Abstract

Experimental observations of spatiotemporal mode-locked multiple-soliton, including harmonic mode locking and multiple pulses, in multimode fiber (MMF) lasers are reported. Numerical simulations are conducted to investigate the nonlinear dynamics of multi-pulsing. The influences of cavity parameters on the spatiotemporal outputs are analyzed by simulations, which agree with the experimental observations qualitatively. This work would contribute to understanding the complex spatiotemporal nonlinear dynamics in MMF lasers.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10(1), 830 (2019).
[Crossref] [PubMed]

2018 (6)

K. Krupa, A. Tonello, V. Couderc, A. Barthélémy, G. Millot, D. Modotto, and S. Wabnitz, “Spatiotemporal light-beam compression from nonlinear mode coupling,” Phys. Rev. A (Coll. Park) 97(4), 043836 (2018).
[Crossref]

O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12(6), 368–374 (2018).
[Crossref]

P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. M. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (2018).
[Crossref]

X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121(2), 023905 (2018).
[Crossref] [PubMed]

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–16 (2018).
[Crossref]

H. Qin, X. Xiao, P. Wang, and C. Yang, “Observation of soliton molecules in a spatiotemporal mode-locked multimode fiber laser,” Opt. Lett. 43(9), 1982–1985 (2018).
[Crossref] [PubMed]

2017 (9)

R. Dupiol, A. Bendahmane, K. Krupa, A. Tonello, M. Fabert, B. Kibler, T. Sylvestre, A. Barthelemy, V. Couderc, S. Wabnitz, and G. Millot, “Far-detuned cascaded intermodal four-wave mixing in a multimode fiber,” Opt. Lett. 42(7), 1293–1296 (2017).
[Crossref] [PubMed]

M. Conforti, C. Mas Arabi, A. Mussot, and A. Kudlinski, “Fast and accurate modeling of nonlinear pulse propagation in graded-index multimode fibers,” Opt. Lett. 42(19), 4004–4007 (2017).
[Crossref] [PubMed]

U. Teğin and B. Ortaç, “Spatiotemporal Instability of Femtosecond Pulses in Graded-Index Multimode Fibers,” IEEE Photonics Technol. Lett. 29(24), 2195–2198 (2017).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning in multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Spatiotemporal mode-locking in multimode fiber lasers,” Science 358(6359), 94–97 (2017).
[Crossref] [PubMed]

P. Wang, X. Xiao, H. Zhao, and C. Yang, “Observation of duration-tunable soliton explosion in passively mode-locked fiber laser,” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Y. Yu, B. Li, X. Wei, Y. Xu, K. K. M. Tsia, and K. K. Y. Wong, “Spectral-temporal dynamics of multipulse mode-locking,” Appl. Phys. Lett. 110(20), 201107 (2017).
[Crossref]

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356(6333), 50–54 (2017).
[Crossref] [PubMed]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118(24), 243901 (2017).
[Crossref] [PubMed]

2016 (5)

2015 (2)

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9(5), 306–310 (2015).
[Crossref]

A. F. J. Runge, N. G. R. Broderick, and M. Erkintalo, “Observation of soliton explosions in a passively mode-locked fiber laser,” Optica 2(1), 36–39 (2015).
[Crossref]

2013 (3)

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4(1), 1719 (2013).
[Crossref] [PubMed]

Z.-C. Luo, M. Liu, H. Liu, X.-W. Zheng, A.-P. Luo, C.-J. Zhao, H. Zhang, S.-C. Wen, and W.-C. Xu, “2 GHz passively harmonic mode-locked fiber laser by a microfiber-based topological insulator saturable absorber,” Opt. Lett. 38(24), 5212–5215 (2013).
[Crossref] [PubMed]

2012 (3)

2011 (1)

E. Ding, S. Lefrancois, J. N. Kutz, and F. W. Wise, “Scaling fiber lasers to large mode area: an investigation of passive mode-locking using a multi-mode fiber,” IEEE J. Quantum Electron. 47(5), 597–606 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (1)

2007 (1)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[Crossref] [PubMed]

2003 (1)

1998 (1)

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34(9), 1749–1757 (1998).
[Crossref]

1992 (1)

A. Grudinin, D. Richardson, and D. Payne, “Energy quantisation in figure eight fibre laser,” Electron. Lett. 28(1), 67–68 (1992).
[Crossref]

1974 (1)

Akhmediev, N.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[Crossref]

Amezcua Correa, R.

Andral, U.

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118(24), 243901 (2017).
[Crossref] [PubMed]

Antonio Lopez, J.

Barthelemy, A.

Barthélémy, A.

K. Krupa, A. Tonello, V. Couderc, A. Barthélémy, G. Millot, D. Modotto, and S. Wabnitz, “Spatiotemporal light-beam compression from nonlinear mode coupling,” Phys. Rev. A (Coll. Park) 97(4), 043836 (2018).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning in multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref] [PubMed]

Béal, J.

Bendahmane, A.

R. Dupiol, A. Bendahmane, K. Krupa, A. Tonello, M. Fabert, B. Kibler, T. Sylvestre, A. Barthelemy, V. Couderc, S. Wabnitz, and G. Millot, “Far-detuned cascaded intermodal four-wave mixing in a multimode fiber,” Opt. Lett. 42(7), 1293–1296 (2017).
[Crossref] [PubMed]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref] [PubMed]

Bergman, K.

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34(9), 1749–1757 (1998).
[Crossref]

Billet, C.

P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. M. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (2018).
[Crossref]

Broderick, N. G. R.

Caravaca-Aguirre, A. M.

O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12(6), 368–374 (2018).
[Crossref]

Christodoulides, D.

Christodoulides, D. N.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–16 (2018).
[Crossref]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Spatiotemporal mode-locking in multimode fiber lasers,” Science 358(6359), 94–97 (2017).
[Crossref] [PubMed]

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded-index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

Z. Liu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber,” Opt. Lett. 41(16), 3675–3678 (2016).
[Crossref] [PubMed]

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
[Crossref] [PubMed]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9(5), 306–310 (2015).
[Crossref]

Coillet, A.

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10(1), 830 (2019).
[Crossref] [PubMed]

Collings, B. C.

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34(9), 1749–1757 (1998).
[Crossref]

Conforti, M.

Couderc, V.

K. Krupa, A. Tonello, V. Couderc, A. Barthélémy, G. Millot, D. Modotto, and S. Wabnitz, “Spatiotemporal light-beam compression from nonlinear mode coupling,” Phys. Rev. A (Coll. Park) 97(4), 043836 (2018).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning in multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

R. Dupiol, A. Bendahmane, K. Krupa, A. Tonello, M. Fabert, B. Kibler, T. Sylvestre, A. Barthelemy, V. Couderc, S. Wabnitz, and G. Millot, “Far-detuned cascaded intermodal four-wave mixing in a multimode fiber,” Opt. Lett. 42(7), 1293–1296 (2017).
[Crossref] [PubMed]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref] [PubMed]

Cui, Y.

X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121(2), 023905 (2018).
[Crossref] [PubMed]

Ding, E.

E. Ding, S. Lefrancois, J. N. Kutz, and F. W. Wise, “Scaling fiber lasers to large mode area: an investigation of passive mode-locking using a multi-mode fiber,” IEEE J. Quantum Electron. 47(5), 597–606 (2011).
[Crossref] [PubMed]

Du, J.

Dudley, J. M.

P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. M. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (2018).
[Crossref]

Dupiol, R.

Eftekhar, M. A.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–16 (2018).
[Crossref]

G. Lopez-Galmiche, Z. Sanjabi Eznaveh, M. A. Eftekhar, J. Antonio Lopez, L. G. Wright, F. Wise, D. Christodoulides, and R. Amezcua Correa, “Visible supercontinuum generation in a graded index multimode fiber pumped at 1064 nm,” Opt. Lett. 41(11), 2553–2556 (2016).
[Crossref] [PubMed]

Erkintalo, M.

Fabert, M.

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning in multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

R. Dupiol, A. Bendahmane, K. Krupa, A. Tonello, M. Fabert, B. Kibler, T. Sylvestre, A. Barthelemy, V. Couderc, S. Wabnitz, and G. Millot, “Far-detuned cascaded intermodal four-wave mixing in a multimode fiber,” Opt. Lett. 42(7), 1293–1296 (2017).
[Crossref] [PubMed]

Fini, J.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Genty, G.

P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. M. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (2018).
[Crossref]

Gloge, D.

Grelu, P.

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10(1), 830 (2019).
[Crossref] [PubMed]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118(24), 243901 (2017).
[Crossref] [PubMed]

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[Crossref]

P. Grelu, J. Béal, and J. Soto-Crespo, “Soliton pairs in a fiber laser: from anomalous to normal average dispersion regime,” Opt. Express 11(18), 2238–2243 (2003).
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Grudinin, A.

A. Grudinin, D. Richardson, and D. Payne, “Energy quantisation in figure eight fibre laser,” Electron. Lett. 28(1), 67–68 (1992).
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Hao, Y.

Herink, G.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356(6333), 50–54 (2017).
[Crossref] [PubMed]

Jalali, B.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356(6333), 50–54 (2017).
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D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
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Kibler, B.

Knize, R. J.

Knox, W. H.

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34(9), 1749–1757 (1998).
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Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
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Krupa, K.

K. Krupa, A. Tonello, V. Couderc, A. Barthélémy, G. Millot, D. Modotto, and S. Wabnitz, “Spatiotemporal light-beam compression from nonlinear mode coupling,” Phys. Rev. A (Coll. Park) 97(4), 043836 (2018).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning in multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118(24), 243901 (2017).
[Crossref] [PubMed]

R. Dupiol, A. Bendahmane, K. Krupa, A. Tonello, M. Fabert, B. Kibler, T. Sylvestre, A. Barthelemy, V. Couderc, S. Wabnitz, and G. Millot, “Far-detuned cascaded intermodal four-wave mixing in a multimode fiber,” Opt. Lett. 42(7), 1293–1296 (2017).
[Crossref] [PubMed]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref] [PubMed]

Kudlinski, A.

Kurtz, F.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356(6333), 50–54 (2017).
[Crossref] [PubMed]

Kutz, J. N.

E. Ding, S. Lefrancois, J. N. Kutz, and F. W. Wise, “Scaling fiber lasers to large mode area: an investigation of passive mode-locking using a multi-mode fiber,” IEEE J. Quantum Electron. 47(5), 597–606 (2011).
[Crossref] [PubMed]

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34(9), 1749–1757 (1998).
[Crossref]

Lefrancois, S.

E. Ding, S. Lefrancois, J. N. Kutz, and F. W. Wise, “Scaling fiber lasers to large mode area: an investigation of passive mode-locking using a multi-mode fiber,” IEEE J. Quantum Electron. 47(5), 597–606 (2011).
[Crossref] [PubMed]

Li, B.

Y. Yu, B. Li, X. Wei, Y. Xu, K. K. M. Tsia, and K. K. Y. Wong, “Spectral-temporal dynamics of multipulse mode-locking,” Appl. Phys. Lett. 110(20), 201107 (2017).
[Crossref]

Li, H.

Li, M.-J.

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded-index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

Li, X.

Liu, H.

Liu, M.

Liu, X.

X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121(2), 023905 (2018).
[Crossref] [PubMed]

Liu, Z.

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded-index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

Z. Liu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber,” Opt. Lett. 41(16), 3675–3678 (2016).
[Crossref] [PubMed]

Lopez-Galmiche, G.

Luo, A.-P.

Luo, Z.-C.

Lushnikov, P. M.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–16 (2018).
[Crossref]

Mafi, A.

Mas Arabi, C.

Meng, Y.

Merolla, J.-M.

P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. M. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (2018).
[Crossref]

Millot, G.

K. Krupa, A. Tonello, V. Couderc, A. Barthélémy, G. Millot, D. Modotto, and S. Wabnitz, “Spatiotemporal light-beam compression from nonlinear mode coupling,” Phys. Rev. A (Coll. Park) 97(4), 043836 (2018).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning in multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

R. Dupiol, A. Bendahmane, K. Krupa, A. Tonello, M. Fabert, B. Kibler, T. Sylvestre, A. Barthelemy, V. Couderc, S. Wabnitz, and G. Millot, “Far-detuned cascaded intermodal four-wave mixing in a multimode fiber,” Opt. Lett. 42(7), 1293–1296 (2017).
[Crossref] [PubMed]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref] [PubMed]

Modotto, D.

K. Krupa, A. Tonello, V. Couderc, A. Barthélémy, G. Millot, D. Modotto, and S. Wabnitz, “Spatiotemporal light-beam compression from nonlinear mode coupling,” Phys. Rev. A (Coll. Park) 97(4), 043836 (2018).
[Crossref]

Mussot, A.

Närhi, M.

P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. M. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (2018).
[Crossref]

Nelson, L.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Nithyanandan, K.

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10(1), 830 (2019).
[Crossref] [PubMed]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118(24), 243901 (2017).
[Crossref] [PubMed]

Nolan, D. A.

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded-index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

Olivier, M.

Ortaç, B.

U. Teğin and B. Ortaç, “Spatiotemporal Instability of Femtosecond Pulses in Graded-Index Multimode Fibers,” IEEE Photonics Technol. Lett. 29(24), 2195–2198 (2017).
[Crossref]

Payne, D.

A. Grudinin, D. Richardson, and D. Payne, “Energy quantisation in figure eight fibre laser,” Electron. Lett. 28(1), 67–68 (1992).
[Crossref]

Piché, M.

Piestun, R.

O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12(6), 368–374 (2018).
[Crossref]

Qin, H.

Renninger, W. H.

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4(1), 1719 (2013).
[Crossref] [PubMed]

Richardson, D.

D. Richardson, J. Fini, and L. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

A. Grudinin, D. Richardson, and D. Payne, “Energy quantisation in figure eight fibre laser,” Electron. Lett. 28(1), 67–68 (1992).
[Crossref]

Ropers, C.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356(6333), 50–54 (2017).
[Crossref] [PubMed]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[Crossref] [PubMed]

Runge, A. F. J.

Ryczkowski, P.

P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. M. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (2018).
[Crossref]

Sanjabi Eznaveh, Z.

Shalaby, B. M.

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning in multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref] [PubMed]

Solli, D. R.

G. Herink, F. Kurtz, B. Jalali, D. R. Solli, and C. Ropers, “Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules,” Science 356(6333), 50–54 (2017).
[Crossref] [PubMed]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[Crossref] [PubMed]

Soto-Crespo, J.

Sylvestre, T.

Tang, D. Y.

Tchofo-Dinda, P.

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10(1), 830 (2019).
[Crossref] [PubMed]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118(24), 243901 (2017).
[Crossref] [PubMed]

Tegin, U.

U. Teğin and B. Ortaç, “Spatiotemporal Instability of Femtosecond Pulses in Graded-Index Multimode Fibers,” IEEE Photonics Technol. Lett. 29(24), 2195–2198 (2017).
[Crossref]

Tonello, A.

K. Krupa, A. Tonello, V. Couderc, A. Barthélémy, G. Millot, D. Modotto, and S. Wabnitz, “Spatiotemporal light-beam compression from nonlinear mode coupling,” Phys. Rev. A (Coll. Park) 97(4), 043836 (2018).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning in multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

R. Dupiol, A. Bendahmane, K. Krupa, A. Tonello, M. Fabert, B. Kibler, T. Sylvestre, A. Barthelemy, V. Couderc, S. Wabnitz, and G. Millot, “Far-detuned cascaded intermodal four-wave mixing in a multimode fiber,” Opt. Lett. 42(7), 1293–1296 (2017).
[Crossref] [PubMed]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref] [PubMed]

Tsia, K. K. M.

Y. Yu, B. Li, X. Wei, Y. Xu, K. K. M. Tsia, and K. K. Y. Wong, “Spectral-temporal dynamics of multipulse mode-locking,” Appl. Phys. Lett. 110(20), 201107 (2017).
[Crossref]

Tzang, O.

O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12(6), 368–374 (2018).
[Crossref]

Wabnitz, S.

K. Krupa, A. Tonello, V. Couderc, A. Barthélémy, G. Millot, D. Modotto, and S. Wabnitz, “Spatiotemporal light-beam compression from nonlinear mode coupling,” Phys. Rev. A (Coll. Park) 97(4), 043836 (2018).
[Crossref]

K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning in multimode fibres,” Nat. Photonics 11(4), 237–241 (2017).
[Crossref]

R. Dupiol, A. Bendahmane, K. Krupa, A. Tonello, M. Fabert, B. Kibler, T. Sylvestre, A. Barthelemy, V. Couderc, S. Wabnitz, and G. Millot, “Far-detuned cascaded intermodal four-wave mixing in a multimode fiber,” Opt. Lett. 42(7), 1293–1296 (2017).
[Crossref] [PubMed]

K. Krupa, A. Tonello, A. Barthélémy, V. Couderc, B. M. Shalaby, A. Bendahmane, G. Millot, and S. Wabnitz, “Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves,” Phys. Rev. Lett. 116(18), 183901 (2016).
[Crossref] [PubMed]

Wagner, K.

O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12(6), 368–374 (2018).
[Crossref]

Wang, P.

H. Qin, X. Xiao, P. Wang, and C. Yang, “Observation of soliton molecules in a spatiotemporal mode-locked multimode fiber laser,” Opt. Lett. 43(9), 1982–1985 (2018).
[Crossref] [PubMed]

P. Wang, X. Xiao, H. Zhao, and C. Yang, “Observation of duration-tunable soliton explosion in passively mode-locked fiber laser,” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Wang, Z. Q.

Z. Q. Wang, K. Nithyanandan, A. Coillet, P. Tchofo-Dinda, and P. Grelu, “Optical soliton molecular complexes in a passively mode-locked fibre laser,” Nat. Commun. 10(1), 830 (2019).
[Crossref] [PubMed]

Wei, X.

Y. Yu, B. Li, X. Wei, Y. Xu, K. K. M. Tsia, and K. K. Y. Wong, “Spectral-temporal dynamics of multipulse mode-locking,” Appl. Phys. Lett. 110(20), 201107 (2017).
[Crossref]

Wen, S.-C.

Wise, F.

Wise, F. W.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–16 (2018).
[Crossref]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Spatiotemporal mode-locking in multimode fiber lasers,” Science 358(6359), 94–97 (2017).
[Crossref] [PubMed]

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded-index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
[Crossref] [PubMed]

Z. Liu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber,” Opt. Lett. 41(16), 3675–3678 (2016).
[Crossref] [PubMed]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9(5), 306–310 (2015).
[Crossref]

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4(1), 1719 (2013).
[Crossref] [PubMed]

E. Ding, S. Lefrancois, J. N. Kutz, and F. W. Wise, “Scaling fiber lasers to large mode area: an investigation of passive mode-locking using a multi-mode fiber,” IEEE J. Quantum Electron. 47(5), 597–606 (2011).
[Crossref] [PubMed]

Wong, K. K. Y.

Y. Yu, B. Li, X. Wei, Y. Xu, K. K. M. Tsia, and K. K. Y. Wong, “Spectral-temporal dynamics of multipulse mode-locking,” Appl. Phys. Lett. 110(20), 201107 (2017).
[Crossref]

Wright, L. G.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–16 (2018).
[Crossref]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Spatiotemporal mode-locking in multimode fiber lasers,” Science 358(6359), 94–97 (2017).
[Crossref] [PubMed]

L. G. Wright, Z. Liu, D. A. Nolan, M.-J. Li, D. N. Christodoulides, and F. W. Wise, “Self-organized instability in graded-index multimode fibres,” Nat. Photonics 10(12), 771–776 (2016).
[Crossref]

G. Lopez-Galmiche, Z. Sanjabi Eznaveh, M. A. Eftekhar, J. Antonio Lopez, L. G. Wright, F. Wise, D. Christodoulides, and R. Amezcua Correa, “Visible supercontinuum generation in a graded index multimode fiber pumped at 1064 nm,” Opt. Lett. 41(11), 2553–2556 (2016).
[Crossref] [PubMed]

Z. Liu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber,” Opt. Lett. 41(16), 3675–3678 (2016).
[Crossref] [PubMed]

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
[Crossref] [PubMed]

L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9(5), 306–310 (2015).
[Crossref]

Xiao, X.

H. Qin, X. Xiao, P. Wang, and C. Yang, “Observation of soliton molecules in a spatiotemporal mode-locked multimode fiber laser,” Opt. Lett. 43(9), 1982–1985 (2018).
[Crossref] [PubMed]

P. Wang, X. Xiao, H. Zhao, and C. Yang, “Observation of duration-tunable soliton explosion in passively mode-locked fiber laser,” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Xu, W.-C.

Xu, Y.

Y. Yu, B. Li, X. Wei, Y. Xu, K. K. M. Tsia, and K. K. Y. Wong, “Spectral-temporal dynamics of multipulse mode-locking,” Appl. Phys. Lett. 110(20), 201107 (2017).
[Crossref]

Yang, C.

H. Qin, X. Xiao, P. Wang, and C. Yang, “Observation of soliton molecules in a spatiotemporal mode-locked multimode fiber laser,” Opt. Lett. 43(9), 1982–1985 (2018).
[Crossref] [PubMed]

P. Wang, X. Xiao, H. Zhao, and C. Yang, “Observation of duration-tunable soliton explosion in passively mode-locked fiber laser,” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Yao, X.

X. Liu, X. Yao, and Y. Cui, “Real-time observation of the buildup of soliton molecules,” Phys. Rev. Lett. 121(2), 023905 (2018).
[Crossref] [PubMed]

Yu, Y.

Y. Yu, B. Li, X. Wei, Y. Xu, K. K. M. Tsia, and K. K. Y. Wong, “Spectral-temporal dynamics of multipulse mode-locking,” Appl. Phys. Lett. 110(20), 201107 (2017).
[Crossref]

Zhang, H.

Zhang, S.

Zhao, C.-J.

Zhao, H.

P. Wang, X. Xiao, H. Zhao, and C. Yang, “Observation of duration-tunable soliton explosion in passively mode-locked fiber laser,” IEEE Photonics J. 9(6), 1–8 (2017).
[Crossref]

Zhao, L. M.

Zheng, X.-W.

Zhu, Z.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–16 (2018).
[Crossref]

Z. Zhu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Observation of multimode solitons in few-mode fiber,” Opt. Lett. 41(20), 4819–4822 (2016).
[Crossref] [PubMed]

Ziegler, Z. M.

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–16 (2018).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Y. Yu, B. Li, X. Wei, Y. Xu, K. K. M. Tsia, and K. K. Y. Wong, “Spectral-temporal dynamics of multipulse mode-locking,” Appl. Phys. Lett. 110(20), 201107 (2017).
[Crossref]

Electron. Lett. (1)

A. Grudinin, D. Richardson, and D. Payne, “Energy quantisation in figure eight fibre laser,” Electron. Lett. 28(1), 67–68 (1992).
[Crossref]

IEEE J. Quantum Electron. (2)

E. Ding, S. Lefrancois, J. N. Kutz, and F. W. Wise, “Scaling fiber lasers to large mode area: an investigation of passive mode-locking using a multi-mode fiber,” IEEE J. Quantum Electron. 47(5), 597–606 (2011).
[Crossref] [PubMed]

J. N. Kutz, B. C. Collings, K. Bergman, and W. H. Knox, “Stabilized pulse spacing in soliton lasers due to gain depletion and recovery,” IEEE J. Quantum Electron. 34(9), 1749–1757 (1998).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

L. G. Wright, Z. M. Ziegler, P. M. Lushnikov, Z. Zhu, M. A. Eftekhar, D. N. Christodoulides, and F. W. Wise, “Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook,” IEEE J. Sel. Top. Quantum Electron. 24(3), 1–16 (2018).
[Crossref]

IEEE Photonics J. (1)

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U. Teğin and B. Ortaç, “Spatiotemporal Instability of Femtosecond Pulses in Graded-Index Multimode Fibers,” IEEE Photonics Technol. Lett. 29(24), 2195–2198 (2017).
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Figures (8)

Fig. 1
Fig. 1 Experimental setup. (a) The MMF laser (SPDM, short pass dichroic mirror; L1 and L2, lens; OM4, passive GRIN multimode fiber; HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarization beam splitter; BS, beam splitter; ISO, isolator; SF, spectral filter; M1-3, mirrors); (b) Measurement setup. Method 1: spectral filtering; Method 2: spatial sampling (BS: beam splitter; OSA: optical spectrum analyzer; PD, photodetector).
Fig. 2
Fig. 2 Second-order harmonic mode locking state. (a) Pulse train measured by oscilloscope; (b) RF spectrum of pulse train with a resolution bandwidth of 1 Hz (inset: RF spectrum over a 1 GHz span with a resolution bandwidth of 2 kHz); (c) Autocorrelation trace of output pulses; (d) Spectra of the whole output (solid curve) and the spectral-filtered outputs (dashed curves), with the corresponding beam profiles shown in (e)-(h); (e) Beam profile of the whole output, with black circles represented the spatial sampling positions (one sampler fixed at the center, and another sampler moving along the direction of arrow); (f)-(h) Beam profiles corresponding to different spectrum regions by tunable spectral-filtering of the output; (i) Pulse intensities and pulse intervals of the pulse trains sampled by the moving sampler at different position (the intensity corresponding to the fixed sampler is 53); (j) pulse train sampled by the fixed sampler; (k) a typical pulse train sampled by the moving sampler; (l) and (n) are the corresponding optical and RF spectra of (j) and (k), respectively; (m) RF spectra of the spectral-filtered outputs corresponding to (f)-(h).
Fig. 3
Fig. 3 Multiple pulses state. (a) Pulse train measured by oscilloscope; (b) Optical spectrum (inset: beam profile); (c) Pulse intensities and pulse intervals of the pulse trains sampled at different position.
Fig. 4
Fig. 4 Soliton molecule state. (a) Pulse train measured by oscilloscope; (b) Optical spectrum (inset: beam profile); (c) Autocorrelation traces of different spatial samplings, S1 and S2.
Fig. 5
Fig. 5 Mode-resolved simulation results for soliton molecule in the MMF laser. Esat = 2 nJ, small signal gain g0 = 15 m−1 and Psat of the SA is 180 W. (a) Mode-resolved pulse evolution with roundtrip (inset: beam profile); (b) Pulse evolution with roundtrip; (c) Intracavity pulse evolution in the last roundtrip; (d) Temporal output of the last roundtrip; (e) Pulse energy evolution with roundtrip. In (a), the initial pulses intensities are enlarged 200 times for clarity. In mode-resolved figures, the modes are color-coded. Among those modes, mode 2 is the highest, modes 1, 3 and 4 are almost overlapped, modes 5 and 6 are almost overlapped. OC: output coupler, SA: saturable absorber, BF: bandpass filter, SF: spatial filter.
Fig. 6
Fig. 6 Evolution of multiple pulses with different initial conditions. Small signal gain g0 = 20 m−1 and Psat of the SA is 180 W. (a) Evolution with two unequal pulse input, and (b) is the corresponding mode-resolved steady output; (c) Evolution with random noise input, and (d) is the corresponding steady output.
Fig. 7
Fig. 7 Mode-resolved output intensities and the corresponding beam profiles with various coupling coefficients (CCs) operating in multiple pulses state. CC I = [4,2,2,1,1,1], CC II = [2,4,2,2,1,1], CC III = [1,1,1,2,2,4], and other parameters are the same as Fig. 6.
Fig. 8
Fig. 8 The intensities of modes 2 and 3, normalized to that of mode 1, of the steady output versus (a) small signal gain g0 and (b) Psat of the SA. Regimes in different colors represent different operation states of the STML MMF laser.

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z A p (z,t)=i( β 0 (p) [ β 0 (0) ]) A p ( β 1 (p) [ β 1 (0) ]) A p t i β 2 (p) 2 t 2 A p i n 2 ω 0 c l,m,n { (1 f R ) S plmn K A l A m A n * + f R A l S plmn R t d τ A m (z,tτ) A n * (z,tτ) h R (τ) }

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