, the observed speed of light propagation depends heavily on the imaging geometry and the propagation angle of the light. The resultant superluminal motion will distort the spatiotemporal profile of the ultrafast laser pulse, leading to inaccurate interpretations of the dynamics of the laser inside the medium. With accurate 3D information, LIFT can correctly identify the superluminal motions of the ultrafast laser and clarify the temporal variations of the laser pulse at each spatial position, owing to its high spatial resolution (128×128), large depth of field, and deep time sequence (up to 1016 points) acquired with a single snapshot. This paves the way for fully correcting the spatiotemporal distortion of ultrafast lasers caused by superluminal motions, which we aim to achieve in future research.

Optical fiber tapering is a key process in the fabrication of optical fiber devices such as fiber combiners, fiber sensors, and fiber multiplexers. The tapered section has a significant influence on the light propagation state and directly relates to the performance of the fiber devices. Consequently, the precise prediction of the diameters of tapered optical fibers is increasingly important for the design and fabrication of high-performance optical devices. A straightforward and convenient analytical model based on volume conservation during the optical fiber deformation process can be used to obtain the expressions for the tapered optical fibers. However, this model only focuses on the tapering process under an ideal uniform heat source and scanning point heat source. A fluid dynamics model is an alternative method for studying the tapering process of optical fibers. With the help of numerical methods such as finite element method and finite difference method, the fluid dynamics model can also be used to obtain the diameters of the tapered optical fibers. Because more practical boundary conditions can be applied, the fluid dynamics model is applicable to the tapering process under complicated conditions, such as scanning nonuniform heat sources. In this study, a nonisothermal flow model is built using the finite element method to study the tapering process of optical fibers. With the tapering diameters obtained from the nonisothermal flow model, a back propagation (BP) neural network is then built and trained to achieve fast prediction of the tapering diameter for engineering applications.

First, a nonisothermal flow model of optical fiber tapering is implemented in the finite element software COMSOL Multiphysics. A two-dimensional axisymmetric model of optical fiber is built, normal outflow velocity is applied to both ends of the optical fiber, and general inward heat flux and free surface conditions are applied to the surface of the optical fiber (Fig. 1). With this numerical model, the tapering of optical fibers under different conditions can be simulated. Second, tapering experiments are conducted using tapering equipment with an oxyhydrogen flame (Fig. 3(a)), and the tapered optical fibers are then scanned to obtain the diameters. The comparison of the simulation and experimental results verifies the validity of the nonisothermal flow model. Third, a BP neural network including one input layer, two hidden layers, and one output layer is built in Matlab (Fig. 4). The input of the network includes the initial fiber diameter, length of the heat zone, distribution coefficient of the heat source, and tapering time, and the output of the network is the final taper diameter. The training dataset for the network is generated using the simulation results of the tapering diameters under a fixed Gaussian heat source. Specifically, the training dataset includes 240 simulations with initial input diameters of 100, 200, 300, and 400 μm, heat zone lengths of 4, 6, and 8 mm, heat source distribution coefficients of 0.002, 0.003, 0.004, and 0.005, and tapering time of 20, 40, 60, 80, and 100 s.

The diameter differences between tapered profiles calculated using the nonisothermal flow model and those measured in the tapering experiments are within 6 μm, which verifies the accuracy of this numerical model (Fig. 3(b)). The simulation also successfully predicts the absence of a waist in the tapered profile, which is due to the nonuniform temperature distribution in the heat zone and the overlap effect of the heat source during scanning. The BP neural network predicts the tapering diameter of 360 μm fiber, and the difference between the predicted and simulated results is within 1.7 μm (Fig. 5).

In this study, the tapering processes under a uniform heat source, fixed Gaussian heat source, and scanning Gaussian heat source are successfully simulated using a nonisothermal flow model. The simulation results for the tapered profiles are in good agreement with the tapering experimental results, and the differences are within 6 μm. A BP neural network is built and trained with the dataset obtained from the nonisothermal flow simulations. Fast prediction of the final tapering diameters of optical fibers is achieved, and the difference between the predicted and simulated results is within 1.7 μm.

Passively mode-locked fiber lasers are typical nonlinear systems with abundant physical phenomena such as soliton collisions, soliton molecules, and soliton explosions. With the rise of ultrafast detection technologies such as the time-stretching dispersion Fourier transform (TS-DFT), the number of soliton dynamics phenomena has increased, generating large amounts of analyzable data. Laser self-tuning is an important method for optimizing laser mode-locking; however, traditional algorithms limit the efficiency of laser self-tuning. Thus, it is necessary to reduce the dimensions of high-dimensional data and extract features to reduce irrelevant and redundant parameters in complex nonlinear systems. Furthermore, using an autoencoder to study the interaction processes of dissipative solitons in a passively mode-locked fiber laser can not only extract the main characteristic parameters of the soliton structure but also enhance the physical analysis ability of the network by mining the relationship between the full connection layer parameters and the soliton characteristic parameters.

This study proposes a passively mode-locked fiber laser that operates in the 1550 nm wavelength band based on nonlinear polarization rotation technology. The total cavity length, dispersion, and repetition frequency of the laser were 7.9 m, -0.133 ps², and 26.8 MHz, respectively. When the output power of the fixed pump source was 127 mW, three soliton bound states were obtained by adjusting the polarization controller. Additionally, multiple sets of real-time spectral information was obtained using TS-DFT technology. The solitons exhibited obvious interference fringes owing to spectral coherence superposition. We observed and collected data on the dynamics of different soliton bound states, thereby introducing a large amount of analyzable data into the network model. Furthermore, we designed an evolutionary convolutional autoencoder model based on the operational methods of convolution and pooling in neural networks. The model was comprised of two parts: a dynamic encoder, which compresses the input multidimensional data through a convolutional transformation for feature compression, and a propagation decoder, which generates convolutional kernels and bias matrices using the feature parameters. The initial spectrum was then convolved layer-by-layer and finally reconstructed into multidimensional data. By minimizing the deviation between the input and output spectral matrices for network learning, data dimensionality reduction and system evolution feature extraction can be achieved.

An evolutionary convolutional autoencoder model was used to extract characteristic parameters from the dynamics of different soliton bound states, and they were predicted and reconstructed them. After 200 iterations, the training and testing losses were approximately 0.0952 and 0.1017, respectively. Through continuous parameter debugging, we found that the network was most effective when the number of latent parameters was 35. We believe that there is a correspondence between this and the dimensions of the parameter space in dissipative systems. The reconstructed spectrum showed an interference stripe distribution and changes similar to the actual spectrum, with an average Pearson correlation coefficient of 98.52%. To further characterize the effectiveness of the network structure reconstruction, Fourier transforms were applied to the original and reconstructed spectra to obtain their autocorrelation traces and phase difference evolution curves. The phase evolution information of the original and reconstructed spectra was consistent, and the network model reproduced the high-frequency oscillation dynamics of the soliton pairs.

In this study, a 1550 nm band passively mode-locked fiber laser was developed based on nonlinear polarization rotation technology. The dynamics of the soliton bound states in the laser were measured using TS-DFT real-time detection technology, and the evolution of the soliton spacing and phase difference was analyzed based on the autocorrelation algorithm. Simultaneously, a design for an evolutionary convolution self-coding model was presented for feature extraction and the prediction of soliton bound state dynamics. This study provides new insights into soliton dynamics and helps to explore the physical mechanisms of soliton interactions.

Recently, high-pressure CO₂ laser amplifiers have become an important research direction for chirped pulse amplification, multi-stage MOPA (master oscillator power amplifier) oscillator amplifier, and high-energy laser systems because of their large gain volume, wide gain line width, smooth gain spectrum, and the ability to output TW lever pulse near 10 μm. These amplifiers have important applications in laser isotope separation, laser-driven particle acceleration, laser-induced nuclear fusion, etc. When the gas pressure is higher than 10 bar, the gain spectrum is quasi-continuous with a bandwidth of more than 1 THz, which can amplify picosecond pulses. However, the periodic frequency modulation of the gain spectrum generated by rotating energy-level spacing limits the amplification effect. In the time domain, a single input pulse splits into a series of pulses, which affects pulse extraction and energy amplification. Limited by the high-voltage pulse discharge pumping technology, the pressure cannot be infinitely increased to eliminate pulse splitting. The difference in quality of isotopes shifts the frequency of the central spectral line such that several discrete spectra are mixed into a smooth continuous spectrum, overcoming the periodic spectral modulation of the gain spectral line and amplifying picosecond pulses without generating secondary pulses.

The output characteristics of a long-wave infrared picosecond pulse, amplified using a CO₂ amplifier, were numerically simulated. By fully considering the transitions of regular, sequence, and hot bands, the pumping/relaxation dynamics of the laser energy level were modeled. Spectral data were mainly obtained from the latest version of the HITRAN 2016 database. To determine the optimal isotope ratio, analyze the amplified output of different bands, and compare the influence of pressure broadening on pure ¹²C¹⁶O₂ and mixed isotopes, we calculate the output characteristics of ¹²C¹⁶O₂, ¹²C¹⁶O¹⁸O, ¹²C¹⁸O₂, ¹³C¹⁶O₂, ¹³C¹⁶O¹⁸O, ¹³C¹⁸O₂ under different ratios of six isotopes, the molecular number ratio of ¹²C¹⁶O₂ , ¹²C¹⁶O¹⁸O, and ¹²C¹⁸O₂ is 1∶2∶1, at the four strong lines of 9R, 9P, 10R, and 10P bands and pure ¹²C¹⁶O₂ and ¹³C, ¹⁸O, both accounting for 50% at different pressures. Eventually, we simulated the output characteristics at 10 bar of the ultrashort pulse with a 0.3 ps pulse width, 1.466 THz bandwidth, and 0.01 J energy at 9 μm band passing through the gain medium^{where 13C and 18O account for 50% while 13C accounts for 0% and 18O accounts for 50%, and at 10 μm band passing through the gain medium where 13C and 18O account for 50% while 13C accounts for 100% and 18O accounts for 50%. The calculation results were analyzed and conclusions were drawn.}

When isotopes of 50% ¹³C and 50% ¹⁸O are added, no secondary pulse is generated; however, the output energy and peak power of the main pulse are the lowest. When the ratio of ¹³C to ¹⁸O is higher or lower than 50%, the output energy and peak power of the main pulse increased; however, the energy ratio of the main pulse decreased, and the number and energy ratio of the secondary pulses increased. This corresponds to the amplitude and modulation of the amplifier gain spectrum. Switching from the P- to the R-band has advantages: the peak power and energy ratio of the main pulse increase as well as the number of secondary pulses and their energy ratios decrease. The spectral line density of the R?band is 1.5 times that of the P-band. More gain overlaps result in higher gain and better smoothness. Increasing the gas pressure can increase the collision linewidth, gain overlap, output energy, and peak power; make the gain envelope smoother; and reduce the gain spectral modulation and pulse splitting. However, when no isotopes are added, the smoothing effect of pressure broadening on the gain spectrum is insignificant. Pulse splitting is completely suppressed only in the isotopic mixtures. When the ratios of ¹³C and ¹⁸O are 50% at 10 bar, the amplified energies of the 9 and 10 μm bands are close. At the 9 μm band, the gain spectrum range of ¹³C and ¹⁸O accounting for 50% is 0.533 THz wider than that of ¹³C accounting for 0% and ¹⁸O accounting for 50%; in contrast, at the 10 μm band, the gain spectrum range of ¹³C and ¹⁸O accounting for 50% is 0.094 THz wider than that of ¹³C accounting for 100% and ¹⁸O accounting for 50%. The pulse width of the six isotopes at 9 μm is reduced by 0.130 ps (28.14%), and the proportion of trailing energy is reduced by 46.37% compared with the three isotopes of ¹²C, while the pulse width of the six isotopes at 10 μm is reduced by 0.104 ps (23.26%) and the trailing energy proportion is reduced by 40.06% compared with the three isotopes of ¹³C (Fig. 7). Unlike Polyanskiy et al. who used the same seed passing through three isotopes of ¹²C with ¹⁸O accounting for 47% at the 9 μm band and obtained an amplified output pulse with a width of 0.5 ps, and energy tailing ratio of 25%, six isotope mixtures are used to expand the amplifier gain bandwidth, smooth the gain envelope, and obtain narrower pulse width and a lower tailing energy ratio after amplification.

In this study, numerical simulations were conducted to investigate the output characteristics of six isotopic CO₂ lasers with different proportions of CO₂ isotopes, as well as different wavelengths and gas pressures. The results show that, under the condition of 50% ¹³C and ¹⁸O atom ratios and a pressure of 5 bar, the gain modulation near 10.591 μm is 19.65%, and the gain modulation of the R-band is reduced by about 40% compared to the P-band, effectively suppressing the output of secondary pulses. Under a pressure of 10 bar, for a seed light with a pulse width of 0.3 ps and energy of 0.01 J, the laser pulse width is 0.332 ps with a tail energy ratio of 1.85% after amplification by six isotopes of ¹²C and ¹³C in the 9 μm band and 0.343 ps with a tail energy ratio of 3.77% after amplification by six isotopes of ¹²C and ¹³C in the 10 μm band. Compared with the simulation results by Polyanskiy et al. who used three isotopes of ¹²C to amplify the same seed laser in the 9 μm band, the pulse laser width and tail energy ratio are reduced by 0.168 ps and 23.15%, respectively. The calculations and analyses in this study provide a reference for parameter selection for high-pressure isotopic CO₂ lasers.

Direct diode laser has many applications, such as pump source of fiber laser, laser illumination, laser fuze, beacon laser, and wireless energy transmission. However, it is subject to low beam quality and broad spectrum, leading to limited applications at high polymer absorption, coherent light source, spectrum analysis, and industrial processing. High beam quality can be achieved by improving the chip brightness or beam combing. Single-wavelength or narrow linewidth can be achieved through volume Bragg grating (VBG) locking, distributed Bragg reflector (DBR), or distributed feedback (DFB) grating structure on a chip. Unfortunately, under low power conditions, the wavelength cannot be locked because of weak feedback. Therefore, a novel method for wavelength locking was developed using an electric switch and a fiber beam combiner to solve the problem. We developed an LD (laser diode) source comprising a single LD module, electric function module, thermoelectric (TEC) heat dissipation module, fiber beam combiner, and collimation lens barrel. An LD with power exceeding 120 W, center wavelength of 809±1 nm, beam divergence smaller than 1°, spot inhomogeneity lower than 10% (root mean square) was realized. In addition, the relative environment experimentc were conducted.

The gain spectrum of LD changes with current and temperature. Therefore, we kept the work current and temperature constant and controlled the number of LDs to adjust power through the electric function module and fiber beam combiner. We conducted electric, optics, and thermal designs. Compared to the traditional approach, we utilized a separate power supply for each single LD to prevent extinguishing with the LD overload voltage. For the optics, a 19×1 fiber beam combiner was used to combine several LDs to achieve power combing and high uniformity. In addition, the TEC module was responsible for the heat dissipation of multiple LDs; in this manner, the maintainability of LDs which were distributed was improved. After estimation, we selected 12 pieces of 55 mm×55 mm TEC coolers for refrigeration. The total cooling capacity was approximately 200 W. We designed the structure of the entire LD source. The size was approximately 420 mm×400 mm×200 mm, and the interface included an electric component, communication module, and fiber optic flange.

As mentioned above, an integrated design of optics, mechanics, thermotics, and electricity was performed. Next, we demonstrated the feasibility and correctness of the design. The power was measured at -55-50 ℃. The power value can reach a maximum of 124.7 W, and the e-o efficiency was approximately 45%-48%. The temperature of the LDs ranged from approximately 28 to 38 ℃, and the wavelength drifted by approximately 2 nm. Correspondingly, it increased at 0.2 nm/℃ on average (Fig. 14). The beam uniformity was tested. The inhomogeneity is 7% (RMS) lower than 10% based on the scattering image (Fig. 15). The temperature of the fiber flange was monitored in real time to guarantee usability. The temperature of the flange was lower than 80 ℃, which ensured the safety of the LD source (Fig. 16). The environmental experiments of high- and low-temperature, vibration, and electromagnetic compatibility were developed. Under these conditions, the main index of the LD exhibited no abnormality, and the results demonstrated the correctness of the proposed design and product.

In this study, we developed a novel method to stabilize the wavelength of the LD source with 12 single-LD modules of 12 W, whose spectrum was constant. The power, wavelength, beam divergence, and uniformity were measured. The power was 120 W, wavelength stability was ±1 nm, divergence was less than 1°, and inhomogeneity was lower than 10%. The environment experiments, including high- and low-temperature, vibration, and electromagnetic compatibility, were conducted successfully. The proposed design and demonstration provide support for advancements in military-grade laser sources. Finally, more than 10 sets of the LD sources using this method have been applied in relative programs.

Investigations of silicon-based optoelectrical integration have become a development trend for an increased transmission rate in optical networks. Currently, most photonic devices achieve on-chip integration, except for silicon-based lasers, which are essential light sources. Heterogeneous epitaxial growth has been used to construct silicon-based Ⅲ-Ⅴ semiconductor laser structures, and it is one of the most promising solutions offering high yield and low costs. Significant efforts have been made to enhance the performance of silicon-based lasers by improving the quality of the as-grown material. However, only a few studies have been conducted on optimizing the laser-chip structure and the fabrication process that directly influences the lasing modes, differential resistances, and other properties of the lasers. Moreover, high differential resistance can reduce the output power, slope efficiency, and wall-plug efficiency (WPE) of the lasers and can even cause lasing failure owing to excessive waste heat. Therefore, reducing the differential resistance of silicon-based lasers is critical for significantly improving laser performance and realizing high-performance silicon-based lasers.

Combined with the advantages of metalorganic chemical vapor deposition (MOCVD) and molecular beam epitaxy (MBE), the quantum-dot (QD) laser structure was grown on a two-inch complementary metal-oxide semiconductor (CMOS)-compatible Si (001) substrate (Fig. 1). Moreover, Fabry-Perot (F-P) laser devices were fabricated using two different chip structures. The ridges were etched using inductively coupled plasma (ICP) via standard photolithography. Ti/Pt/Au and AuGe/Ni/Au were deposited via physical vapor deposition (PVD) as p- and n-type contact electrodes, respectively. A 300 nm thick SiO₂ layer was deposited via plasma-enhanced chemical vapor deposition (PECVD) for electrical isolation. The as-fabricated wafers were fabricated into different chip sizes by adequate cleaving and then mounted on Cu heatsinks with C-mount packages. Finally, the main performance of the lasers with these two chip structures was determined for further comparison and analysis.

The main performance of the silicon-based quantum dot laser was determined under CW conditions at room temperature (25 ℃). The F-P lasers, each with a cavity length of 1.5 mm and a stripe width of 50 μm, achieve a single-facet output power of 70 mW and differential resistance of 1.52 Ω (Fig. 4). The voltage of the lasers with the conventional cathode structure is approximately 3.8 times that with the symmetrical cathode structure under the same injection currents (Fig. 5). The lasing wavelength of the lasers with conventional cathode structure exhibits a red shift by approximately 18.4 nm owing to additional waste heat, whereas the laser with symmetrical cathode structures exhibits a red shift by only approximately 4.1 nm when the injection current increases from 1.2 to 2.8 times the threshold current (Fig. 5). Moreover, compared with the conventional cathode structure, the symmetrical cathode structure can significantly reduce the device differential resistance by approximately 75%, increasing the characteristic temperature from 27.2 to 43.3 K (Fig. 5). In addition, the slope efficiency and maximum wall-plug efficiency increased by 26.4% and 4.7 times, respectively (Fig. 6).

In this study, a new chip structure of lasers on silicon was designed, which could reduce the differential resistance compared with the conventional cathode structure, significantly improving the laser performance. QD lasers on a two-inch CMOS-compatible Si (001) substrate were fabricated using this structure, and the influence of the chip structure on laser performance was investigated experimentally. The results show that the differential resistance of the lasers with symmetrical cathode structures is only 1.52 Ω, which is significantly low differential resistance. Compared with the conventional cathode structure, the chip structure can significantly reduce the differential resistance of the device by approximately 75% and increase the characteristic temperature by approximately 59.6%. In addition, the slope efficiency and maximum wall-plug efficiency increase by 26.4% and 4.7 times, respectively, the output power reaches 70 mW, and the stability improves significantly. In summary, the laser performance can be significantly enhanced by decreasing the differential resistance, which provides another critical approach to enhancing the laser performance and offers an optimized technical solution for producing high-performance and highly reliable lasers on silicon.

The mid-infrared waveband is the vibrational and rotational spectral region of molecules, of which 3-5 μm is the most important atmospheric window, making it an increasingly popular research topic. The wide-tuning characteristics of the external cavity quantum cascade laser in the mid-infrared waveband make it widely used in gas molecule sensing, difference-frequency THz generation, free-space optical communication, and other fields. We design a tunable quantum cascade laser with a 4-μm wavelength to realize these applications. The laser can achieve different light emission performances by replacing blazed grating, making it suitable for different conditions.

The experiment in this study is performed with the Littrow structure as the main body and quantum cascade gain chip with a central wavelength of 4 μm. During the experiment, the working temperature of the gain chip is kept at 25 ℃, and the quantum cascade laser gain chip is integrated with the thermoelectric cooler and even aspherical lens. Blazed gratings with groove spacings of 450 line/mm and 300 line/mm are selected as the feedback elements, and the zero-order diffraction light of the grating is selected as the output light; the first-order diffraction light is fed back to the active region of the gain chip to form an external cavity resonance. The feedback light is returned to the laser active region and the laser wavelength is selected by adjusting the grating pitch angle and rotation angle.

Based on the above results, the laser maximum power and spectral tuning range are 7.30 mW (Fig. 8) and 380 nm and the grating rotational angle is 11.06° when 450 line/mm gratings are used. With this configuration, the laser has a higher power value and wider spectral tuning characteristics, which is more suitable for applications requiring narrow linewidth and high-precision wavelength tuning, such as spectroscopy. When a 300 line/mm blazed grating is used, the highest power is 5.24 mW (Fig. 8), spectral tuning range is 297 nm (Fig. 5), and the rotation angle of the grating is 3.15°. This configuration is more suitable for space optical communication and other applications requiring high beam quality. The laser side-mode suppression ratio (SMSR) in both configurations is 20 dB (Fig. 6), which is suitable for practical use.

In this study, a widely tunable external cavity quantum cascade laser based on the Littrow structure is developed. A blazed grating is used as the feedback element for mode selection, and two gratings with different grating constants are selected for comparison. Experimental comparisons show that when a 450 line/mm blazed grating is used, a maximum power value of 7.30 W, tuning range of 3774-4154 nm, tuning width of 380 nm, and grating rotation angle of 11.06° are obtained. The laser has a higher power value and a wider spectral tuning range. When a 300 line/mm blazed grating is used, the laser beam quality is improved, with a maximum power value of 5.24 mW, tuning range of 3779-4154 nm, tuning width of 297 nm, and grating rotation angle of 3.15°. The 300 line/mm blazed grating configuration is more suitable for high beam quality applications, such as space optical communication. The performance of the laser obtained by using the 450 line/mm blazed grating configuration is more suitable for spectral applications requiring narrow linewidth and high-precision spectral tuning. An external cavity quantum cascade laser can achieve different performance indices by using different external cavity configurations and meet the use requirements of different application scenarios. It plays an important role in molecular gas sensing, difference-frequency terahertz generation, free-space optical communication, and other fields.

Optical vortices in the Laguerre-Gaussian (LG) mode that have a unique hollow intensity profile and non-zero orbital angular momentum are highly significant for various applications. The LG mode laser can be generated using external-cavity devices, such as holograms or cylindrical lens pairs, to transform a Hermite-Gaussian beam into a LG beam, or using the intracavity, where the intracavity components are utilized to preferentially oscillate the certain high-order modes within a laser resonator. In comparison to the external-cavity approaches, intracavity approaches typically yield superior power handling, beam quality, and conversion efficiency. However, there are very few demonstrations regarding high-order LG mode laser oscillations with angular indices (m) beyond 30. The main challenge is that the beam patterns of the very-high-order mode lasers become highly complex, which makes it difficult to fabricate mode-selecting elements with a sufficient accuracy to precisely manage the loss and gain of a certain mode. In this study, we demonstrate the generation of an ultra-high-order LG mode output based on mode selection enabled by intracavity spherical aberration (SA). By calculating the focusing behavior of the high-order LG mode beam and the SA of the intracavity lens, the relationship between the angular indices m of the high-order LG_0,±m vortex laser and the cavity parameters is determined. In the experiment, the ultra-high-order LG_0,±m vortex lasers with tunable angular indices m of up to 280 are obtained with an end-pumped Nd∶YVO₄ laser at a wavelength of 1064 nm, under an incident diode pump power of only 2.06 W.

The experimental arrangement of the laser that generates the ultra-high-order LG mode output is depicted in Fig. 1. Two lenses, L1 and L2, with focal lengths of f₁=150 mm and f₂=51.8 mm, respectively, are inserted into the cavity of an end-pumped Nd∶YVO₄ laser to collimate the beam and introduce SA for mode selection. The laser is pumped by a fiber-coupled diode laser at 878.6 nm, with a pump beam radius of approximately 120 μm at the input facet of the a-cut Nd∶YVO₄ crystal and a Rayleigh length of approximately 0.9 mm. The crystal is located near the total reflector M1, while the distances between the crystal and lens L1 (d₁) and between lenses L1 and L2 (d₂) are 155 mm and 20 mm, respectively. The plano-concave input mirror M1 with a small radius of curvature of 50 mm generates a small beam waist near it, enabling the beam to expand significantly when it reached the lenses, thus enhancing the SA and resultant mode selection capability. The output coupler M2 is a flat mirror with a transmittance of 10% at 1064 nm. The beam waist position of the LG beam behind the focusing lens L2 can be obtained using Eq. (1). Considering that the beam arriving at lens L2 is well-collimated by lens L1, the relationship can be simplified as indicated in Eq. (3). Because the output coupler M2 is a flat mirror, the oscillating beam should have its waist exactly on the mirror surface. The defocused modes (with the beam waist deviated from M2) suffered a loss larger than that of the "on-focus" mode with the beam waist on M2. The spherical lens with SA is used as L2, and the focal length is not a constant but varies with the incident beam height. Therefore, mode selection can be achieved by adjusting the location of M2 within a small range to have different orders of modes focused on it. Moving the output coupler M2 toward lens L2 will result in modes with a larger m and vice versa.

Figure 4 presents certain typical beam patterns recorded during the experiment. With an incident pump power of 2.06 W, the lowest order propagation-invariant single-mode LG_0,±m mode laser is LG_0,±38, which is obtained at distance between M2 and L2 of d₃=51.48 mm, and the highest order is LG_0,±280, which is obtained at d₃=48.91 mm. The beams are petal-like because both the +m and -m components have a similar intensity, and the mode order can be determined by counting the surrounding dark bars. The high-order LG mode optical vortices demonstrate good mode purity and stability. Figure 5 presents the theoretical relationship of the mode order and the d₃ obtained using Eq. (3), as well as the experimental results, which sufficiently match the theoretical results. The slope efficiency of the laser decreases with the mode order owing to the increasing SA-induced cavity loss and decreasing mode matching.

In summary, ultra-high-order LG mode vortex beams with selective angular indicesare obtained by utilizing the SA of an off-the-shelf spherical lens in the laser cavity. By calculating the focusing behavior of the high-order LG mode beam and the SA of the intracavity lens, the relationship between the angular indices m of the high-order LG_0,±m vortex laser and the cavity parameters is determined. In the experiment, an ultra-high-order LG_0,±m vortex laser with tunable angular indices m of up to 280 is obtained with an end-pumped Nd∶YVO₄ laser at a wavelength of 1064 nm, under an incident diode pump power of only 2.06 W. The ultra-high-order LG_0,±m vortex laser exhibits good stability in terms of power and the transverse mode. The mode evolution in the experiment sufficiently matches with that in the theoretical model. This study provides theoretical and experimental references for the generation of ultra-high-order LG mode vortex lasers. By increasing the pump power or pump overlap to enhance the laser gain, arbitrary high-order modes can be expected using this method.

The existence of edge modes in the distributed Bragg reflector(DBR)semiconductor laser emission spectrum has a significant influence on the beam quality. The output multi-edge modes and high side lobes deteriorate the semiconductor laser beam and output power. The F-P effect formed on the sides of the DBR laser with a homogeneous duty cycle is one reason for this, resulting in side-mode resonance enhancement. Second, the energy coupled to the narrow-ridge waveguide through the grating decreases near the rim of the narrow ridge. This study proposes a modification scheme of the regular DBR structure to inhibit the edge mode on the DBR laser spectrum, ensuring maximized reflectance at the central wavelength while weakening the side lobe strength.

Based on coupled-mode theory, a rectangular grating model with a gradual duty cycle is established for the DBR laser. The influence of the duty cycle distribution on the edge mode suppression and the reflectivity maximization at the central wavelength is analyzed using the finite-difference time-domain (FDTD) method and changing the DBR duty cycle. The electro-optic model of the rectangular grating with gradient duty cycle is simulated, and the reflectance at the central wavelength and the side mode suppression ratio are obtained after device optimization. A tapered duty cycle model for the DBR is established, and the influence of the grating structure with tapered duty cycle on the output side lobe intensity of the DBR laser is analyzed.

In DBR lasers, the F-P effect exists in rectangular uniform duty cycle gratings, resulting in edge-mode oscillation enhancement (Fig. 5). From the relationship of coupling coefficient and duty cycle (Fig. 6) and the duty cycle under the maximum reflectivity at the central wavelength, the grating duty-cycle range can be determined. Within the gradient range, the simulation of grating when the duty cycle is truncated sinc function distribution is carried out. Within the gradient ranges of 0.545-0.580 and 0.580-0.545, the reflection intensity of the edge mode is suppressed, and the reflection peak value at the central wavelength reaches 0.8 (Fig.7). For a grating with length of 0.6 mm, comparing the reflection spectra of rectangular uniform grating and rectangular grating with gradient duty cycle, it can be observed that, although the edge mode is suppressed for the rectangular grating with gradient duty cycle, its reflection peak value at the central wavelength is lower than that of the rectangular uniform grating. Setting the duty cycle at 0.58 in the center of the grating, the edge mode suppressing effect is studied for the case when the duty cycle decreases from the center of the grating length to the two ends . The results show that the edge mode suppression under truncated sinc functions is enhanced, but the reflectivity at the central wavelength does not improve (Figs.9 and 10). When the grating length increases to 1 mm, the central reflection peak value of the grating with gradient duty cycle remains unchanged (Fig.11). When adopting the grating with gradient duty cycle, the coupling coefficient at the center of the grating length is small; thus, using the combination of duty cycle that presents truncated sinc function distribution and constant duty cycle can increase the coupling coefficient at the center of the grating. Although the reflection peak value at the central wavelength is nearly similar to that of the uniform grating, the edge mode suppression ratio reaches 48 dB (Fig.13). Finally, by observing the field intensity distribution of tapered grating with gradient duty cycle and rectangular uniform grating on the far-field lateral tangent, we find that tapered gratings with gradient duty cycle can reduce the sidelobe intensity of the DBR laser output.

The existence of the F-P effect in the rectangular uniform grating for conventional DBR lasers results in side-mode oscillation enhancement. In addition, more side modes in the reflectance spectra of semiconductor lasers not only deteriorate the beam quality but also reduce the output power at the central wavelength. It is found that changing the duty-ratio distribution in the DBR laser can destroy the grating effect, leading to a reduction in the side-mode reflection intensity. Furthermore, using a gradual duty cycle at both ends of the grating and a constant duty cycle in the center of the rectangular grating length, not only reduces the side mode in the reflection spectrum, but also ensures a larger reflectivity at the central wavelength. It is found that the optical field propagating at the edge of the narrow ridge waveguide, when passing through a tapered gratings with gradient duty cycle, can be better coupled into the narrow ridge waveguide, leading to an effective reduction in the intensity of the side lobe. Compared with previous schemes, this requires less complex process steps while enhancing the side mode suppressing ratio. Additionally, it can reduce the side lobe strength, providing a valuable reference for the structural design of high-power and high-beam-quality semiconductor lasers.