[1] Fermann ME, Hartl I. Ultrafast fiber laser technology. IEEE J Select Topics Quantum Electron. 2009;15(1):191–204. .

[2] Fermann ME, Hartl I. Ultrafast fibre lasers. Nat Photonics. 2013;7(11):868–74. .

[3] Zervas MN, Codemard CA. High power fiber lasers: A review. IEEE J Select Topics Quantum Electron. 2014;20(5):219–41. .

[4] Jauregui C, Limpert J, Tünnermann A. High-power fibre lasers. Nat Photonics. 2013;7(11):861–7. .

[5] Liu Z, et al. High-power coherent beam polarization combination of fiber lasers: progress and prospect [Invited]. J Opt Soc Am B. 2017;34(3):A7. .

[6] Xu C, Wise FW. Recent advances in fibre lasers for nonlinear microscopy. Nat Photonics. 2013;7(11):875–82. .

[7] Kapron FP, Keck DB. Pulse Transmission Through a Dielectric Optical Waveguide. Appl Opt. 1971;10(7):1519. .

[8] Li T. Optical Fibers for Communications. Opt News. 1977;3(3):10–5. .

[9] Olsen FO, Hansen KS, Nielsen JS. Multibeam fiber laser cutting. J Laser Appl. 2009;21(3):133–8. .

[10] Yang J, Tang Y, Xu J. Development and applications of gain-switched fiber lasers [Invited]. Photonics Res. 2013;1(1):52. .

[11] Churkin DV, et al. Recent advances in fundamentals and applications of random fiber lasers. Adv Opt Photon. 2015;7(3):516. .

[12] Fu S, et al. Review of recent progress on single-frequency fiber lasers. J Opt Soc Am B. 2017;34(3):A49. .

[13] Shang C, et al. Review on wavelength-tunable pulsed fiber lasers based on 2D materials. Opt Laser Technol. 2020;131(September 2019). .

[14] Dragic PD, Cavillon M, Ballato J. Materials for optical fiber lasers: A review. Appl Phys Rev. 2018;5(4). .

[15] Samuel AL. Some studies in machine learning using the game of checkers. IBM J Res Dev. 2000;44(1–2):207–19. .

[16] De Santana LMQ, et al. Deep Neural Networks for Acoustic Modeling in the Presence of Noise. IEEE Lat Am Trans. 2018;16(3):918–25. .

[17] Krizhevsky A, Sutskever I, Hinton GE. ImageNet classification with deep convolutional neural networks. Commun ACM. 2017;60(6):84–90. .

[18] Jiao Z, et al. Machine learning and deep learning in chemical health and safety: A systematic review of techniques and applications. J Chem Health Saf. 2020;27(6):316–34. .

[19] Ongie G, et al. Deep Learning Techniques for Inverse Problems in Imaging. IEEE J Select Areas Inform Theory. 2020;1(1):39–56. .

[20] Barbastathis G, Ozcan A, Situ G. On the use of deep learning for computational imaging. Optica. 2019;6(8):921. .

[21] Zhao R, Huang L, Wang Y. Recent advances in multi-dimensional metasurfaces holographic technologies. PhotoniX. 2020;1(1):1–24. .

[22] Zuo C, et al. Deep learning in optical metrology: a review. Light Sci Appl. 2022;11(1). .

[23] Musumeci F, et al. An Overview on Application of Machine Learning Techniques in Optical Networks. IEEE Commun Surv Tutorials. 2019;21(2):1383–408. .

[24] Wang D, et al. Data-driven Optical Fiber Channel Modeling: A Deep Learning Approach. J Lightwave Technol. 2020;38(17):4730–43. .

[25] Zhang Y, et al. Ultrafast and Accurate Temperature Extraction via Kernel Extreme Learning Machine for BOTDA Sensors. J Lightwave Technol. 2021;39(5):1537–43. .

[26] Ma W, et al. Deep learning for the design of photonic structures. Nat Photonics. 2021;15(2):77–90. .

[27] Wiecha PR, et al. Deep learning in nano-photonics: inverse design and beyond. Photonics Res. 2021;9(5):B182. .

[28] Malkiel I, et al. Plasmonic nanostructure design and characterization via Deep Learning. Light Sci Appl. 2018;7(1). .

[29] Situ G, Westbrook P. AI boosts photonics and vice versa AI boosts photonics and vice versa: AIP Publishing, LLC; 2020. .

[30] Woodward RI, Kelleher EJR. Genetic algorithm-based control of birefringent filtering for self-tuning, self-pulsing fiber lasers. Opt Lett. 2017;42(15):2952. .

[31] Wu X, et al. Intelligent Breathing Soliton Generation in Ultrafast Fiber Lasers. Laser Photonics Rev. 2022;16(2):2100191. .

[32] Nathan Kutz J, Fu X, Brunton S. Self-tuning fiber lasers: Machine learning applied to optical systems. Nonlinear Photonics. 2014;2014:1–2. .

[33] Mitchell TM. Machine Learning. New York: McGraw-Hill; 1997.

[34] Radford A, Metz L, Chintala S. Unsupervised representation learning with deep convolutional generative adversarial networks. In: 4th International Conference on Learning Representations, ICLR 2016 - Conference Track Proceedings; 2016. p. 1–16.

[35] Tamir JI, Yu SX, Lustig M. Unsupervised Deep Basis Pursuit: Learning inverse problems without ground-truth data; 2019. p. 1–5.

[36] van Engelen JE, Hoos HH. A survey on semi-supervised learning. Mach Learn. 2020;109(2):373–440. .

[37] Nilsson NJ. Introduction to Machine Learning. An early draft of a proposed textbook. Mach Learn. 2005;56(2):387–99 10.1.1.167.8023.

[38] Shalev-Shwartz S, Ben-David S. Understanding Machine Learning, in Understanding Machine Learning: From Theory to Algorithms 9781107057. Cambridge: Cambridge University Press; 2014. .

[39] Qiu J, et al. A survey of machine learning for big data processing. Eurasip J Adv Signal Process. 2016;(1). .

[40] Martin E, et al. Semi-Supervised Learning. In: Encyclopedia of Machine Learning. Boston: Springer; 2011. p. 892–7. .

[41] Morales EF, Zaragoza JH. An introduction to reinforcement learning. In: Decision Theory Models for Applications in Artificial Intelligence: Concepts and Solutions; 2011. p. 63–80. .

[42] Nousiainen J, et al. Adaptive optics control using model-based reinforcement learning. Opt Express. 2021;29(10):15327. .

[43] Brereton RG, Lloyd GR. Support Vector Machines for classification and regression. Analyst. 2010;135(2):230–67. .

[44] Bo D, et al. Structural Deep Clustering Network. In: The Web Conference 2020 - Proceedings of the World Wide Web Conference, WWW 2020; 2020. p. 1400–10. .

[45] Min E, et al. A Survey of Clustering with Deep Learning: From the Perspective of Network Architecture. IEEE Access. 2018;6(July):39501–14. .

[46] LeCun Y, et al. Backpropagation Applied to Handwritten Zip Code Recognition. Neural Comput. 1989;1(4):541–51. .

[47] Lecun Y, et al. Gradient-based learning applied to document recognition. Proc IEEE. 1998;86(11):2278–324. .

[48] Kipf TN, Welling M. Semi-supervised classification with graph convolutional networks. In: 5th International Conference on Learning Representations, ICLR 2017 - Conference Track Proceedings; 2017. p. 1–14.

[49] Solomatine D, See LM, Abrahart RJ. Data-Driven Modelling: Concepts, Approaches and Experiences. Pract Hydroinf. 2008:17–30. .

[50] Karniadakis GE, et al. Physics-informed machine learning. Nat Rev Physics. 2021;3(6):422–40. .

[51] Raissi M, Perdikaris P, Karniadakis GE. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys. 2019;378(October):686–707. .

[52] Raissi M. Deep hidden physics models: Deep learning of nonlinear partial differential equations. J Mach Learn Res. 2018;19:1–24.

[53] Brunton SL, et al. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc Natl Acad Sci U S A. 2016;113(15):3932–7. .

[54] Bengio Y, Courville A, Vincent P. Representation Learning: A Review and New Perspectives. IEEE Trans Pattern Anal Mach Intell. 2013;35(8):1798–828. .

[55] Yu D, et al. Deep learning and its applications to signal and information processing. IEEE Signal Process Mag. 2011;28(1):145–50. .

[56] Lecun Y, Bengio Y, Hinton G. Deep learning. Nature. 2015;521(7553):436–44. .

[57] McCulloch WS, Pitts W. A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys. 1943;5(4):115–33. .

[58] Salehinejad H, et al. Recent Advances in Recurrent Neural Networks; 2017. p. 1–21.

[59] Bennett KP, Parrado-Hernández E. The interplay of optimization and machine learning research. J Mach Learn Res. 2006;7:1265–81. .

[60] Zhang J, et al. Why gradient clipping accelerates training: A theoretical justification for adaptivity; 2019. p. 1–21.

[61] Wilson AC, et al. The marginal value of adaptive gradient methods in machine learning. Adv Neural Inf Proces Syst. 2017;(Nips):4149–59. http://arxiv.org/abs/1705.08292.

[62] Ruder S. An overview of gradient descent optimization algorithms. In: arXiv preprint arXiv:160904747; 2016. p. 1–14. http://arxiv.org/abs/1609.04747.

[63] Yao X. Evolving artificial neural networks. Proc IEEE. 1999;87(9):1423–47. .

[64] F. P. Such et al., “Deep Neuroevolution: Genetic Algorithms Are a Competitive Alternative for Training Deep Neural Networks for Reinforcement Learning” (2017).

[65] Conti E, et al. Improving exploration in evolution strategies for deep reinforcement learning via a population of novelty-seeking agents. Adv Neural Inf Proces Syst. 2018;(NeurIPS):5027–38. http://arxiv.org/abs/1712.06560.

[66] Rere LMR, Fanany MI, Arymurthy AM. Simulated Annealing Algorithm for Deep Learning. Procedia Comput Sci. 2015;72:137–44. .

[67] Hinton GE, Salakhutdinov RR. Reducing the dimensionality of data with neural networks. Science. 2006;313(5786):504–7. .

[68] Wang H, Czerminski R, Jamieson AC. Neural Networks and Deep Learning. In: The Machine Age of Customer Insight; 2021. p. 91–101. .

[69] Mnih V, et al. Playing Atari with Deep Reinforcement Learning. In: Deep Reinforcement Learning; 2013. p. 135–60.

[70] Vlachas PR, et al. Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics. Neural Netw. 2020;126:191–217. .

[71] Pandey S, Schumacher J. Reservoir computing model of two-dimensional turbulent convection. Phys Rev Fluids. 2020;5(11):113506. .

[72] Vlachas PR, et al. Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks. (arXiv:1802.07486v4 [physics.comp-ph] UPDATED). Phys Today. 2018. .

[73] Salmela L, et al. Predicting ultrafast nonlinear dynamics in fibre optics with a recurrent neural network. Nat Machine Intell. 2021;3(4):344–54. .

[74] Teğin U, et al. Reusability report: Predicting spatiotemporal nonlinear dynamics in multimode fibre optics with a recurrent neural network. Nat Machine Intell. 2021;3(5):387–91. .

[75] Sui H, et al. Deep learning based pulse prediction of nonlinear dynamics in fiber optics. Opt Express. 2021;29(26):44080. .

[76] Lim J, Psaltis D. MaxwellNet: Physics-driven deep neural network training based on Maxwell’s equations. APL Photonics. 2022;7(1):011301. .

[77] Tünnermann H, Shirakawa A. Deep reinforcement learning for coherent beam combining applications. Opt Express. 2019;27(17):24223. .

[78] Tünnermann H, Shirakawa A. Deep reinforcement learning for tiled aperture beam combining in a simulated environment. JPhys Photonics. 2021;3(1). .

[79] Chen J, Jiang H. Optimal Design of Gain-Flattened Raman Fiber Amplifiers Using a Hybrid Approach Combining Randomized Neural Networks and Differential Evolution Algorithm. IEEE Photonics J. 2018;10(2). .

[80] Hou T, et al. Deep-learning-assisted, two-stage phase control method for high-power mode-programmable orbital angular momentum beam generation. Photonics Res. 2020;8(5):715. .

[81] Vincent P, et al. Stacked denoising autoencoders: Learning Useful Representations in a Deep Network with a Local Denoising Criterion. J Mach Learn Res. 2010;11:3371–408.

[82] Vincent P, et al. Extracting and composing robust features with denoising autoencoders. In: Proceedings of the 25th International Conference on Machine Learning, vol. 311. New York: ACM Press; 2008. p. 1096–103. .

[83] An Y, et al. Suppressing the Influence of CCD Vertical Blooming on M2 Determination through Deep Learning. In: 2019 18th International Conference on Optical Communications and Networks, ICOCN 2019(1); 2019. p. 2–4. .

[84] Mathew RS, et al. The Raspberry Pi auto-aligner: Machine learning for automated alignment of laser beams. Rev Sci Instrum. 2021;92(1). .

[85] Arismar Cerqueira S. Recent progress and novel applications of photonic crystal fibers. Rep Prog Phys. 2010;73(2):024401. .

[86] Chugh S, et al. Machine learning approach for computing optical properties of a photonic crystal fiber. Opt Express. 2019;27(25):36414. .

[87] Zibar D, et al. Inverse System Design Using Machine Learning: The Raman Amplifier Case. J Lightwave Technol. 2020;38(4):736–53. .

[88] Zhou J, et al. Robust, compact, and flexible neural model for a fiber Raman amplifier. J Lightwave Technol. 2006;24(6):2362–7. .

[89] Singh S, Kaler RS. Performance optimization of EDFA-Raman hybrid optical amplifier using genetic algorithm. Opt Laser Technol. 2015;68:89–95. .

[90] M. Ionescu, A. Ghazisaeidi, and J. Renaudier, “Machine Learning Assisted Hybrid EDFA-Raman Amplifier Design for C+L Bands,” 2020 European Conference on Optical Communications, ECOC 2020(1), 2020–2022. 2020. .

[91] Jiang X, et al. Solving the nonlinear Schrödinger equation in optical fibers using physics-informed neural network. In: Optics InfoBase Conference Papers: OSA; 2021. p. 3–5. .

[92] Teǧin U, et al. Controlling spatiotemporal nonlinearities in multimode fibers with deep neural networks. APL Photonics. 2020;5(3):030804. .

[93] Valensise CM, et al. Deep reinforcement learning control of white-light continuum generation. Optica. 2021;8(2):239. .

[94] Su R, et al. Active coherent beam combining of a five-element, 800 W nanosecond fiber amplifier array. Opt Lett. 2012;37(19):3978. .

[95] Su R, et al. Active coherent beam combination of two high-power single-frequency nanosecond fiber amplifiers. Opt Lett. 2012;37(4):497. .

[96] Vu KT, et al. Adaptive pulse shape control in a diode-seeded nanosecond fiber MOPA system. Opt Express. 2006;14(23):10996. .

[97] Malinowski A, et al. High power pulsed fiber MOPA system incorporating electro-optic modulator based adaptive pulse shaping. Opt Express. 2009;17(23):20927. .

[98] Malinowski A, et al. High peak power, high-energy, high-average power pulsed fibre laser system with versatile pulse duration and shape. Optics InfoBase Conf Pap. 2013;38(22):4686. .

[99] Schimpf DN, et al. Compensation of pulse-distortion in saturated laser amplifiers. Opt Express. 2008;16(22):17637. .

[100] Shi H, et al. High-power diode-seeded thulium-doped fiber MOPA incorporating active pulse shaping. Appl Phys B Lasers Opt. 2016;122(10). .

[101] Kutuzyan AA, et al. Dispersive regime of spectral compression. Quantum Electron. 2008;38(4):383–7. .

[102] Finot C, et al. Parabolic pulse generation and applications. In: 2nd IEEE LEOS Winter Topicals, WTM 2009 45(11); 2009. p. 110–1. .

[103] Boscolo S, Finot C. Artificial neural networks for nonlinear pulse shaping in optical fibers. Opt Laser Technol. 2020;131(February):106439. .

[104] Boscolo S, Dudley JM, Finot C. Modelling self-similar parabolic pulses in optical fibres with a neural network. Results in Optics. 2021;3(November 2020):100066. .

[105] Gupta RK, et al. Deep Learning Enabled Laser Speckle Wavemeter with a High Dynamic Range. Laser Photonics Rev. 2020;14(9):1–19. .

[106] Xiong W, et al. Deep learning of ultrafast pulses with a multimode fiber. APL Photonics. 2020;5(9). .

[107] Genty G, et al. Machine learning and applications in ultrafast photonics. Nat Photonics. 2021;15(2):91–101. .

[108] Bendory T, Beinert R, Eldar YC. Fourier phase retrieval: Uniqueness and algorithms. Appl Numer Harmon Anal. 2017;(9783319698014):55–91. .

[109] Escoto E, et al. Advanced phase retrieval for dispersion scan: a comparative study. J Opt Soc Am B. 2018;35(1):8. .

[110] Kane DJ. Principal components generalized projections: a review [Invited]. J Opt Soc Am B. 2008;25(6):A120. .

[111] Sidorenko P, et al. Ptychographic reconstruction algorithm for FROG: Supreme robustness and super-resolution. In: 2016 Conference on Lasers and Electro-Optics, CLEO 2016 3(12); 2016. .

[112] Zahavy T, et al. Deep learning reconstruction of ultrashort pulses. Optica. 2018;5(5):666. .

[113] Zhu Z, et al. Attosecond pulse retrieval from noisy streaking traces with conditional variational generative network. Sci Rep. 2020;10(1):1–7. .

[114] White J, Chang Z. Attosecond streaking phase retrieval with neural network. Opt Express. 2019;27(4):4799. .

[115] Kokhanovskiy A, et al. Machine learning-based pulse characterization in figure-eight mode-locked lasers. Opt Lett. 2019;44(13):3410. .

[116] Bruning R, et al. Comparative analysis of numerical methods for the mode analysis of laser beams. Appl Opt. 2013;52(32):7769–77. .

[117] An Y, et al. Learning to decompose the modes in few-mode fibers with deep convolutional neural network. Opt Express. 2019;27(7):10127. .

[118] An Y, et al. Numerical mode decomposition for multimode fiber: From multi-variable optimization to deep learning. Opt Fiber Technol. 2019;52(June):101960. .

[119] An Y, et al. Deep Learning-Based Real-Time Mode Decomposition for Multimode Fibers. IEEE J Select Topics Quantum Electron. 2020;26(4):1–6. .

[120] An Y, et al. Fast modal analysis for Hermite–Gaussian beams via deep learning. Appl Opt. 2020;59(7):1954. .

[121] Fan X, et al. Mitigating ambiguity by deep-learning-based modal decomposition method. Opt Commun. 2020;471(February):125845. .

[122] Rothe S, et al. Intensity-Only Mode Decomposition on Multimode Fibers Using a Densely Connected Convolutional Network. J Lightwave Technol. 2021;39(6):1672–9. .

[123] Gao H, et al. Rapid Mode Decomposition of Few-Mode Fiber by Artificial Neural Network. J Lightwave Technol. 2021;39(19):6294–300. .

[124] Scaggs M, Haas G. Real time laser beam analysis system for high power lasers. In: Laser Resonators and Beam Control XIII 7913; 2011. p. 791306. .

[125] Du Y, Fu Y, Zheng L. Complex amplitude reconstruction for dynamic beam quality M^2 factor measurement with self-referencing interferometer wavefront sensor. Appl Opt. 2016;55(36):10180. .

[126] Han Z-G, et al. Determination of the laser beam quality factor (M^2) by stitching quadriwave lateral shearing interferograms with different exposures. Appl Opt. 2017;56(27):7596. .

[127] Pan S, et al. Real-time complex amplitude reconstruction method for beam quality M^2 factor measurement. Opt Express. 2017;25(17):20142. .

[128] Yoda H, Polynkin P, Mansuripur M. Beam quality factor of higher order modes in a step-index fiber. J Lightwave Technol. 2006;24(3):1350–5. .

[129] Huang L, et al. Real-time mode decomposition for few-mode fiber based on numerical method. Opt Express. 2015;23(4):4620. .

[130] Flamm D, et al. Fast M2 measurement for fiber beams based on modal analysis. Appl Opt. 2012;51(7):987–93. .

[131] An Y, et al. Deep learning enabled superfast and accurate M 2 evaluation for fiber beams. Opt Express. 2019;27(13):18683. .

[132] Pu G, et al. Automatic mode-locking fiber lasers: progress and perspectives. Sci China Inf Sci. 2020;63(6):1–24. .

[133] Pu G, et al. Intelligent programmable mode-locked fiber laser with a human-like algorithm. Optica. 2019;6(3):362. .

[134] Brunton SL, Fu X, Kutz JN. Extremum-seeking control of a mode-locked laser. IEEE J Quantum Electron. 2013;49(10):852–61. .

[135] Andral U, et al. Toward an autosetting mode-locked fiber laser cavity. J Opt Soc Am B. 2016;33(5):825. .

[136] Woodward RI, Kelleher EJR. Towards ‘smart lasers’: Self-optimisation of an ultrafast pulse source using a genetic algorithm. Sci Rep. 2016;6(November):1–9. .

[137] Andra U, et al. Fiber laser mode locked through an evolutionary algorithm. In: Proceedings 2015 European Conference on Lasers and Electro-Optics - European Quantum Electronics Conference, CLEO/Europe-EQEC 2015 2(April); 2015. p. 2–6. .

[138] Fu X, Brunton SL, Nathan Kutz J. Classification of birefringence in mode-locked fiber lasers using machine learning and sparse representation. Opt Express. 2014;22(7):8585. .

[139] Brunton SL, Fu X, Kutz JN. Self-Tuning Fiber Lasers. IEEE J Select Topics Quantum Electron. 2014;20(5):464–71. .

[140] Baumeister T, Brunton SL, Nathan Kutz J. Deep learning and model predictive control for self-tuning mode-locked lasers. J Opt Soc Am B. 2018;35(3):617. .

[141] Yan Q, et al. Low-latency deep-reinforcement learning algorithm for ultrafast fiber lasers. Photonics Res. 2021;9(8):1493. .

[142] Su R, et al. High Power Narrow-Linewidth Nanosecond Coherent Beam Combination. Ieee J Select Topics Quantum Electron. 2014;20(5):IEEE.

[143] Chang H, et al. First experimental demonstration of coherent beam combining of more than 100 beams. Photonics Res. 2020;8(12):1943. .

[144] Goodno GD, et al. Active phase and polarization locking of a 14 kW fiber amplifier. Opt Lett. 2010;35(10):1542. .

[145] Goodno GD, et al. Brightness-scaling potential of actively phase-locked solid-state laser arrays. IEEE J Select Topics Quantum Electron. 2007;13(3):460–71. .

[146] Fsaifes I, et al. Coherent Beam combining of 37 femtosecond fiber amplifiers. In: Optics InfoBase Conference Papers Part F140-(14); 2019. p. 20152. .

[147] Kabeya D, et al. Efficient phase-locking of 37 fiber amplifiers by phase-intensity mapping in an optimization loop. Opt Express. 2017;25(12):13816. .

[148] Du Q, et al. Deterministic stabilization of eight-way 2D diffractive beam combining using pattern recognition. Opt Lett. 2019;44(18):4554. .

[149] Ahn HK, Kong HJ. Cascaded multi-dithering theory for coherent beam combining of multiplexed beam elements. Opt Express. 2015;23(9):12407. .

[150] Ahn HK, Kong HJ. Feasibility of cascaded multi-dithering technique for coherent addition of a large number of beam elements. Appl Opt. 2016;55(15):4101. .

[151] Ma Y, et al. Coherent beam combination with single frequency dithering technique. Opt Lett. 2010;35(9):1308. .

[152] Jiang M, et al. Coherent beam combining of fiber lasers using a CDMA-based single-frequency dithering technique. Appl Opt. 2017;56(15):4255. .

[153] Ma P, et al. 7.1 kW coherent beam combining system based on a seven-channel fiber amplifier array. Opt Laser Technol. 2021;140(October 2020):107016. .

[154] Shpakovych M, et al. Experimental phase control of a 100 laser beam array with quasi-reinforcement learning of a neural network in an error reduction loop. Opt Express. 2021;29(8):12307. .

[155] Zhang X, et al. Coherent beam combination based on Q-learning algorithm. Opt Commun. 2021;490(February):126930. .

[156] Hou T, et al. High-power vortex beam generation enabled by a phased beam array fed at the nonfocal-plane. Opt Express. 2019;27(4):4046. .

[157] Hou T, et al. Deep-learning-based phase control method for tiled aperture coherent beam combining systems. High Power Laser Sci Eng. 2019;7:e59. .

[158] Chen J, Wan C, Zhan Q. Engineering photonic angular momentum with structured light: a review. Adv Photonics. 2021;3(06):1–15. .

[159] Qiao Z, et al. Multi-vortex laser enabling spatial and temporal encoding. PhotoniX. 2020;1(1):13. .

[160] Chen Y, Cai Y. Optical coherence structure: A novel tool for light manipulation. Sci China Technol Sci. 2021. .

[161] Forbes A, de Oliveira M, Dennis MR. Structured light. Nat Photonics. 2021;15(4):253–62. .

[162] Chang Q, et al. Phase-locking System in Fiber Laser Array through Deep Learning with Diffusers. In: 2020 Asia Communications and Photonics Conference, ACP 2020 and International Conference on Information Photonics and Optical Communications, IPOC 2020 - Proceedings; 2020. p. 7–9. .

[163] Liu R, et al. Coherent beam combination far-field measuring method based on amplitude modulation and deep learning. Chin Opt Lett. 2020;18(4):041402. .

[164] Wang D, et al. Stabilization of the 81-channel coherent beam combination using machine learning. Opt Express. 2021;29(4):5694. .

[165] Abadi M, et al. TensorFlow: A system for large-scale machine learning. In: Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation, OSDI 2016; 2016. p. 265–83.

[166] Imambi S, Prakash KB, Kanagachidambaresan GR. PyTorch. 2021:87–104. .

[167] Li K, Malik J. Learning to optimize. In: 5th International Conference on Learning Representations, ICLR 2017 - Conference Track Proceedings; 2017.

[168] Andrychowicz M, et al. Learning to learn by gradient descent by gradient descent. In: Advances in Neural Information Processing Systems(Nips); 2016. p. 3988–96.