[1] J. Du, W. Shen, J. Liu, Y. Chen, X. Chen, Z. He. Mode division multiplexing: from photonic integration to optical fiber transmission. Chin. Opt. Lett., 19, 091301(2021).
[2] Y. Yamamoto, Y. Kawaguchi, M. Hirano. Low-loss and low-nonlinearity pure-silica-core fiber for C- and L-band broadband transmission. J. Light. Technol., 34, 321(2016).
[3] S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Sälter, G.-D. Khoe, H. de Waardt. Long-haul DWDM transmission systems employing optical phase conjugation. IEEE J. Sel. Top. Quantum Electron., 12, 505(2006).
[4] X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, S. Chandrasekhar. Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit. Nat. Photonics, 7, 560(2013).
[5] R. J. Essiambre, P. J. Winzer, X. Q. Wang, W. Lee, C. A. White, E. C. Burrows. Electronic predistortion and fiber nonlinearity. IEEE Photon. Technol. Lett., 18, 1804(2006).
[6] Y. Gao, J. C. Cartledge, A. S. Karar, S. S.-H. Yam, M. O’Sullivan, C. Laperle, A. Borowiec, K. Roberts. Reducing the complexity of perturbation based nonlinearity pre-compensation using symmetric EDC and pulse shaping. Opt. Express, 22, 1209(2014).
[7] M. Secondini, E. Forestieri. On XPM mitigation in WDM fiber-optic systems. IEEE Photon. Technol. Lett., 26, 2252(2014).
[8] K. Zhang, G. Gao, J. Zhang, A. Fei, M. Cvijetic. Mitigation of nonlinear fiber distortion using optical phase conjugation for mode-division multiplexed transmission. Opt. Fiber Technol., 43, 169(2018).
[9] E. Ip. Nonlinear compensation using backpropagation for polarization-multiplexed transmission. J. Light. Technol., 28, 939(2010).
[10] L. B. Du, A. J. Lowery. Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems. Opt. Express, 18, 17075(2010).
[11] L. Jiang, L. Yan, Z. Chen, A. Yi, Y. Pan, W. Pan, B. Luo, G. Li. Adaptive digital backward propagation based on variance of intensity noise. Chin. Opt. Lett., 13, 110602(2015).
[12] R. Maher, T. Xu, L. Galdino, M. Sato, A. Alvarado, K. Shi, S. J. Savory, B. C. Thomsen, R. I. Killey, P. Bayvel. Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation. Sci. Rep., 5, 8214(2015).
[13] G. P. Agrawal. Nonlinear Fiber Optics(2019).
[14] Q. Fan, G. Zhou, T. Gui, L. Chao, A. P. T. Lau. Advancing theoretical understanding and practical performance of signal processing for nonlinear optical communications through machine learning. Nat. Commun., 11, 3694(2020).
[15] B. I. Bitachon, A. Ghazisaeidi, M. Eppenberger, B. Baeuerle, M. Ayata, J. Leuthold. Deep learning based digital backpropagation demonstrating SNR gain at low complexity in a 1200 km transmission link. Opt. Express, 28, 29318(2020).
[16] A. Mecozzi, C. Antonelli, M. Shtaif. Coupled Manakov equations in multimode fibers with strongly coupled groups of modes. Opt. Express, 20, 23436(2012).
[17] A. Mecozzi, C. Antonelli, M. Shtaif. Nonlinear propagation in multimode fibers in the strong coupling regime. Opt. Express, 20, 11673(2012).
[18] S. Mumtaz, R.-J. Essiambre, G. P. Agrawal. Nonlinear propagation in multimode and multicore fibers: generalization of the Manakov equations. J. Light. Technol., 31, 398(2013).
[19] F. Ferreira, S. Jansen, P. Monteiro, H. Silva. Nonlinear semi-analytical model for simulation of few-mode fiber transmission. IEEE Photon. Technol. Lett., 24, 240(2012).
[20] L. G. Wright, D. N. Christodoulides, F. W. Wise. Controllable spatiotemporal nonlinear effects in multimode fibres. Nat. Photonics, 9, 306(2015).
[21] K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, V. Couderc. Spatial beam self-cleaning in multimode fibres. Nat. Photonics, 11, 237(2017).
[22] M. A. Eftekhar, Z. Sanjabi-Eznaveh, H. E. Lopez-Aviles, S. Benis, J. E. Antonio-Lopez, M. Kolesik, F. Wise, R. Amezcua-Correa, D. N. Christodoulides. Accelerated nonlinear interactions in graded-index multimode fibers. Nat. Commun., 10, 1638(2019).
[23] G. Rademacher, R. Ryf, N. K. Fontaine, H. Chen, R.-J. Essiambre, B. J. Puttnam, R. S. Luís, Y. Awaji, N. Wada, S. Gross, N. Riesen, M. Withford, Y. Sun, R. Lingle. Long-haul transmission over few-mode fibers with space-division multiplexing. J. Light. Technol., 36, 1382(2018).
[24] G. Rademacher, R. S. Luís, B. J. Puttnam, Y. Awaji, M. Suzuki, T. Hasegawa, H. Furukawa, N. Wada. Wideband intermodal nonlinear signal processing with a highly nonlinear few-mode fiber. IEEE J. Sel. Top. Quantum Electron., 26, 7702007(2020).
[25] F. M. Ferreira, C. S. Costa, S. Sygletos, A. D. Ellis. Nonlinear performance of few-mode fiber links with intermediate coupling. J. Light. Technol., 37, 989(2019).
[26] F. M. Ferreira, S. Sygletos, E. Sillekens, R. Killey, A. D. Ellis, N. J. Doran. On the performance of digital back propagation in spatial multiplexing systems. J. Light. Technol., 38, 2790(2020).
[27] L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, F. W. Wise. Multimode nonlinear fiber optics: massively parallel numerical solver, tutorial, and outlook. IEEE J. Sel. Top. Quantum Electron., 24, 5100516(2018).
[28] J. Li, X. Zhang, Y. Zheng, F. Li, X. Shan, Z. Han, R. Zhu. Fast fiber mode decomposition with a lensless fiber-point-diffraction interferometer. Opt. Lett., 46, 2501(2021).
[29] S. G. Leon-Saval, N. K. Fontaine, J. R. Salazar-Gil, B. Ercan, R. Ryf, J. Bland-Hawthorn. Mode-selective photonic lanterns for space-division multiplexing. Opt. Express, 22, 1036(2014).
[30] E. Manuylovich, V. Dvoyrin, S. Turitsyn. Fast mode decomposition in few-mode fibers. Nat. Commun., 11, 5507(2020).
[31] P. S. Anisimov, V. V. Zemlyakov, J. Gao. 2D least-squares mode decomposition for mode division multiplexing. Opt. Express, 30, 8804(2022).
[32] Y. An, L. Huang, J. Li, J. Leng, L. Yang, P. Zhou. Learning to decompose the modes in few-mode fibers with deep convolutional neural network. Opt. Express, 27, 10127(2019).
[33] Q. Zhang, S. Rothe, N. Koukourakis, J. Czarske. Learning the matrix of few-mode fibers for high-fidelity spatial mode transmission. APL Photonics, 7, 066104(2022).
[34] B. Rahmani, D. Loterie, G. Konstantinou, D. Psaltis, C. Moser. Multimode optical fiber transmission with a deep learning network. Light Sci. Appl., 7, 69(2018).
[35] U. Teğin, B. Rahmani, E. Kakkava, N. Borhani, C. Moser, D. Psaltis. Controlling spatiotemporal nonlinearities in multimode fibers with deep neural networks. APL Photonics, 5, 030804(2020).
[36] F. Poletti, P. Horak. Description of ultrashort pulse propagation in multimode optical fibers. J. Opt. Soc. Am. B, 25, 1645(2008).
[37] P. S. Anisimov, V. S. Motolygin, V. V. Zemlyakov, J. Gao. Fast multi step-index mode solver for analysis and optimization of optical fiber performance. J. Light. Technol., 40, 2980(2022).
[38] I. Loshchilov, F. Hutter. Decoupled weight decay regularization(2019).