Abstract

Collisions of femtosecond solitons in silica core photonic crystal fibers are investigated experimentally and theoretically. Clear spectral signatures of the significant energy exchange between the interacting pulses are reported. Two primary and competing effects causing energy exchange are interpulse Raman scattering, which is insensitive to the phase difference of the colliding solitons, and the phase sensitive interaction via the Kerr nonlinearity.

©2006 Optical Society of America

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  1. W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
    [Crossref]
  2. X. Liu, C. Xu, W.H. Knox, J.K. Chandalia, B.J. Eggleton, S.G. Kosinski, and B.S. Windeler, “Soliton self-frequency shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26, 358–360 (2001).
    [Crossref]
  3. D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).
    [Crossref] [PubMed]
  4. F. Luan, A. Yulin, J.C. Knight, and D.V. Skryabin, “Polarization instability of solitons in photonic crystal fibers,” Opt. Express 14, 6550–6556 (2006).
    [Crossref] [PubMed]
  5. J.K. Ranka, R.S. Windeler, and A.J. Stentz, “Visible continuum generation in air silica microstructure optical fibers with anomalous dispersion at 800nm,” Opt. Lett. 25, 25–27 (2000).
    [Crossref]
  6. A.V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
    [Crossref] [PubMed]
  7. D.V. Skryabin and A.V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
    [Crossref]
  8. A. Betlej, S. Suntsov, K.G. Makris, L. Jankovic, D. N. Christodoulides, G.I. Stegeman, J. Fini, R.T. Bise, and D.J. DiGiovanni, “All-optical switching and multifrequency generation in a dual-core photonic crystal fiber,” Opt. Lett. 31, 1480 (2006).
    [Crossref] [PubMed]
  9. D.G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
    [Crossref] [PubMed]
  10. D.V. Skryabin, F. Biancalana, D.M. Bird, and F. Benabid, “Effective Kerr nonlinearity and two-color solitons in photonic band-gap fibers filled with a Raman active gas,” Phys. Rev. Lett.,  93, 143907 (2004).
    [Crossref] [PubMed]
  11. D.V. Skryabin, “Coupled core-surface solitons in photonic crystal fibers,” Opt. Express 12, 4841–4846 (2004).
    [Crossref] [PubMed]
  12. G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001).
  13. F.M. Mitschke and L.F. Mollenauer, “Experimental observation of interaction forces between solitons in optical fibers,” Opt. Lett. 12, 355–357 (1987).
    [Crossref] [PubMed]
  14. K. Kurokawa, H. Kubota, and M. Nakazawa, “Soliton self-frequency shift accelerated by femtosecond soliton interaction,” Electron. Lett. 28, 2052–2054 (1992).
    [Crossref]
  15. S. Chi and S. Wen, “Raman cross talk of soliton collision in a lossless fiber,” Opt. Lett. 14, 1216–1218 (1989).
    [Crossref] [PubMed]
  16. V.V. Afanasjev, V.A. Vysloukh, and V.N. Serkin, “Decay and interaction of femtosecond optical solitons induced by the Raman self-scattering effect,” Opt. Lett. 15, 1479–1481 (1990).
  17. B.J. Hong and C.C. Yang, “Interactions between femtosecond solitons in optical fibers,” J. Opt. Soc. Am. B 8, 1114 (1991).
    [Crossref]
  18. B.A. Malomed, “Soliton-collision problem in the nonlinear Schrödinger equation with a nonlinear damping term,” Phys. Rev. A 44, 1412–1414 (1991).
    [Crossref] [PubMed]
  19. D. Anderson, “Bandwidth limits due to incoherent soliton interaction in optical-fiber communication-systems,” Phys. Rev. A 32, 2270 (1985).
    [Crossref] [PubMed]
  20. L.F. Mollenauer, S.G. Evangelides, and J.P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 1362–1367 (1991).
    [Crossref]
  21. S.G. Evangelides and J.P. Gordon, “Energy transfers and frequency shifts from three soliton collisions in a multiplexed transmission line with periodic amplification,” J. Lightwave Technol. 14, 1639–1643 (1996).
    [Crossref]
  22. N.C. Panoiu, I.V. Mel’nikov, D. Mihalache, C. Etrich, and F. Lederer, “Soliton generation from a multi-frequency optical signal,” J. Opt. B: Quantum Semiclass. Opt. 4, R53–R68 (2002) and references therein.
    [Crossref]
  23. A. Peleg, “Log-normal distribution of pulse amplitudes due to Raman cross talk in wavelength division multiplexing soliton transmission,” Opt. Lett. 29, 1980–1982 (2004).
    [Crossref] [PubMed]
  24. G.I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science 286, 1518–1523 (1999) and references therein.
    [Crossref] [PubMed]
  25. K.A. Gorshkov and L.A. Ostrovsky, “Interactions of solitons in non-integrable systems - direct perturbation method and applications,” Physica D 3, 428–438 (1981).
    [Crossref]

2006 (2)

2005 (1)

D.V. Skryabin and A.V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[Crossref]

2004 (3)

2003 (2)

D.G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[Crossref] [PubMed]

D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).
[Crossref] [PubMed]

2002 (1)

N.C. Panoiu, I.V. Mel’nikov, D. Mihalache, C. Etrich, and F. Lederer, “Soliton generation from a multi-frequency optical signal,” J. Opt. B: Quantum Semiclass. Opt. 4, R53–R68 (2002) and references therein.
[Crossref]

2001 (2)

A.V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

X. Liu, C. Xu, W.H. Knox, J.K. Chandalia, B.J. Eggleton, S.G. Kosinski, and B.S. Windeler, “Soliton self-frequency shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26, 358–360 (2001).
[Crossref]

2000 (2)

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

J.K. Ranka, R.S. Windeler, and A.J. Stentz, “Visible continuum generation in air silica microstructure optical fibers with anomalous dispersion at 800nm,” Opt. Lett. 25, 25–27 (2000).
[Crossref]

1999 (1)

G.I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science 286, 1518–1523 (1999) and references therein.
[Crossref] [PubMed]

1996 (1)

S.G. Evangelides and J.P. Gordon, “Energy transfers and frequency shifts from three soliton collisions in a multiplexed transmission line with periodic amplification,” J. Lightwave Technol. 14, 1639–1643 (1996).
[Crossref]

1992 (1)

K. Kurokawa, H. Kubota, and M. Nakazawa, “Soliton self-frequency shift accelerated by femtosecond soliton interaction,” Electron. Lett. 28, 2052–2054 (1992).
[Crossref]

1991 (3)

B.A. Malomed, “Soliton-collision problem in the nonlinear Schrödinger equation with a nonlinear damping term,” Phys. Rev. A 44, 1412–1414 (1991).
[Crossref] [PubMed]

B.J. Hong and C.C. Yang, “Interactions between femtosecond solitons in optical fibers,” J. Opt. Soc. Am. B 8, 1114 (1991).
[Crossref]

L.F. Mollenauer, S.G. Evangelides, and J.P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 1362–1367 (1991).
[Crossref]

1990 (1)

1989 (1)

1987 (1)

1985 (1)

D. Anderson, “Bandwidth limits due to incoherent soliton interaction in optical-fiber communication-systems,” Phys. Rev. A 32, 2270 (1985).
[Crossref] [PubMed]

1981 (1)

K.A. Gorshkov and L.A. Ostrovsky, “Interactions of solitons in non-integrable systems - direct perturbation method and applications,” Physica D 3, 428–438 (1981).
[Crossref]

Afanasjev, V.V.

Agrawal, G.P.

G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001).

Ahmad, F.R.

D.G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[Crossref] [PubMed]

Anderson, D.

D. Anderson, “Bandwidth limits due to incoherent soliton interaction in optical-fiber communication-systems,” Phys. Rev. A 32, 2270 (1985).
[Crossref] [PubMed]

Arriaga, J.

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

Benabid, F.

D.V. Skryabin, F. Biancalana, D.M. Bird, and F. Benabid, “Effective Kerr nonlinearity and two-color solitons in photonic band-gap fibers filled with a Raman active gas,” Phys. Rev. Lett.,  93, 143907 (2004).
[Crossref] [PubMed]

Betlej, A.

Biancalana, F.

D.V. Skryabin, F. Biancalana, D.M. Bird, and F. Benabid, “Effective Kerr nonlinearity and two-color solitons in photonic band-gap fibers filled with a Raman active gas,” Phys. Rev. Lett.,  93, 143907 (2004).
[Crossref] [PubMed]

Bird, D.M.

D.V. Skryabin, F. Biancalana, D.M. Bird, and F. Benabid, “Effective Kerr nonlinearity and two-color solitons in photonic band-gap fibers filled with a Raman active gas,” Phys. Rev. Lett.,  93, 143907 (2004).
[Crossref] [PubMed]

Bise, R.T.

Chandalia, J.K.

Chi, S.

Christodoulides, D. N.

DiGiovanni, D.J.

Eggleton, B.J.

Etrich, C.

N.C. Panoiu, I.V. Mel’nikov, D. Mihalache, C. Etrich, and F. Lederer, “Soliton generation from a multi-frequency optical signal,” J. Opt. B: Quantum Semiclass. Opt. 4, R53–R68 (2002) and references therein.
[Crossref]

Evangelides, S.G.

S.G. Evangelides and J.P. Gordon, “Energy transfers and frequency shifts from three soliton collisions in a multiplexed transmission line with periodic amplification,” J. Lightwave Technol. 14, 1639–1643 (1996).
[Crossref]

L.F. Mollenauer, S.G. Evangelides, and J.P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 1362–1367 (1991).
[Crossref]

Fini, J.

Gaeta, A.L.

D.G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[Crossref] [PubMed]

Gallagher, M.T.

D.G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[Crossref] [PubMed]

Gordon, J.P.

S.G. Evangelides and J.P. Gordon, “Energy transfers and frequency shifts from three soliton collisions in a multiplexed transmission line with periodic amplification,” J. Lightwave Technol. 14, 1639–1643 (1996).
[Crossref]

L.F. Mollenauer, S.G. Evangelides, and J.P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 1362–1367 (1991).
[Crossref]

Gorshkov, K.A.

K.A. Gorshkov and L.A. Ostrovsky, “Interactions of solitons in non-integrable systems - direct perturbation method and applications,” Physica D 3, 428–438 (1981).
[Crossref]

Herrmann, J.

A.V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Hong, B.J.

Husakou, A.V.

A.V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Jankovic, L.

Knight, J.C.

F. Luan, A. Yulin, J.C. Knight, and D.V. Skryabin, “Polarization instability of solitons in photonic crystal fibers,” Opt. Express 14, 6550–6556 (2006).
[Crossref] [PubMed]

D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).
[Crossref] [PubMed]

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

Knox, W.H.

Koch, K.W.

D.G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[Crossref] [PubMed]

Kosinski, S.G.

Kubota, H.

K. Kurokawa, H. Kubota, and M. Nakazawa, “Soliton self-frequency shift accelerated by femtosecond soliton interaction,” Electron. Lett. 28, 2052–2054 (1992).
[Crossref]

Kurokawa, K.

K. Kurokawa, H. Kubota, and M. Nakazawa, “Soliton self-frequency shift accelerated by femtosecond soliton interaction,” Electron. Lett. 28, 2052–2054 (1992).
[Crossref]

Lederer, F.

N.C. Panoiu, I.V. Mel’nikov, D. Mihalache, C. Etrich, and F. Lederer, “Soliton generation from a multi-frequency optical signal,” J. Opt. B: Quantum Semiclass. Opt. 4, R53–R68 (2002) and references therein.
[Crossref]

Liu, X.

Luan, F.

F. Luan, A. Yulin, J.C. Knight, and D.V. Skryabin, “Polarization instability of solitons in photonic crystal fibers,” Opt. Express 14, 6550–6556 (2006).
[Crossref] [PubMed]

D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).
[Crossref] [PubMed]

Makris, K.G.

Malomed, B.A.

B.A. Malomed, “Soliton-collision problem in the nonlinear Schrödinger equation with a nonlinear damping term,” Phys. Rev. A 44, 1412–1414 (1991).
[Crossref] [PubMed]

Mel’nikov, I.V.

N.C. Panoiu, I.V. Mel’nikov, D. Mihalache, C. Etrich, and F. Lederer, “Soliton generation from a multi-frequency optical signal,” J. Opt. B: Quantum Semiclass. Opt. 4, R53–R68 (2002) and references therein.
[Crossref]

Mihalache, D.

N.C. Panoiu, I.V. Mel’nikov, D. Mihalache, C. Etrich, and F. Lederer, “Soliton generation from a multi-frequency optical signal,” J. Opt. B: Quantum Semiclass. Opt. 4, R53–R68 (2002) and references therein.
[Crossref]

Mitschke, F.M.

Mollenauer, L.F.

L.F. Mollenauer, S.G. Evangelides, and J.P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 1362–1367 (1991).
[Crossref]

F.M. Mitschke and L.F. Mollenauer, “Experimental observation of interaction forces between solitons in optical fibers,” Opt. Lett. 12, 355–357 (1987).
[Crossref] [PubMed]

Muller, D.

D.G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[Crossref] [PubMed]

Nakazawa, M.

K. Kurokawa, H. Kubota, and M. Nakazawa, “Soliton self-frequency shift accelerated by femtosecond soliton interaction,” Electron. Lett. 28, 2052–2054 (1992).
[Crossref]

Ortigosa-Blanch, A.

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

Ostrovsky, L.A.

K.A. Gorshkov and L.A. Ostrovsky, “Interactions of solitons in non-integrable systems - direct perturbation method and applications,” Physica D 3, 428–438 (1981).
[Crossref]

Ouzounov, D.G.

D.G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[Crossref] [PubMed]

Panoiu, N.C.

N.C. Panoiu, I.V. Mel’nikov, D. Mihalache, C. Etrich, and F. Lederer, “Soliton generation from a multi-frequency optical signal,” J. Opt. B: Quantum Semiclass. Opt. 4, R53–R68 (2002) and references therein.
[Crossref]

Peleg, A.

Ranka, J.K.

Russell, P.St.J.

D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).
[Crossref] [PubMed]

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

Segev, M.

G.I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science 286, 1518–1523 (1999) and references therein.
[Crossref] [PubMed]

Serkin, V.N.

Silcox, J.

D.G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[Crossref] [PubMed]

Silvestre, E.

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

Skryabin, D.V.

F. Luan, A. Yulin, J.C. Knight, and D.V. Skryabin, “Polarization instability of solitons in photonic crystal fibers,” Opt. Express 14, 6550–6556 (2006).
[Crossref] [PubMed]

D.V. Skryabin and A.V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[Crossref]

D.V. Skryabin, F. Biancalana, D.M. Bird, and F. Benabid, “Effective Kerr nonlinearity and two-color solitons in photonic band-gap fibers filled with a Raman active gas,” Phys. Rev. Lett.,  93, 143907 (2004).
[Crossref] [PubMed]

D.V. Skryabin, “Coupled core-surface solitons in photonic crystal fibers,” Opt. Express 12, 4841–4846 (2004).
[Crossref] [PubMed]

D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).
[Crossref] [PubMed]

Stegeman, G.I.

Stentz, A.J.

Suntsov, S.

Thomas, M.G.

D.G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[Crossref] [PubMed]

Venkataraman, N.

D.G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[Crossref] [PubMed]

Vysloukh, V.A.

Wadsworth, W.J.

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

Wen, S.

Windeler, B.S.

Windeler, R.S.

Xu, C.

Yang, C.C.

Yulin, A.

Yulin, A.V.

D.V. Skryabin and A.V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[Crossref]

Electron. Lett. (2)

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

K. Kurokawa, H. Kubota, and M. Nakazawa, “Soliton self-frequency shift accelerated by femtosecond soliton interaction,” Electron. Lett. 28, 2052–2054 (1992).
[Crossref]

J. Lightwave Technol. (2)

L.F. Mollenauer, S.G. Evangelides, and J.P. Gordon, “Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers,” J. Lightwave Technol. 9, 1362–1367 (1991).
[Crossref]

S.G. Evangelides and J.P. Gordon, “Energy transfers and frequency shifts from three soliton collisions in a multiplexed transmission line with periodic amplification,” J. Lightwave Technol. 14, 1639–1643 (1996).
[Crossref]

J. Opt. B: Quantum Semiclass. Opt. (1)

N.C. Panoiu, I.V. Mel’nikov, D. Mihalache, C. Etrich, and F. Lederer, “Soliton generation from a multi-frequency optical signal,” J. Opt. B: Quantum Semiclass. Opt. 4, R53–R68 (2002) and references therein.
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Opt. Lett. (7)

Phys. Rev. A (2)

B.A. Malomed, “Soliton-collision problem in the nonlinear Schrödinger equation with a nonlinear damping term,” Phys. Rev. A 44, 1412–1414 (1991).
[Crossref] [PubMed]

D. Anderson, “Bandwidth limits due to incoherent soliton interaction in optical-fiber communication-systems,” Phys. Rev. A 32, 2270 (1985).
[Crossref] [PubMed]

Phys. Rev. E (1)

D.V. Skryabin and A.V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[Crossref]

Phys. Rev. Lett. (2)

D.V. Skryabin, F. Biancalana, D.M. Bird, and F. Benabid, “Effective Kerr nonlinearity and two-color solitons in photonic band-gap fibers filled with a Raman active gas,” Phys. Rev. Lett.,  93, 143907 (2004).
[Crossref] [PubMed]

A.V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Physica D (1)

K.A. Gorshkov and L.A. Ostrovsky, “Interactions of solitons in non-integrable systems - direct perturbation method and applications,” Physica D 3, 428–438 (1981).
[Crossref]

Science (3)

D.G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[Crossref] [PubMed]

D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).
[Crossref] [PubMed]

G.I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: Universality and diversity,” Science 286, 1518–1523 (1999) and references therein.
[Crossref] [PubMed]

Other (1)

G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001).

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Figures (6)

Fig. 1.
Fig. 1. (A) Measured group index ng (lines with circles and squares) and group velocity dispersion D (continuous lines) of the fibre. D>0 corresponds to the anomalous GVD. (B) Setup of the experiment. PB: polarising beamsplitter, PL polariser, OSA optical spectrum analyser.

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Fig. 2.
Fig. 2. (A) Composite of multiple output spectra from the fiber recorded as a function of the pulse delay. The power of the front pulse (which appears at a longer wavelength) was fixed at 18pJ and the power of the rear pulse was fixed at 16pJ. (B) The pulse delay is fixed at 1.5ps. Spectra were recorded for a fixed pulse energy of 18pJ in the second pulse and for various first pulse energies.

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Fig. 3.
Fig. 3. (A) Raman gain profiles. The one marked by the full line with the peak is Re[f(δ)] and the straight dashed line is the linear approximation (see section 4) valid for small detunings. (B,C) collision of two solitons. (B) shows spectra of the colliding solitons vs propagation distance. (C) shows intensity vs propagation distance and time. Note different z intervals in B and C. The widths of the frequency intervals in (A) and (B) are made equal, to allow direct estimate of the interpulse Raman gain at the collision moment (see vertical dashed lines).

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Fig. 4.
Fig. 4. Modeling of Eq. (1) corresponding to the experimental conditions as in Fig. 2(A,B). Initial phase difference of the colliding pulses has been fixed to zero. The side arrows, dashed lines and δ values indicate the interval in which the frequency detuning between the solitons varies at the moment of collision. The values of δ are indicated in THz. The white horizontal lines mark the parameters, when collision happens exactly at the output end of the fiber. Interaction becomes more incoherent for larger δ.

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Fig. 5.
Fig. 5. The same as Fig. 4, but the results are averaged over the initial phase difference of the colliding pulses varying from 0 to 2π.

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Fig. 6.
Fig. 6. The coherent (strongly oscillating black line) and incoherent (smooth blue line) contributions to the energy transfer rate between interacting 100fs solitons with energies 16pJ and pulse separation 400fs as function of the frequency detuning between the pulses.

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Equations (15)

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[ ∂ z − i D ( i ∂ t ) ] A = i γ ( 1 − θ ) ∣ A ∣ 2 A + i γ θ A ∫ 0 ∞ dt ′ R ( t ′ ) ∣ A ( t − t ′ , z ) ∣ 2 .
A = A 1 ( t ) e − i δ 1 t + A 2 ( t ) e − i δ 2 t .
i γ ( 1 − θ ) ∣ A ∣ 2 A + i γ θ A ∫ 0 ∞ dt ' R ( t ' ) ∣ A ( t − t ' , z ) ∣ 2 =
A 1 e − i δ 1 t ( i γ ∣ A 1 ∣ 2 + i 2 γ ( 1 − θ ) ∣ A 2 ∣ 2 − f ( δ ) ∣ A 2 ∣ 2 + i γ ( 1 − θ ) A 1 A 2 * e − i δ t ) +
A 2 e − i δ 2 t ( i γ ∣ A 2 ∣ 2 + i 2 γ ( 1 − θ ) ∣ A 1 ∣ 2 − f * ( δ ) ∣ A 1 ∣ 2 + i γ ( 1 − θ ) A 1 * A 2 e i δ t ) + …
f ( δ ) = − i γ θ ∫ 0 ∞ R ( t ) e i δ t d t .
[ ∂ z + β 1 ( 1 ) ∂ t + i 2 β 1 ( 2 ) ∂ t 2 ] A 1 = i γ ( ∣ A 1 ∣ 2 + 2 ( 1 − θ ) ∣ A 2 ∣ 2 ) A 1 − f ( δ ) ∣ A 2 ∣ 2 A 1 ,
[ ∂ z + β 2 ( 1 ) ∂ t + i 2 β 2 ( 2 ) ∂ t 2 ] A 2 = i γ ( ∣ A 2 ∣ 2 + 2 ( 1 − θ ) ∣ A 1 ∣ 2 ) A 2 − f * ( δ ) ∣ A 1 ∣ 2 A 2 .
∂ z ∫ − ∞ ∞ ( ∣ A 2 ∣ 2 − ∣ A 1 ∣ 2 ) d t = 2 R e [ f ( δ ) ] ∫ − ∞ ∞ ∣ A 1 ∣ 2 ∣ A 2 ∣ 2 d t .
[ ∂ z + β 1 ( 1 ) ∂ t + i 2 β 1 ( 2 ) ∂ t 2 ] A 1 = i γ ∣ A 1 ∣ 2 A 1 +
[ i 2 γ ( 1 − θ ) − f ( δ ) ] ∣ A 2 ∣ 2 A 1 + i γ A 1 2 A 2 * e − i δ t + i 2 γ ( 1 − θ ) A 2 ∣ A 1 ∣ 2 e i δ t + …
[ ∂ z + β 2 ( 1 ) ∂ t + i 2 β 2 ( 2 ) ∂ t 2 ] A 2 = i γ ∣ A 2 ∣ 2 A 2 +
[ i 2 γ ( 1 − θ ) + f * ( δ ) ] ∣ A 1 ∣ 2 A 2 + i γ A 2 2 A 1 * e i δ t + i 2 γ ( 1 − θ ) A 1 e − i δ t ∣ A 2 ∣ 2 + …
∂ z ∫ − ∞ ∞ ( ∣ A 2 ∣ 2 − ∣ A 1 ∣ 2 ) d t =
2 ∫ − ∞ ∞ ∣ A 1 ∣ ∣ A 2 ∣ ( R e [ f ( δ ) ] ∣ A 1 ∣ ∣ A 2 ∣ + 2 γ ( 1 − θ ) ( ∣ A 1 ∣ 2 + ∣ A 2 ∣ 2 ) sin [ δ t + ϕ 2 − ϕ 1 ] ) d t ,

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