[1] Xie Y H, Yang Z, Shi M Y et al. 100 Gb/s coherent chaotic optical communication over 800 km fiber transmission via advanced digital signal processing[J]. Advanced Photonics Nexus, 3, 016003(2024).

[2] Wu Q, Xu Z P, Zhu Y X et al. Beyond 200-Gb/s O-band intensity modulation and direct detection optics with joint look-up-table-based predistortion and digital resolution enhancement for low-cost data center interconnects[J]. Advanced Photonics Nexus, 3, 036007(2024).

[3] Liu H X, Pan B C, Li H et al. First demonstration of lithium niobate photonic chip for dense wavelength-division multiplexing transmitters[J]. Advanced Photonics, 6, 066001(2024).

[4] Ferrari A, Napoli A, Fischer J K et al. Assessment on the achievable throughput of multi-band ITU-T G.652.D fiber transmission systems[J]. Journal of Lightwave Technology, 38, 4279-4291(2020).

[5] Zuo M Q, Zhang D C, Zou H Q et al. Field trial of real-time 80-λ×400-Gb/s single-carrier 128-GBD DP-QPSK transmission covering 12-THz C+L band over 2502-km terrestrial G.652.D fibre[J]. IET Conference Proceedings, 843-846(2023).

[6] Ge D W, Zuo M Q, Liu H B et al. Fully-loaded 80×400 Gb/s DP-QPSK transmission with commercial 12-THz C6T L6T EDFAs over record distance of 7000 km[C], 1-4(2023).

[7] Escobar-Landero S, Lorences-Riesgo A, Zhao X H et al. S+C+L high-capacity transmission systems: challenges and opportunities[J]. Journal of Lightwave Technology, 42, 4260-4270(2024).

[8] Frignac Y, Le Gac D, Lorences-Riesgo A et al. Record 158.4 Tb/s transmission over 2×60 km field SMF using S+C+L 18 THz-bandwidth lumped amplification[J]. IET Conference Proceedings, 550-553(2023).

[9] Zhang Y, Pang X H, Song Y C et al. Optical power control for GSNR optimization based on C+L-band digital twin systems[J]. Journal of Lightwave Technology, 42, 95-105(2024).

[10] Correia B, Sadeghi R, Virgillito E et al. Optical power control strategies for optimized C+L+S-bands network performance[C]. DC, W1F.8-10(2021).

[11] Roberts I, Kahn J M, Harley J et al. Channel power optimization of WDM systems following Gaussian noise nonlinearity model in presence of stimulated Raman scattering[J]. Journal of Lightwave Technology, 35, 5237-5249(2017).

[12] Song Y C, Fan Q R, Lu C et al. Efficient three-step amplifier configuration algorithm for dynamic C+L-band links in presence of stimulated Raman scattering[J]. Journal of Lightwave Technology, 41, 1445-1453(2023).

[13] Zhang C Y, Wang D S, Jia J W et al. Potential failure cause identification for optical networks using deep learning with an attention mechanism[J]. Journal of Optical Communications and Networking, 14, A122-A133(2022).

[14] Zhang Y, Zhang M, Song Y C et al. Building a digital twin for large-scale and dynamic C+L-band optical networks[J]. Journal of Optical Communications and Networking, 15, 985-998(2023).

[15] Li M Y, Wu J T, Yang J Y et al. Simplified multi-channel parallel optical performance monitoring based on deep learning[J]. Acta Optica Sinica, 43, 0715002(2023).

[16] Ju J Z, Liu Q T, Li H Z et al. Multi-task optical performance monitoring based on convolutional neural network[J]. Acta Optica Sinica, 42, 2206002(2022).

[17] Liu X M, Zhang Y H, Chen Y L et al. Digital twin modeling and controlling of optical power evolution enabling autonomous-driving optical networks: a Bayesian approach[J]. Advanced Photonics, 6, 026006(2024).

[18] Napoli A, Maalej Z, Sleiffer V A J M et al. Reduced complexity digital back-propagation methods for optical communication systems[J]. Journal of Lightwave Technology, 32, 1351-1362(2014).

[19] Vassilieva O, Kim I, Ikeuchi T. Enabling technologies for fiber nonlinearity mitigation in high capacity transmission systems[J]. Journal of Lightwave Technology, 37, 50-60(2019).

[20] Fan Q R, Zhou G, Gui T et al. Advancing theoretical understanding and practical performance of signal processing for nonlinear optical communications through machine learning[J]. Nature Communications, 11, 3694(2020).

[21] Sidelnikov O, Redyuk A, Sygletos S et al. Advanced convolutional neural networks for nonlinearity mitigation in long-haul WDM transmission systems[J]. Journal of Lightwave Technology, 39, 2397-2406(2021).

[22] Lin X, Luo S H, Soman S K O et al. Perturbation theory-aided learned digital back-propagation scheme for optical fiber nonlinearity compensation[J]. Journal of Lightwave Technology, 40, 1981-1988(2022).

[23] Niu Z K, Yang H, Li L et al. Learnable digital signal processing: a new benchmark of linearity compensation for optical fiber communications[J]. Light: Science & Applications, 13, 188(2024).

[24] Zhang L F, Zhang T, Li M Y et al. Digital back propagation optimization algorithm based on step-size optimization and power compensation factor[J]. Acta Optica Sinica, 44, 1619002(2024).

[25] Meng J Y, Zhang H B, Zhang M et al. Fiber nonlinear impairments compensation based on IPCA-DNN algorithm[J]. Acta Optica Sinica, 41, 2406002(2021).

[26] Lin Z Y, Yang Y F, Xiang Q et al. Adaptive carrier phase recovery algorithm for probabilistically shaped signals[J]. Acta Optica Sinica, 40, 2306001(2020).

[27] Karanov B, Lavery D, Bayvel P et al. End-to-end optimized transmission over dispersive intensity-modulated channels using bidirectional recurrent neural networks[J]. Optics Express, 27, 19650-19663(2019).

[28] Karanov B, Chagnon M, Aref V et al. Optical fiber communication systems based on end-to-end deep learning: (invited paper)[C], 1-2(2020).

[29] Niu Z K, Yang H, Zhao H C et al. End-to-end deep learning for long-haul fiber transmission using differentiable surrogate channel[J]. Journal of Lightwave Technology, 40, 2807-2822(2022).

[30] Xu Y X, Huang L Y, Jiang W Q et al. End-to-end learning for 100G-PON based on noise adaptation network[J]. Journal of Lightwave Technology, 42, 2328-2337(2024).

[31] Li M Y, Wang S W. End-to-end learning for chromatic dispersion compensation in optical fiber communication[J]. IEEE Communications Letters, 26, 1829-1832(2022).

[32] Song J X, Häger C, Schröder J et al. Model-based end-to-end learning for WDM systems with transceiver hardware impairments[J]. IEEE Journal of Selected Topics in Quantum Electronics, 28, 7700114(2022).

[33] Karanov B, Chagnon M, Thouin F et al. End-to-end deep learning of optical fiber communications[J]. Journal of Lightwave Technology, 36, 4843-4855(2018).

[34] Gloge D. Optical fibers for communication[J]. Applied Optics, 13, 249-254(1974).

[35] Poggiolini P. The GN model of non-linear propagation in uncompensated coherent optical systems[J]. Journal of Lightwave Technology, 30, 3857-3879(2012).

[36] Carena A, Bosco G, Curri V et al. EGN model of non-linear fiber propagation[J]. Optics Express, 22, 16335-16362(2014).

[37] Agrawal G P. Nonlinear fiber optics[M]. Nonlinear science at the dawn of the 21st Century, 542, 195-211(2007).

[38] Serena P, Lasagni C, Musetti S et al. On numerical simulations of ultra-wideband long-haul optical communication systems[J]. Journal of Lightwave Technology, 38, 1019-1031(2020).

[39] Hornik K, Stinchcombe M, White H. Multilayer feedforward networks are universal approximators[J]. Neural Networks, 2, 359-366(1989).

[40] Wei J, Zhang X J, Ji Z Y et al. Deploying and scaling distributed parallel deep neural networks on the Tianhe-3 prototype system[J]. Scientific Reports, 11, 20244(2021).

[41] Wang D S, Song Y C, Li J et al. Data-driven optical fiber channel modeling: a deep learning approach[J]. Journal of Lightwave Technology, 38, 4730-4743(2020).

[42] Yang H, Niu Z K, Xiao S L et al. Fast and accurate optical fiber channel modeling using generative adversarial network[J]. Journal of Lightwave Technology, 39, 1322-1333(2021).

[43] Yuan M Z, Chang H, Ma M et al. A Conditional Generative Adversarial Network aided Few-mode Fiber Channel Modeling for large-capacity optical fiber communication[C], 1-3(2023).

[44] Zhu Y, Ye J, Yan L S et al. Transformer-based high-fidelity modeling method for radio over fiber link[J]. Journal of Lightwave Technology, 41, 2657-2665(2023).

[45] Zhang N Y, Yang H, Niu Z K et al. Transformer-based long distance fiber channel modeling for optical OFDM systems[J]. Journal of Lightwave Technology, 40, 7779-7789(2022).

[46] Chen W B, Zhang M, Wang D D et al. Deep learning-based channel modeling for free space optical communications[J]. Journal of Lightwave Technology, 41, 183-198(2023).

[47] Boscolo S, Finot C. Artificial neural networks for nonlinear pulse shaping in optical fibers[J]. Optics & Laser Technology, 131, 106439(2020).

[48] Zahavy T, Dikopoltsev A, Moss D et al. Deep learning reconstruction of ultrashort pulses[J]. Optica, 5, 666-673(2018).

[49] Salmela L, Tsipinakis N, Foi A et al. Predicting ultrafast nonlinear dynamics in fibre optics with a recurrent neural network[J]. Nature Machine Intelligence, 3, 344-354(2021).

[50] Yang H, Zhao H C, Niu Z K et al. Low-complexity full-field ultrafast nonlinear dynamics prediction by a convolutional feature separation modeling method[J]. Optics Express, 30, 43691-43705(2022).

[51] Teğin U, Rahmani B, Kakkava E et al. Controlling spatiotemporal nonlinearities in multimode fibers with deep neural networks[J]. APL Photonics, 5, 030804(2020).

[52] Raissi M, Perdikaris P, Karniadakis G E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J]. Journal of Computational Physics, 378, 686-707(2019).

[53] Liu X M, Zhang Z Y, Liu W J. Physics-informed neural network method for predicting soliton dynamics supported by complex parity-time symmetric potentials[J]. Chinese Physics Letters, 40, 070501(2023).

[54] Xu S Y, Zhou Q, Liu W. Prediction of soliton evolution and equation parameters for NLS-MB equation based on the phPINN algorithm[J]. Nonlinear Dynamics, 111, 18401-18417(2023).

[55] Jiang X T, Wang D S, Fan Q R et al. Solving the nonlinear Schrödinger equation in optical fibers using physics-informed neural network[C]. DC, M3H.8-10(2021).

[56] Wang D S, Jiang X T, Song Y C et al. Applications of physics-informed neural network for optical fiber communications[J]. IEEE Communications Magazine, 60, 32-37(2022).

[57] Jiang X T, Wang D S, Fan Q R et al. Physics-informed neural network for nonlinear dynamics in fiber optics[J]. Laser & Photonics Reviews, 16, 2100483(2022).

     Jiang X T, Wang D S, Fan Q R et al. Physics-informed neural network for nonlinear dynamics in fiber optics[J]. Laser & Photonics Reviews, 16, 2100483(2022).

[58] Zeng C Y, Niu Z K, Yang H et al. Neural channel model-aided distributed dispersion manage optimization for mitigation of nonlinearities and dispersion in fibre transmission[C], 1-4(2024).

[59] Menyuk C. Nonlinear pulse propagation in birefringent optical fibers[J]. IEEE Journal of Quantum Electronics, 23, 174-176(1987).

[60] Marcuse D, Manyuk C R, Wai P K A. Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence[J]. Journal of Lightwave Technology, 15, 1735-1746(1997).

[61] Evangelides S G, Mollenauer L F, Gordon J P et al. Polarization multiplexing with solitons[J]. Journal of Lightwave Technology, 10, 28-35(1992).

[62] Shao J, Liang X J, Kumar S. Comparison of split-step Fourier schemes for simulating fiber optic communication systems[J]. IEEE Photonics Journal, 6, 7200515(2014).

[63] Sinkin O V, Holzlohner R, Zweck J et al. Optimization of the split-step Fourier method in modeling optical-fiber communications systems[J]. Journal of Lightwave Technology, 21, 61-68(2003).

[64] Ip E, Kahn J M. Compensation of dispersion and nonlinear impairments using digital backpropagation[J]. Journal of Lightwave Technology, 26, 3416-3425(2008).

[65] Eriksson T A, Bülow H, Leven A. Applying neural networks in optical communication systems: possible pitfalls[J]. IEEE Photonics Technology Letters, 29, 2091-2094(2017).

[66] Yi L L, Liao T, Huang L Y et al. Machine learning for 100 Gb/s/λ passive optical network[J]. Journal of Lightwave Technology, 37, 1621-1630(2019).

[67] Yang H, Niu Z K, Zhao H C et al. Fast and accurate waveform modeling of long-haul multi-channel optical fiber transmission using a hybrid model-data driven scheme[J]. Journal of Lightwave Technology, 40, 4571-4580(2022).

[68] Shi M H, Yang H, Niu Z K et al. Accurate and efficient optical fiber WDM transmission modeling using the encoder-only transformer with feature decoupling distributed method[C], 1-5(2023).

[69] Zhang J S, Li X Y, Hu Y X et al. Spectrally efficient integrated silicon photonic phase-diverse DD receiver with near-ideal phase response for C-band DWDM transmission[J]. Laser & Photonics Reviews, 18, 2300623(2024).

[70] Ye G, Xiang J J, Zhou G et al. Impact of the input OSNR on data-driven optical fiber channel modeling[J]. Journal of Optical Communications and Networking, 15, 78-86(2023).

[71] Jiang R, Fu Z L, Bao Y S et al. Data-driven method for nonlinear optical fiber channel modeling based on deep neural network[J]. IEEE Photonics Journal, 14, 8537608(2022).

[72] Jiang R, Wang Z, Jia T et al. Flexible optical fiber channel modeling based on a neural network module[J]. Optics Letters, 48, 4332-4335(2023).

[73] Zang Y B, Yu Z M, Xu K et al. Multi-span long-haul fiber transmission model based on cascaded neural networks with multi-head attention mechanism[J]. Journal of Lightwave Technology, 40, 6347-6358(2022).

[74] Zang Y B, Yu Z M, Xu K et al. Data-driven fiber model based on the deep neural network with multi-head attention mechanism[J]. Optics Express, 30, 46626-46648(2022).

[75] He X C, Yan L S, Jiang L et al. Fourier neural operator for accurate optical fiber modeling with low complexity[J]. Journal of Lightwave Technology, 41, 2301-2311(2023).

[76] Qiu Q Z, Lun H Z, Liu X M et al. Fourier neural operator based fibre channel modelling for optical transmission[C], 1-4(2022).

[77] Zhang X M, Zhang M, Song Y C et al. DeepONet-based waveform-level simulation for a wideband nonlinear WDM system[J]. Journal of Lightwave Technology, 41, 6908-6922(2023).

[78] Song Y C, Wang D S, Fan Q R et al. Physics-informed neural operator for fast and scalable optical fiber channel modelling in multi-span transmission[C], 1-4(2022).

[79] Zeng C Y, Niu Z K, Yang H et al. Enhancing generalization in neural channel model for optical fiber WDM transmission through learned encoding of system parameters[C], M4K.1-28(2024).

[80] Zheng J Y, Zhang T H, Zhang F et al. Co-LSTM-based fiber link modeling with ASE noise tracking for long-haul coherent optical transmission[J]. Optics Letters, 49, 1848-1851(2024).

[81] Shi M H, Niu Z K, Yang H et al. Fast and accurate waveform modeling based on sequence-to-sequence framework for multi-channel and high-rate optical fiber transmission[J]. Optics Letters, 50, 2286-2289(2025).

[82] Zhang T H, Pan Y T, Zheng J Y et al. Fourier neural operator accelerated fast and accurate optical fiber transmission modeling[J]. Journal of Lightwave Technology, 43, 3592-3604(2025).

[83] Saxena D, Cao J N. Generative adversarial networks (GANs): challenges, solutions, and future directions[J]. ACM Computing Surveys, 54, 63(2022).

[84] Gui J, Sun Z N, Wen Y G et al. A review on generative adversarial networks: algorithms, theory, and applications[J]. IEEE Transactions on Knowledge and Data Engineering, 35, 3313-3332(2023).

[85] Lu L, Jin P Z, Pang G F et al. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators[J]. Nature Machine Intelligence, 3, 218-229(2021).

[86] Wang S F, Wang H W, Perdikaris P. Learning the solution operator of parametric partial differential equations with physics-informed DeepONets[J]. Science Advances, 7, eabi8605(2021).

[87] Vaswani A, Shazeer N, Parmar N et al. Attention is all you need[EB/OL]. https:∥arxiv.org/abs/1706.03762

[88] Karniadakis G E, Kevrekidis I G, Lu L et al. Physics-informed machine learning[J]. Nature Reviews Physics, 3, 422-440(2021).

[89] Jovanovic O, da Ros F, Zibar D et al. Geometric constellation shaping for fiber-optic channels via end-to-end learning[J]. Journal of Lightwave Technology, 41, 3726-3736(2023).

[90] Li S, Häger C, Garcia N et al. Achievable information rates for nonlinear fiber communication via end-to-end autoencoder learning[C], 1-3(2018).

[91] Jones R T, Eriksson T A, Yankov M P et al. Deep learning of geometric constellation shaping including fiber nonlinearities[C], 1-3(2018).

[92] Neskorniuk V, Carnio A, Bajaj V et al. End-to-end deep learning of long-haul coherent optical fiber communications via regular perturbation model[C], 1-4(2021).

[93] Gümüş K, Alvarado A, Chen B et al. End-to-end learning of geometrical shaping maximizing generalized mutual information[C], W3D.4-12(2020).

[94] Aref V, Chagnon M. End-to-end learning of joint geometric and probabilistic constellation shaping[C], W4I.3-10(2022).

[95] Neskorniuk V, Carnio A, Marsella D et al. Model-based deep learning of joint probabilistic and geometric shaping for optical communication[C], SW4E.5-20(2022).

[96] Gaiarin S, da Ros F, Jones R T et al. End-to-end optimization of coherent optical communications over the split-step Fourier method guided by the nonlinear Fourier transform theory[J]. Journal of Lightwave Technology, 39, 418-428(2021).

[97] Gaiarin S, Jones R T, Da Ros F et al. End-to-end optimized nonlinear Fourier transform-based coherent communications[C]. DC, SF2L.4-15(2020).

[98] Karanov B, Chagnon M, Aref V et al. Concept and experimental demonstration of optical IM/DD end-to-end system optimization using a generative model[C], Th2A.48-12(2020).

[99] Li M L, Wang D S, Cui Q C et al. End-to-end learning for optical fiber communication with data-driven channel model[C], 1-3(2020).

[100] Xu Y X, Guan X K, Jiang W Q et al. Low-complexity end-to-end deep learning framework for 100G-PON[J]. Journal of Optical Communications and Networking, 16, 1093(2024).

[101] Li Z Y, Wang C X, Jia J L et al. Model-driven deep-learning for end-to-end optimization in fiber-terahertz communication systems[J]. Journal of Lightwave Technology, 43, 3099-3117(2025).

[102] Bakhshali A, Najafi H, Hamgini B B et al. Neural network architectures for optical channel nonlinear compensation in digital subcarrier multiplexing systems[J]. Optics Express, 31, 26418-26434(2023).

[103] Karita S, Chen N X, Hayashi T et al. A comparative study on transformer vs RNN in speech applications[C], 449-456(2019).

[104] Brown T B, Mann B, Ryder N et al. Language models are few-shot learners[EB/OL]. https:∥arxiv.org/abs/2005.14165

[105] Achiam J, Adler S, Agarwal S. GPT-4 technical report[EB/OL]. https:∥arxiv.org/abs/2303.08774v6

[106] Zhao W X, Zhou K, Li J. A survey of large language models[EB/OL]. https:∥arxiv.org/abs/2303.18223