Abstract

As optical fiber communications and fiber lasers approach fundamental limits there is considerable interest in multimode fibers. In nonlinear science, they represent an exciting environment for complex nonlinear waves. As in single-mode fiber, solitons may be particularly important. Multimode solitons consist of synchronized, non-dispersive pulses in multiple spatial modes, which interact via the Kerr nonlinearity of the fiber. They are expected to exhibit novel spatiotemporal characteristics, dynamics and, like single-mode solitons, may provide a convenient intuitive tool for understanding more complex nonlinear phenomena in multimode fibers. Here we explore experimentally and numerically basic properties and spatiotemporal behaviors of these solitons: their formation, fission, and Raman dynamics.

© 2015 Optical Society of America

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2015 (1)

S. Buch and G. P. Agrawal, “Soliton stability and trapping in multimode fibers,” Opt. Lett 40, 225–228 (2015).
[Crossref]

2014 (2)

F. Tani, J. C. Travers, and P. St.J. Russell, “Multimode ultrafast nonlinear optics in optical waveguides: numerical modeling and experiments in kagomé photonic-crystal fiber,” J. Opt. Soc. Am. B 31, 311 (2014).
[Crossref]

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

2013 (3)

H. Pourbeyram, G. P. Agrawal, and A. Mafi, “Stimulated Raman scattering cascade spanning the wavelength range of 523 to 1750 nm using a graded-index multimode optical fiber,” Appl. Phys. Lett. 102, 201107 (2013).
[Crossref]

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

D. A. B. Miller, “Reconfigurable add-drop multiplexer for spatial modes,” Opt. Express 21, 20220–20229 (2013).
[Crossref] [PubMed]

2012 (7)

2011 (2)

J. Cheng, J. H. Lee, K. Wang, C. Xu, K. G. Jespersen, M. Garmund, L. Grüner-Nielsen, and D. Jakobsen, “Generation of Cerenkov radiation at 850 nm in higher-order-mode fiber,” Opt. Express 19, 8774–8780 (2011).
[Crossref] [PubMed]

H. Li, I. V. Bazarov, B. M. Dunham, and F. W. Wise, “Three-dimensional laser pulse intensity diagnostic for photoinjectors,” Phys. Rev. ST AB 14, 112802 (2011).

2010 (1)

D. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[Crossref]

2009 (4)

F. Poletti and P. Horak, “Dynamics of femtosecond supercontinuum generation in multimode fibers,” Opt. Express 17, 6134 (2009).
[Crossref] [PubMed]

N. Nishizawa, “Highly Functional All-Optical Control Using Ultrafast Nonlinear Effects in Optical Fibers,” IEEE J. Quantum Electron. 45, 1446–1455 (2009).
[Crossref]

E. Rubino, D. Faccio, L. Tartara, P. K. Bates, O. Chalus, M. Clerici, F. Bonaretti, J. Biegert, and P. Di Trapani, “Spatiotemporal amplitude and phase retrieval of space-time coupled ultrashort pulses using the Shackled-FROG technique,” Opt. Lett. 34, 3854–3856 (2009).
[Crossref] [PubMed]

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
[Crossref]

2008 (4)

2007 (2)

2004 (1)

F. Lu, Q. Lin, W. Knox, and G. Agrawal, “Vector Soliton Fission,” Phys. Rev. Lett. 93, 183901 (2004).
[Crossref] [PubMed]

2002 (1)

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, “Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[Crossref] [PubMed]

2000 (2)

S. Raghavan and G. P. Agrawal, “Spatiotemporal solitons in inhomogeneous nonlinear media,” Opt. Commun. 180, 377–382 (2000).
[Crossref]

N. Akhmediev and A. Ankiewicz, “Multi-soliton complexes,” Chaos (Woodbury, N.Y.) 10, 600–612 (2000).
[Crossref]

1996 (1)

C.-H. Chien, S.-S. Yu, Y. Lai, and J. Wang, “Off-axial pulse propagation in graded-index materials with Kerr nonlinearity a variational approach,” Opt. Commun. 128, 145–157 (1996).
[Crossref]

1995 (1)

S.-S. Yu, C.-H. Chien, Y. Lai, and J. Wang, “Spatio-temporal solitary pulses in graded-index materials with Kerr nonlinearity,” Opt. Commun. 119, 167–170 (1995).
[Crossref]

1994 (1)

1988 (1)

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, and D. V. Khaĭdarov, “Nonlinear mode coupling in multimode optical fibers; excitation of femtosecond-range stimulated-Raman-scattering solitons,” J. Exp. Theor. Phys. 47297–300 (1988).

1987 (1)

1986 (2)

1985 (1)

H. Haus and M. Islam, “Theory of the soliton laser,” IEEE J. Quantum Electron. 21, 1172–1188 (1985).
[Crossref]

1984 (1)

1982 (2)

B. Crosignani, A. Cutolo, and P. D. Porto, “Coupled-mode theory of nonlinear propagation in multimode and single-mode fibers: envelope solitons and self-confinement,” J. Opt. Soc. Am. 72, 1136 (1982).
[Crossref]

J. Goldhar and J. Murray, “Intensity averaging and four-wave mixing in Raman amplifiers,” IEEE Journal of Quantum Electronics 18, 399–409 (1982).
[Crossref]

1981 (1)

1980 (2)

A. Hasegawa, “Self-confinement of multimode optical pulse in a glass fiber,” Opt. Lett. 5, 416 (1980).
[Crossref] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[Crossref]

1976 (1)

1974 (1)

R. H. Stolen, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308 (1974).
[Crossref]

1973 (1)

A. Hasegawa, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142 (1973).
[Crossref]

Abdolvand, A.

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

Agrawal, G.

F. Lu, Q. Lin, W. Knox, and G. Agrawal, “Vector Soliton Fission,” Phys. Rev. Lett. 93, 183901 (2004).
[Crossref] [PubMed]

Y. Kivshar and G. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Agrawal, G. P.

S. Buch and G. P. Agrawal, “Soliton stability and trapping in multimode fibers,” Opt. Lett 40, 225–228 (2015).
[Crossref]

H. Pourbeyram, G. P. Agrawal, and A. Mafi, “Stimulated Raman scattering cascade spanning the wavelength range of 523 to 1750 nm using a graded-index multimode optical fiber,” Appl. Phys. Lett. 102, 201107 (2013).
[Crossref]

S. Raghavan and G. P. Agrawal, “Spatiotemporal solitons in inhomogeneous nonlinear media,” Opt. Commun. 180, 377–382 (2000).
[Crossref]

Akhmediev, N.

N. Akhmediev and A. Ankiewicz, “Multi-soliton complexes,” Chaos (Woodbury, N.Y.) 10, 600–612 (2000).
[Crossref]

Alfano, R. R.

Alley, T. G.

Angelow, A. K.

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, “Multi-soliton complexes,” Chaos (Woodbury, N.Y.) 10, 600–612 (2000).
[Crossref]

Antonelli, C.

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Baldeck, P. L.

Bates, P. K.

Bazarov, I. V.

H. Li, I. V. Bazarov, B. M. Dunham, and F. W. Wise, “Three-dimensional laser pulse intensity diagnostic for photoinjectors,” Phys. Rev. ST AB 14, 112802 (2011).

Biegert, J.

Blin, S.

Bonaretti, F.

Bowlan, P.

Bragheri, F.

Buch, S.

S. Buch and G. P. Agrawal, “Soliton stability and trapping in multimode fibers,” Opt. Lett 40, 225–228 (2015).
[Crossref]

Chalus, O.

Chang, W.

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

Charan, K.

Chartier, T.

Cheng, J.

Chien, C.-H.

C.-H. Chien, S.-S. Yu, Y. Lai, and J. Wang, “Off-axial pulse propagation in graded-index materials with Kerr nonlinearity a variational approach,” Opt. Commun. 128, 145–157 (1996).
[Crossref]

S.-S. Yu, C.-H. Chien, Y. Lai, and J. Wang, “Spatio-temporal solitary pulses in graded-index materials with Kerr nonlinearity,” Opt. Commun. 119, 167–170 (1995).
[Crossref]

Christodoulides, D. N.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Clerici, M.

Crosignani, B.

Cutolo, A.

Degiorgio, V.

Di Trapani, P.

Dianov, E. M.

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, and D. V. Khaĭdarov, “Nonlinear mode coupling in multimode optical fibers; excitation of femtosecond-range stimulated-Raman-scattering solitons,” J. Exp. Theor. Phys. 47297–300 (1988).

Dunham, B. M.

H. Li, I. V. Bazarov, B. M. Dunham, and F. W. Wise, “Three-dimensional laser pulse intensity diagnostic for photoinjectors,” Phys. Rev. ST AB 14, 112802 (2011).

Duparré, M.

Faccio, D.

Fini, J. M.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
[Crossref]

Flamm, D.

Forbes, A.

Gabolde, P.

Garmund, M.

Ghalmi, S.

Goldhar, J.

J. Goldhar and J. Murray, “Intensity averaging and four-wave mixing in Raman amplifiers,” IEEE Journal of Quantum Electronics 18, 399–409 (1982).
[Crossref]

Gorbach, A. V.

D. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[Crossref]

Gordon, J. P.

J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662 (1986).
[Crossref] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[Crossref]

Griebner, U.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, “Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[Crossref] [PubMed]

Grudinin, A. B.

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, and D. V. Khaĭdarov, “Nonlinear mode coupling in multimode optical fibers; excitation of femtosecond-range stimulated-Raman-scattering solitons,” J. Exp. Theor. Phys. 47297–300 (1988).

Grüner-Nielsen, L.

Hasegawa, A.

A. Hasegawa, “Self-confinement of multimode optical pulse in a glass fiber,” Opt. Lett. 5, 416 (1980).
[Crossref] [PubMed]

A. Hasegawa, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142 (1973).
[Crossref]

Haus, H.

H. Haus and M. Islam, “Theory of the soliton laser,” IEEE J. Quantum Electron. 21, 1172–1188 (1985).
[Crossref]

Henin, S.

Herrmann, J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, “Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[Crossref] [PubMed]

Hesketh, G.

Hölzer, P.

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

Horak, P.

Husakou, A.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, “Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[Crossref] [PubMed]

Islam, M.

H. Haus and M. Islam, “Theory of the soliton laser,” IEEE J. Quantum Electron. 21, 1172–1188 (1985).
[Crossref]

Jakobsen, D.

Jedrkiewicz, O.

Jespersen, K. G.

Khaidarov, D. V.

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, and D. V. Khaĭdarov, “Nonlinear mode coupling in multimode optical fibers; excitation of femtosecond-range stimulated-Raman-scattering solitons,” J. Exp. Theor. Phys. 47297–300 (1988).

Kircheva, P. P.

Kivshar, Y.

Y. Kivshar and G. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Knight, J. C.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, “Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[Crossref] [PubMed]

Knox, W.

F. Lu, Q. Lin, W. Knox, and G. Agrawal, “Vector Soliton Fission,” Phys. Rev. Lett. 93, 183901 (2004).
[Crossref] [PubMed]

Korbkin, D. V.

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, and D. V. Khaĭdarov, “Nonlinear mode coupling in multimode optical fibers; excitation of femtosecond-range stimulated-Raman-scattering solitons,” J. Exp. Theor. Phys. 47297–300 (1988).

Korn, G.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, “Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[Crossref] [PubMed]

Lai, Y.

C.-H. Chien, S.-S. Yu, Y. Lai, and J. Wang, “Off-axial pulse propagation in graded-index materials with Kerr nonlinearity a variational approach,” Opt. Commun. 128, 145–157 (1996).
[Crossref]

S.-S. Yu, C.-H. Chien, Y. Lai, and J. Wang, “Spatio-temporal solitary pulses in graded-index materials with Kerr nonlinearity,” Opt. Commun. 119, 167–170 (1995).
[Crossref]

Le, S. D.

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Lee, J. H.

Leibolt, W. N.

Li, H.

H. Li, I. V. Bazarov, B. M. Dunham, and F. W. Wise, “Three-dimensional laser pulse intensity diagnostic for photoinjectors,” Phys. Rev. ST AB 14, 112802 (2011).

Liberale, C.

Lin, Q.

F. Lu, Q. Lin, W. Knox, and G. Agrawal, “Vector Soliton Fission,” Phys. Rev. Lett. 93, 183901 (2004).
[Crossref] [PubMed]

Lotti, A.

Lu, F.

F. Lu, Q. Lin, W. Knox, and G. Agrawal, “Vector Soliton Fission,” Phys. Rev. Lett. 93, 183901 (2004).
[Crossref] [PubMed]

Mafi, A.

H. Pourbeyram, G. P. Agrawal, and A. Mafi, “Stimulated Raman scattering cascade spanning the wavelength range of 523 to 1750 nm using a graded-index multimode optical fiber,” Appl. Phys. Lett. 102, 201107 (2013).
[Crossref]

A. Mafi, “Pulse Propagation in a Short Nonlinear Graded-Index Multimode Optical Fiber,” J. Lightwave Technol. 30, 2803–2811 (2012).
[Crossref]

Mecozzi, A.

Mermelstein, M. D.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
[Crossref]

Miller, D. A. B.

Mitschke, F. M.

Mollenauer, L. F.

F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659 (1986).
[Crossref] [PubMed]

L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13 (1984).
[Crossref] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[Crossref]

Murray, J.

J. Goldhar and J. Murray, “Intensity averaging and four-wave mixing in Raman amplifiers,” IEEE Journal of Quantum Electronics 18, 399–409 (1982).
[Crossref]

Naidoo, D.

Nguyen, D. M.

Nguyen, T. N.

Nicholson, J. W.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
[Crossref]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233 (2008).
[Crossref] [PubMed]

Nickel, D.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, “Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[Crossref] [PubMed]

Nishizawa, N.

N. Nishizawa, “Highly Functional All-Optical Control Using Ultrafast Nonlinear Effects in Optical Fibers,” IEEE J. Quantum Electron. 45, 1446–1455 (2009).
[Crossref]

Pedersen, M. E. V.

Pitaevskii, L.

L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University, 2003).

Poletti, F.

Porto, P. D.

Pourbeyram, H.

H. Pourbeyram, G. P. Agrawal, and A. Mafi, “Stimulated Raman scattering cascade spanning the wavelength range of 523 to 1750 nm using a graded-index multimode optical fiber,” Appl. Phys. Lett. 102, 201107 (2013).
[Crossref]

Prokhorov, A. M.

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, and D. V. Khaĭdarov, “Nonlinear mode coupling in multimode optical fibers; excitation of femtosecond-range stimulated-Raman-scattering solitons,” J. Exp. Theor. Phys. 47297–300 (1988).

Provino, L.

Raccah, F.

Raghavan, S.

S. Raghavan and G. P. Agrawal, “Spatiotemporal solitons in inhomogeneous nonlinear media,” Opt. Commun. 180, 377–382 (2000).
[Crossref]

Ramachandran, S.

Renninger, W. H.

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

Rubino, E.

Russell, P. S. J.

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, “Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[Crossref] [PubMed]

Russell, P. St.J.

Russell, T. H.

Schulze, C.

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Shtaif, M.

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Skryabin, D. V.

D. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[Crossref]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Stolen, R. H.

L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13 (1984).
[Crossref] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
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R. H. Stolen and W. N. Leibolt, “Optical fiber modes using stimulated four photon mixing,” Appl. Opt. 15, 239–243 (1976).
[Crossref] [PubMed]

R. H. Stolen, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308 (1974).
[Crossref]

Stringari, S.

L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University, 2003).

Tani, F.

Tartara, L.

Terry, N. B.

Thual, M.

Travers, J. C.

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

F. Tani, J. C. Travers, and P. St.J. Russell, “Multimode ultrafast nonlinear optics in optical waveguides: numerical modeling and experiments in kagomé photonic-crystal fiber,” J. Opt. Soc. Am. B 31, 311 (2014).
[Crossref]

Trebino, R.

Wadsworth, W. J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, “Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[Crossref] [PubMed]

Wang, J.

C.-H. Chien, S.-S. Yu, Y. Lai, and J. Wang, “Off-axial pulse propagation in graded-index materials with Kerr nonlinearity a variational approach,” Opt. Commun. 128, 145–157 (1996).
[Crossref]

S.-S. Yu, C.-H. Chien, Y. Lai, and J. Wang, “Spatio-temporal solitary pulses in graded-index materials with Kerr nonlinearity,” Opt. Commun. 119, 167–170 (1995).
[Crossref]

Wang, K.

Wise, F. W.

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

H. Li, I. V. Bazarov, B. M. Dunham, and F. W. Wise, “Three-dimensional laser pulse intensity diagnostic for photoinjectors,” Phys. Rev. ST AB 14, 112802 (2011).

Xu, C.

Yablon, A. D.

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
[Crossref]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233 (2008).
[Crossref] [PubMed]

Yu, S.-S.

C.-H. Chien, S.-S. Yu, Y. Lai, and J. Wang, “Off-axial pulse propagation in graded-index materials with Kerr nonlinearity a variational approach,” Opt. Commun. 128, 145–157 (1996).
[Crossref]

S.-S. Yu, C.-H. Chien, Y. Lai, and J. Wang, “Spatio-temporal solitary pulses in graded-index materials with Kerr nonlinearity,” Opt. Commun. 119, 167–170 (1995).
[Crossref]

Zhavoronkov, N.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, “Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[Crossref] [PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (3)

R. H. Stolen, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24, 308 (1974).
[Crossref]

H. Pourbeyram, G. P. Agrawal, and A. Mafi, “Stimulated Raman scattering cascade spanning the wavelength range of 523 to 1750 nm using a graded-index multimode optical fiber,” Appl. Phys. Lett. 102, 201107 (2013).
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A. Hasegawa, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142 (1973).
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N. Nishizawa, “Highly Functional All-Optical Control Using Ultrafast Nonlinear Effects in Optical Fibers,” IEEE J. Quantum Electron. 45, 1446–1455 (2009).
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IEEE J. Sel. Top. Quantum Electron. (1)

J. W. Nicholson, A. D. Yablon, J. M. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 61–70 (2009).
[Crossref]

IEEE Journal of Quantum Electronics (1)

J. Goldhar and J. Murray, “Intensity averaging and four-wave mixing in Raman amplifiers,” IEEE Journal of Quantum Electronics 18, 399–409 (1982).
[Crossref]

J. Exp. Theor. Phys. (1)

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, and D. V. Khaĭdarov, “Nonlinear mode coupling in multimode optical fibers; excitation of femtosecond-range stimulated-Raman-scattering solitons,” J. Exp. Theor. Phys. 47297–300 (1988).

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Nat. Commun. (1)

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

Nat. Photon. (1)

P. S. J. Russell, P. Hölzer, W. Chang, A. Abdolvand, and J. C. Travers, “Hollow-core photonic crystal fibres for gas-based nonlinear optics,” Nat. Photon. 8, 278–286 (2014).
[Crossref]

Opt. Commun. (3)

S.-S. Yu, C.-H. Chien, Y. Lai, and J. Wang, “Spatio-temporal solitary pulses in graded-index materials with Kerr nonlinearity,” Opt. Commun. 119, 167–170 (1995).
[Crossref]

C.-H. Chien, S.-S. Yu, Y. Lai, and J. Wang, “Off-axial pulse propagation in graded-index materials with Kerr nonlinearity a variational approach,” Opt. Commun. 128, 145–157 (1996).
[Crossref]

S. Raghavan and G. P. Agrawal, “Spatiotemporal solitons in inhomogeneous nonlinear media,” Opt. Commun. 180, 377–382 (2000).
[Crossref]

Opt. Express (8)

J. Cheng, J. H. Lee, K. Wang, C. Xu, K. G. Jespersen, M. Garmund, L. Grüner-Nielsen, and D. Jakobsen, “Generation of Cerenkov radiation at 850 nm in higher-order-mode fiber,” Opt. Express 19, 8774–8780 (2011).
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F. Poletti and P. Horak, “Dynamics of femtosecond supercontinuum generation in multimode fibers,” Opt. Express 17, 6134 (2009).
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N. B. Terry, T. G. Alley, and T. H. Russell, “An explanation of SRS beam cleanup in graded-index fibers and the absence of SRS beam cleanup in step-index fibers,” Opt. Express 15, 17509 (2007).
[Crossref] [PubMed]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233 (2008).
[Crossref] [PubMed]

P. Bowlan, P. Gabolde, and R. Trebino, “Directly measuring the spatio-temporal electric field of focusing ultra-short pulses,” Opt. Express 15, 10219 (2007).
[Crossref] [PubMed]

D. A. B. Miller, “Reconfigurable add-drop multiplexer for spatial modes,” Opt. Express 21, 20220–20229 (2013).
[Crossref] [PubMed]

A. Mecozzi, C. Antonelli, and M. Shtaif, “Coupled Manakov equations in multimode fibers with strongly coupled groups of modes,” Opt. Express 20, 23436–23441 (2012).
[Crossref] [PubMed]

A. Mecozzi, C. Antonelli, and M. Shtaif, “Nonlinear propagation in multi-mode fibers in the strong coupling regime,” Opt. Express 20, 11673–11678 (2012).
[Crossref] [PubMed]

Opt. Lett (1)

S. Buch and G. P. Agrawal, “Soliton stability and trapping in multimode fibers,” Opt. Lett 40, 225–228 (2015).
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Opt. Lett. (10)

L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13 (1984).
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A. Hasegawa, “Self-confinement of multimode optical pulse in a glass fiber,” Opt. Lett. 5, 416 (1980).
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B. Crosignani and P. D. Porto, “Soliton propagation in multimode optical fibers,” Opt. Lett. 6, 329 (1981).
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F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659 (1986).
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J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662 (1986).
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J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, and D. Jakobsen, “Intermodal Čerenkov radiation in a higher-order-mode fiber,” Opt. Lett. 37, 4410–4412 (2012).
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F. Bragheri, D. Faccio, F. Bonaretti, A. Lotti, M. Clerici, O. Jedrkiewicz, C. Liberale, S. Henin, L. Tartara, V. Degiorgio, and P. Di Trapani, “Complete retrieval of the field of ultrashort optical pulses using the angle-frequency spectrum,” Opt. Lett. 33, 2952 (2008).
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E. Rubino, D. Faccio, L. Tartara, P. K. Bates, O. Chalus, M. Clerici, F. Bonaretti, J. Biegert, and P. Di Trapani, “Spatiotemporal amplitude and phase retrieval of space-time coupled ultrashort pulses using the Shackled-FROG technique,” Opt. Lett. 34, 3854–3856 (2009).
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Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[Crossref]

Phys. Rev. Lett. (3)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental Observation of Picosecond Pulse Narrowing and Solitons in Optical Fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[Crossref]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, “Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[Crossref] [PubMed]

F. Lu, Q. Lin, W. Knox, and G. Agrawal, “Vector Soliton Fission,” Phys. Rev. Lett. 93, 183901 (2004).
[Crossref] [PubMed]

Phys. Rev. ST AB (1)

H. Li, I. V. Bazarov, B. M. Dunham, and F. W. Wise, “Three-dimensional laser pulse intensity diagnostic for photoinjectors,” Phys. Rev. ST AB 14, 112802 (2011).

Rev. Mod. Phys. (1)

D. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[Crossref]

Other (4)

A. Armaroli, C. Conti, and F. Biancalana, “Geometric origin of rogue solitons in optical fibres,” http://arxiv.org/abs/1406.5966

Y. Kivshar and G. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University, 2003).

P. Horak and F. Poletti, “Multimode Nonlinear Fiber Optics: Theory and Applications,” in “Recent Progress in Optical Fiber Research,” M. Yasin, ed. (2012), chap. 1, pp. 3–24.

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Figures (6)

Fig. 1
Fig. 1 Mode-resolved simulation results for 25 m propagation of a pulse equally distributed amongst the first 5 modes of a graded index fiber (zero angular momentum modes). The initial pulse duration is 500 fs and center wavelength 1550 nm. Left: temporal evolution of each mode. Middle: final temporal profiles, linear scale. Right: final spectra. The final spectrum and temporal intensity for each mode are normalized to the maximum spectral and temporal intensity for the given mode and are vertically offset for visibility. The temporal evolution plots are normalized to the initial peak intensity of the fundamental mode. For the temporal evolution plots, the distributions are plotted for 2.5, 8.75, 15 and 21.25 m. The modes are color-coded as in adjacent plots, and offset along the distance axis slightly to increase visibility. Top row: linear propagation. Middle row, energy regime 1: nonlinear propagation with each mode seeded with 0.34 nJ pulse energy. A dotted line shows the center wavelength in each mode. Bottom row, energy regime 2: nonlinear propagation with each mode seeded with 2.74 nJ pulse energy.

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Fig. 2
Fig. 2 Simulated (left) and experimental (right) spectra for increasing pulse energy launched into a 25 m GRIN fiber. For simulated spectra, the full-field spatially-averaged spectra are shown, which accurately represents the spectral energy distribution in the field. The energies are 3.2, 5, 10, 14, 24 and 34 nJ (experiment) and 0 (i.e., linear propagation), 1, 10, 14, 19 and 22 nJ (simulation). The purpose of the comparison is to show the qualitative similarity; the two plots correspond to different initial modal energy distributions, the experimental launched pulse has a non-Gaussian spectrum, and there is a strong wavelength-dependent loss which is not considered in the simulation. Nonetheless, the quantitative agreement is acceptable until loss becomes important (when the Raman soliton exceeds 1800 nm). The energy in the most red-shifted peak is calculated to vary from 0 to approximately 40%, in agreement with a measurement made using a Ge window.

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Fig. 3
Fig. 3 Summary of experimental and simulated results, and a comparison with the fundamental mode plus higher-order background null hypothesis (FHB). For a range of initial seed conditions, plots of pulse energy (Ep) versus the inverse pulse duration (1/τ) exhibit a roughly linear relationship, as in the (1+1) D soliton area theorem. The slope, M, of this curve is a measure of the characteristic scale of energy (nonlinearity) required to balance linear intramodal (group velocity dispersion) and intermodal dispersive (modal velocity mismatch) effects. The y-axis shows M(Rg), the slope calculated from experiment and simulation Ep versus 1/τ data, versus the measured beam size, Rg. Rg is the average size of the multimode beam in the fiber, which can have a minimum size of Ro the fundamental mode size, ≈ 6.5 μm) if only the fundamental mode is excited. Also shown are the slope for single-mode solitons of the same spatial localization (M1(Rg)), and the slope for single-mode solitons in the fundamental mode, with a dispersive multimode background (MFHB(Rg)). The values are normalized to M 1 ( R o ) = | β 2 | R o 2 λ o / n 2, the slope for a single-mode soliton in the fundamental mode. As a point of reference, the result of Ref. 18 is plotted.

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Fig. 4
Fig. 4 Mode content of Gaussian-shaped multimode solitons. The red and blue points are computed from the overlap integrals of the first 30 m = 0 modes of the GRIN fiber. Rg is the size of the (multimode) Gaussian beam. Ro, the size of the fundamental mode, is 6.5 μm. The y-axis shows the number of modes that contribute more than 0.5% of the total energy the beam with size Rg. To provide a continuous measure of the mode content as a function of average beam size, we fit the points, and then averaged the resulting curves to produce the average curve. For Gaussian-shaped beams/solitons, this line represents the number of modes contributing as a function of the average spatial localization of the beam/soliton.

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Fig. 5
Fig. 5 Simulation results using Eq. (1) for 2 m of GRIN fiber. Left: 10 μm waist launched beam, final autocorrelations accounting for spacetime distribution, Middle: same for 15 μm waist launched beam, Right: spacetime spectrum corresponding to the 28 nJ case, top: after 4 cm, bottom: after 200 cm. Energies and durations in the left and middle panels correspond to the total coupled energy and the pulse duration assuming a Gaussian pulse.

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Fig. 6
Fig. 6 Experimental results on MM soliton fission in GRIN fiber. Left: autocorrelations for labelled energy launched into a 7 m GRIN fiber (duration = AC width/1.41). Middle: beam profiles corresponding to the ACs in the left panel, showing the intermodal nonlinear energy transfer during and post-fission. Right, top: by adjusting the launch conditions and energy, the Raman soliton was arranged to center at 1620 nm, where it was spectrally filtered and imaged separately (bottom right, 1620 nm RS) from the full spectrum beam (bottom left). In agreement with simulations, the Raman soliton remains MM (its spatial width is larger than the fundamental mode by a factor of 1.54) but is more biased to lower-order modes. The results all display good qualitative agreement with simulations. All scale bars correspond to 20 μm.

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Equations (9)

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∂ z A ( x , y , z , t ) = i 2 k e ( ω o ) ∇ T 2 A + D ^ A + i k e ( ω o ) 2 ( ( n ( x , y ) / n eff ) 2 − 1 ) A                                                                                             + i γ ( 1 + i ω o ∂ t ) [ ( 1 − f R ) | A | 2 A + f R ∫ − ∞ t d τ h R ( τ ) | A ( x , y , z , t − τ ) | 2 ]
∂ z A p ( z , t ) = i δ β 0 ( p ) A p − δ β 1 ( p ) ∂ t A p + D ^ p A p + i n 2 ω o c ( 1 + i ω o ∂ t ) ∑ l , m , n N [ ( 1 − f R ) S p l m n K A l A m A n *                                                                                                                                                   + f R S p l m n R A l ∫ − ∞ t d τ h R ( τ ) A m ( z , t − τ ) A n * ( z , t − τ ) ]
E p τ = | β 2 | R g 2 λ o / n 2 = M 1 ( R g )
S ( t ) ∝ ∫ − ∞ ∞ d τ ∫ 0 ∞ r d r | ( E ( r , t ) + E ( r , t − τ ) ) 2 | 2
E p T ( R o , R g ) τ = M 1 ( R o ) = | β 2 | R o 2 λ o / n 2
E p τ = M FHB ( R g )
T ( R o , R g ) = | ∫ − ∞ ∞ ∫ − ∞ ∞ E o * ( x , y ) E g ( x , y ) d x d y | 2 ∫ − ∞ ∞ ∫ − ∞ ∞ | E o ( x , y ) | 2 d x d y ∫ − ∞ ∞ ∫ − ∞ ∞ | E g ( x , y ) | 2 d x d y = | ∫ − ∞ ∞ ∫ − ∞ ∞ e − ( x 2 + y 2 ) R o 2 e − ( x 2 + y 2 ) R g 2 d x d y | 2 ∫ − ∞ ∞ ∫ − ∞ ∞ e − 2 ( x 2 + y 2 ) R o 2 d x d y ∫ − ∞ ∞ ∫ − ∞ ∞ e − 2 ( x 2 + y 2 ) R g 2 d x d y = | π ( R o 2 R g 2 ) / R o 2 + R g 2 ) | 2 ( π R o 2 / 2 ) ( π R g 2 / 2 ) = 4 R o 2 R g 2 ( R o 2 + R g 2 ) 2
M FHB ( R g ) = M 1 ( R o ) T ( R o , R g ) = M 1 ( R o ) ( R o 2 + R g 2 ) 2 4 R g 2 R o 2
M MHB ( R g ) = M ′ T ( R g ′ , R g ) = M ′ ( R g ′ 2 + R g 2 ) 2 4 R g 2 R g ′ 2

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