Nonlinear Fourier transform enabled eigenvalue spectrum investigation for fiber laser radiation

Yutian Wang; Songnian Fu; Jian Kong; Andrey Komarov; Mariusz Klimczak; Ryszard Buczyński; Xiahui Tang; Ming Tang; Yuwen Qin; Luming Zhao

doi:10.1364/PRJ.427842

[1] P. M. W. French. The generation of ultrashort pulses. Rep. Prog. Phys., 58, 169-267(1995).

[2] U. Keller. Recent developments in compact ultrafast lasers. Nature, 424, 831-838(2003).

[3] A. Martinez, Z. P. Sun. Nanotube and graphene saturable absorbers for fiber lasers. Nat. Photonics, 7, 842-845(2013).

[4] U. Andral, R. S. Fodil, F. Amrani, F. Billard, E. Hertz, P. Grelu. Fiber laser mode locked through an evolutionary algorithm. Optica, 2, 275-278(2015).

[5] S. Kobtsev, S. Kukarin, S. Smirnov, S. K. Turitsyn, A. Latkin. Generation of double-scale femto/pico-second optical lumps in mode-locked fiber lasers. Opt. Express, 17, 20707-20713(2009).

[6] N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, S. K. Turitsyn. Mode-locking via dissipative Faraday instability. Nat. Commun., 7, 12441(2016).

[7] J. Xu, L. Huang, M. Jiang, J. Ye, P. Ma, J. Leng, J. Wu, H. Zhang, P. Zhou. Near-diffraction-limited linearly polarized narrow-linewidth random fiber laser with record kilowatt output. Photon. Res., 5, 350-354(2017).

[8] A. Chong, J. Buckley, W. Renninger, F. Wise. All-normal-dispersion femtosecond fiber laser. Opt. Express, 14, 10095-10100(2006).

[9] A. F. J. Runge, N. G. R. Broderick, M. Erkintalo. Observation of soliton explosions in a passively mode-locked fiber laser. Optica, 2, 36-39(2015).

[10] G. Herink, F. Kurtz, B. Jalali, D. R. Solli, C. Ropers. Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules. Science, 356, 50-54(2017).

[11] K. Krupa, K. Nithyanandan, G. Grelu. Vector dynamics of incoherent dissipative optical solitons. Optica, 4, 1239-1244(2017).

[12] X. Liu, D. Popa, N. Akhmediev. Revealing the transition dynamics from Q switching to mode locking in a soliton laser. Phys. Rev. Lett., 123, 093901(2019).

[13] X. Liu, M. Pang. Revealing the buildup dynamics of harmonic mode-locking states in ultrafast lasers. Laser Photonics Rev., 13, 1800333(2019).

[14] P. Suret, R. E. Koussaifi, A. Tikan, C. Evain, S. Randoux, C. Szwaj, S. Bielawski. Direct observation of rogue waves in optical turbulence using time microscopy. Nat. Commun., 7, 13136(2016).

[15] A. Tikan, C. Billet, G. El, A. Tovbis, M. Bertola, T. Sylvestre, F. Gustave, S. Randoux, G. Genty, P. Suret, J. M. Dudley. Universality of the peregrine soliton in the focusing dynamics of the cubic nonlinear Schrödinger equation. Phys. Rev. Lett., 119, 033901(2017).

[16] S. M. J. Kelly. Characteristic sideband instability of periodically amplified average soliton. Electron. Lett., 28, 806-807(1992).

[17] M. Liu, H. J. Chen, A. P. Luo, G. Y. Zhou, Z. C. Luo. Identification of coherent and incoherent spectral sidebands in an ultrafast fiber laser. IEEE J. Sel. Top. Quantum Electron., 24, 1100606(2018).

[18] A. Komarov, K. Komarov, A. Niang, F. Sanchez. Nature of soliton interaction in fiber lasers with continuous external optical injection. Phys. Rev. A, 89, 013833(2014).

[19] S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian, S. A. Derevyanko. Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives. Optica, 4, 307-322(2017).

[20] M. I. Yousefi, F. R. Kschischang. Information transmission using the nonlinear Fourier transform. Part II: numerical methods. IEEE Trans. Inf. Theory, 60, 4329-4345(2014).

[21] J. E. Prilepsky, S. A. Derevyanko, K. J. Blow, I. Gabitov, S. K. Turitsyn. Nonlinear inverse synthesis and eigenvalue division multiplexing in optical fiber channels. Phys. Rev. Lett., 113, 013901(2014).

[22] S. T. Le, V. Aref, H. Buelow. Nonlinear signal multiplexing for communication beyond the Kerr nonlinearity limit. Nat. Photonics, 11, 570-576(2017).

[23] S. Randoux, P. Suret, G. El. Inverse scattering transform analysis of rogue waves using local periodization procedure. Sci. Rep., 6, 29238(2016).

[24] J. Wang, A. Sheng, X. Huang, R. Li, G. He. Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform. Chin. Phys. B, 29, 034207(2020).

[25] P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, J. M. Dudley. Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser. Nat. Photonics, 12, 221-227(2018).

[26] S. Sugavanam, M. K. Kopae, J. Peng, J. E. Prilepsky, S. K. Turitsyn. Analysis of laser radiation using the nonlinear Fourier transform. Nat. Commun., 10, 5663(2019).

[27] I. S. Chekhovskoy, O. V. Shtyrina, M. P. Fedoruk, S. B. Medvedev, S. K. Turitsyn. Nonlinear Fourier transform for analysis of coherent structures in dissipative systems. Phys. Rev. Lett., 122, 153901(2019).

[28] Y. Wang, S. Fu, C. Zhang, X. Tang, J. Kong, J. H. Lee, L. M. Zhao. Soliton distillation of pulses from a fiber laser. J. Lightwave Technol., 39, 2542-2546(2021).

[29] L. M. Zhao, D. Y. Tang, F. Lin, B. Zhao. Observation of period-doubling bifurcations in a femtosecond fiber soliton laser with dispersion management cavity. Opt. Express, 12, 4573-4578(2004).

[30] L. Li, H. Huang, L. Su, D. Y. Shen, D. Y. Tang, M. Klimczak, L. M. Zhao. Various soliton molecules in fiber systems. Appl. Opt., 58, 2745-2753(2019).

[31] A. Vasylchenkova, D. Salnikov, D. Karaman, O. G. Vasylchenkov, J. E. Prilepskiy. Fixed-point realisation of fast nonlinear Fourier transform algorithm for FPGA implementation of optical data processing. Proc. SPIE, 11770, 1177016(2021).

[32] V. E. Zakharov, A. B. Shabat. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. J. Exp. Theor. Phys., 34, 62-69(1972).

[33] T. Gui, C. Lu, A. P. L. Lau, P. K. A. Wai. High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform. Opt. Express, 25, 20286-20297(2017).

[34] L. M. Zhao, D. Y. Tang, H. Y. Tam, C. Lu. Pulse breaking recovery in fiber lasers. Opt. Express, 16, 12102-12107(2008).

[35] Z. Zheng, X. Zhang, R. Yu, L. Xi, X. Zhang. Frequency offset estimation for nonlinear frequency division multiplexing with discrete spectrum modulation. Opt. Express, 27, 28223-28238(2019).

[36] Y. Wang, R. Xin, S. Fu, M. Tang, D. Liu. Laser linewidth tolerance for nonlinear frequency division multiplexing transmission with discrete spectrum modulation. Opt. Express, 28, 9642-9652(2020).