Abstract

We demonstrate experimentally the formation and stable propagation of bound soliton pairs in a highly nonlinear photonic crystal fiber. The bound pairs occur at a particular power as the consequence of high-order soliton fission. They propagate over long distances with constant inter-soliton frequency and time separation. During propagation, the soliton self-frequency shift causes the central frequency of the pairs to move towards longer wavelength. The formation and characteristics of the bound soliton pairs are confirmed numerically. We believe this to be the first experimental observation of such bound soliton pairs.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

2006 (4)

J. M. Dudley, G. Genty, S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

F. Luan, D. V. Skryabin, A. V. Yulin and J. C. Knight, "Energy exchange between colliding solitons in photonic crystal fibers," Opt. Express 14, 9844-9853 (2006).
[CrossRef] [PubMed]

A. Zheltikov, "Nanoscale nonlinear optics in photonic crystal fibers," J. Opt. A, Pure Appl. Opt.  8, S47-S72 (2006).
[CrossRef]

Q. Lin and G. P. Agrawal, "Raman response function for silica fibers," Opt. Lett. 31, 3086-3088 (2006).
[CrossRef] [PubMed]

2005 (3)

2003 (2)

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (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)

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St.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]

1997 (1)

1996 (2)

N. Akhmediev, W. Krolikowski and A. J. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996).
[CrossRef]

J. C. Knight, T. A. Birks, P. St. J. Russell and D. M. Atkin, "All-silica single-mode fiber with photonic crystal cladding," Opt. Lett. 21, 1547-1549 (1996).
[CrossRef] [PubMed]

1994 (1)

1991 (2)

1990 (1)

M. Bredol, D. Leers, L. Bosselaar and M. Hutjens, "Improved model for OH absorption in optical fibers," J. Lightwave Technol. 8, 1536-1540 (1990).
[CrossRef]

1989 (2)

K. J.  Blow and D.  Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron.  25, 2665-2673 (1989).
[CrossRef]

S. Chi and S. Wen, "Raman cross talk of soliton collision in a lossless fiber," Opt. Lett. 14, 1216-1218 (1989).
[CrossRef] [PubMed]

1988 (1)

1987 (4)

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, A. M. Prokhorov, V. N. Serkin and D. V. Khaidarov, "Decay of femtosecond pulses in single-mode optical-fibers," JETP Lett. 46, 221-225 (1987).

P. Beaud, W. Hodel, B. Zysset and H. P. Weber, "Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron QE-23, 1938-1946 (1987).
[CrossRef]

Y. Kodama and A. Hasegawa, "Nonlinear pulse propagation in a monomode dielectric guide," IEEE J. Quantum Electron. 23, 510-524 (1987).
[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]

1986 (2)

1983 (1)

1980 (1)

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]

1973 (1)

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion," Appl. Phys. Lett. 12, 142-144 (1973).
[CrossRef]

Agrawal, G. P.

Akhmediev, N.

N. Akhmediev, W. Krolikowski and A. J. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996).
[CrossRef]

Atkin, D. M.

Beaud, P.

P. Beaud, W. Hodel, B. Zysset and H. P. Weber, "Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron QE-23, 1938-1946 (1987).
[CrossRef]

Bekki, N.

Birks, T. A.

Blow, K. J.

K. J.  Blow and D.  Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron.  25, 2665-2673 (1989).
[CrossRef]

Bosselaar, L.

M. Bredol, D. Leers, L. Bosselaar and M. Hutjens, "Improved model for OH absorption in optical fibers," J. Lightwave Technol. 8, 1536-1540 (1990).
[CrossRef]

Bredol, M.

M. Bredol, D. Leers, L. Bosselaar and M. Hutjens, "Improved model for OH absorption in optical fibers," J. Lightwave Technol. 8, 1536-1540 (1990).
[CrossRef]

Chi, S.

Coen, S.

J. M. Dudley, G. Genty, S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

Dianov, E. M.

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, A. M. Prokhorov, V. N. Serkin and D. V. Khaidarov, "Decay of femtosecond pulses in single-mode optical-fibers," JETP Lett. 46, 221-225 (1987).

Dudley, J. M.

J. M. Dudley, G. Genty, S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

Efimov, A.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor and P. St.J. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Feigenbaum, E.

Genty, G.

J. M. Dudley, G. Genty, S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

Gordon, J. P.

J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).
[CrossRef] [PubMed]

J. P. Gordon, "Interaction forces among solitons in optical fibers," Opt. Lett. 8, 596-598 (1983).
[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. St.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. Korobkin, A. M. Prokhorov, V. N. Serkin and D. V. Khaidarov, "Decay of femtosecond pulses in single-mode optical-fibers," JETP Lett. 46, 221-225 (1987).

Hasegawa, A.

Y. Kodama and A. Hasegawa, "Effects of initial overlap on the propagation of optical solitons at different wavelengths," Opt. Lett. 16, 208-210 (1991).
[CrossRef] [PubMed]

K. Tai, A. Hasegawa and N. Bekki, "Fission of optical solitons induced by stimulated Raman effect," Opt. Lett. 13, 392-394 (1988).
[CrossRef] [PubMed]

Y. Kodama and A. Hasegawa, "Nonlinear pulse propagation in a monomode dielectric guide," IEEE J. Quantum Electron. 23, 510-524 (1987).
[CrossRef]

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion," Appl. Phys. Lett. 12, 142-144 (1973).
[CrossRef]

Herrmann, J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St.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]

J. Herrmann, A. Nazarkin, "Soliton self-frequency shift for pulses with a duration less than the period of molecular oscillations," Opt. Lett. 19, 2065-2067 (1994).
[CrossRef] [PubMed]

Hodel, W.

P. Beaud, W. Hodel, B. Zysset and H. P. Weber, "Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron QE-23, 1938-1946 (1987).
[CrossRef]

Hong, B. J.

Husakou, A.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St.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]

Hutjens, M.

M. Bredol, D. Leers, L. Bosselaar and M. Hutjens, "Improved model for OH absorption in optical fibers," J. Lightwave Technol. 8, 1536-1540 (1990).
[CrossRef]

Joly, N.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor and P. St.J. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Khaidarov, D. V.

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, A. M. Prokhorov, V. N. Serkin and D. V. Khaidarov, "Decay of femtosecond pulses in single-mode optical-fibers," JETP Lett. 46, 221-225 (1987).

Knight, J. C.

F. Luan, D. V. Skryabin, A. V. Yulin and J. C. Knight, "Energy exchange between colliding solitons in photonic crystal fibers," Opt. Express 14, 9844-9853 (2006).
[CrossRef] [PubMed]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor and P. St.J. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[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]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St.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]

J. C. Knight, T. A. Birks, P. St. J. Russell and D. M. Atkin, "All-silica single-mode fiber with photonic crystal cladding: errata," Opt. Lett. 22, 484-485 (1997).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell and D. M. Atkin, "All-silica single-mode fiber with photonic crystal cladding," Opt. Lett. 21, 1547-1549 (1996).
[CrossRef] [PubMed]

Kodama, Y.

Y. Kodama and A. Hasegawa, "Effects of initial overlap on the propagation of optical solitons at different wavelengths," Opt. Lett. 16, 208-210 (1991).
[CrossRef] [PubMed]

Y. Kodama and A. Hasegawa, "Nonlinear pulse propagation in a monomode dielectric guide," IEEE J. Quantum Electron. 23, 510-524 (1987).
[CrossRef]

Korn, G.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St.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]

Korobkin, D. V.

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, A. M. Prokhorov, V. N. Serkin and D. V. Khaidarov, "Decay of femtosecond pulses in single-mode optical-fibers," JETP Lett. 46, 221-225 (1987).

Krolikowski, W.

N. Akhmediev, W. Krolikowski and A. J. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996).
[CrossRef]

Leers, D.

M. Bredol, D. Leers, L. Bosselaar and M. Hutjens, "Improved model for OH absorption in optical fibers," J. Lightwave Technol. 8, 1536-1540 (1990).
[CrossRef]

Lin, Q.

Lowery, A. J.

N. Akhmediev, W. Krolikowski and A. J. Lowery, "Influence of the Raman-effect on solitons in optical fibers," Opt. Commun. 131, 260-266 (1996).
[CrossRef]

Luan, F.

F. Luan, D. V. Skryabin, A. V. Yulin and J. C. Knight, "Energy exchange between colliding solitons in photonic crystal fibers," Opt. Express 14, 9844-9853 (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]

Mitschke, F. M.

Mollenauer, L. F.

Nazarkin, A.

Nickel, D.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St.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]

Omenetto, F. G.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor and P. St.J. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Orenstein, M.

Prokhorov, A. M.

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, A. M. Prokhorov, V. N. Serkin and D. V. Khaidarov, "Decay of femtosecond pulses in single-mode optical-fibers," JETP Lett. 46, 221-225 (1987).

Russell, P. St. J.

Russell, P. St.J.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor and P. St.J. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St.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]

Serkin, V. N.

A. B. Grudinin, E. M. Dianov, D. V. Korobkin, A. M. Prokhorov, V. N. Serkin and D. V. Khaidarov, "Decay of femtosecond pulses in single-mode optical-fibers," JETP Lett. 46, 221-225 (1987).

Skryabin, D. V.

F. Luan, D. V. Skryabin, A. V. Yulin and J. C. Knight, "Energy exchange between colliding solitons in photonic crystal fibers," Opt. Express 14, 9844-9853 (2006).
[CrossRef] [PubMed]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor and P. St.J. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[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]

Stolen, R. H.

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]

Tai, K.

Tappert, F.

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion," Appl. Phys. Lett. 12, 142-144 (1973).
[CrossRef]

Taylor, A. J.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor and P. St.J. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Wadsworth, W. J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St.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]

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[CrossRef]

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[CrossRef]

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F. Luan, D. V. Skryabin, A. V. Yulin and J. C. Knight, "Energy exchange between colliding solitons in photonic crystal fibers," Opt. Express 14, 9844-9853 (2006).
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A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor and P. St.J. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Zhavoronkov, N.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St.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]

Zheltikov, A.

A. Zheltikov, "Nanoscale nonlinear optics in photonic crystal fibers," J. Opt. A, Pure Appl. Opt.  8, S47-S72 (2006).
[CrossRef]

Zysset, B.

P. Beaud, W. Hodel, B. Zysset and H. P. Weber, "Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron QE-23, 1938-1946 (1987).
[CrossRef]

Appl. Phys. Lett. (1)

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion," Appl. Phys. Lett. 12, 142-144 (1973).
[CrossRef]

IEEE J. Quantum Electron (1)

P. Beaud, W. Hodel, B. Zysset and H. P. Weber, "Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron QE-23, 1938-1946 (1987).
[CrossRef]

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K. J.  Blow and D.  Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron.  25, 2665-2673 (1989).
[CrossRef]

Y. Kodama and A. Hasegawa, "Nonlinear pulse propagation in a monomode dielectric guide," IEEE J. Quantum Electron. 23, 510-524 (1987).
[CrossRef]

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M. Bredol, D. Leers, L. Bosselaar and M. Hutjens, "Improved model for OH absorption in optical fibers," J. Lightwave Technol. 8, 1536-1540 (1990).
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[CrossRef]

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J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St.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]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor and P. St.J. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
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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).
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R. Trebino, Frequency-Resolved Optical Gaiting: the measurement of ultrashort laser pulses, (Kluwer Academic Publishers, 2000).

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001), 3rd ed.

A. Hasegawa and M. Matsumoto, Optical Solitons in Fibers (Springer Verlag, Berlin, Heidelberg, 2003).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic Press, San Diego, 2003).

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Figures (10)

Fig. 1.
Fig. 1.

Experimental setup: ISO, optical isolator; M1,2,3 mirrors; A, attenuator; λ/2, half-waveplate; T α 1/2, telescope; FM1, flip mirror; PM, power meter; O1,2, objectives; PCF,highly nonlinear photonic crystal fiber; PBS, polarization beam splitter; OSA, optical spectrum analyzer.

Fig. 2.
Fig. 2.

Dispersion of the PCF used in experiments. Inset: scanning electron micrograph of the fiber cross-section.

Fig. 3.
Fig. 3.

Spectral evolution with increasing average power. The fiber length is 44 cm and light was launched and detected with polarization parallel to the slow (A) and fast (B) axis of the fiber.

Fig. 4.
Fig. 4.

Spectral evolution with increasing power. Fiber length was 15 m. Excitation and detection parallel to the slow axis.

Fig. 5.
Fig. 5.

A-Evolution of the spectra with length. B - the spectra for the 1m (black line) and for the 15m (red line) fiber. The input power of ~180 mW (constant throughout) corresponded to the minimum spectral spacing between the solitons. Both excitation and measurement were performed parallel to the slow axis.

Fig. 6.
Fig. 6.

A typical spectrum at the output of the fiber and corresponding FROG spectrograph. The wavelength scale in spectrogram is not recalculated and presents the spectra of the output signal due to the frequency-doubling in the FROG. The white arrows indicate spectral components responsible for the sum frequency peaks.

Fig. 7.
Fig. 7.

FROG spectrographs of the soliton pair in 70 cm fiber for different power levels. The input power is increasing stepwise from image A to image D. The image D corresponds to input power of 180 mW in Fig. 3.

Fig. 8.
Fig. 8.

FROG spectrographs of the soliton pair in 150 cm fiber for different power levels. The input power is increasing stepwise from image A to image C. The image C corresponds to an input power of 180 mW in Fig. 3.

Fig. 9.
Fig. 9.

Numerical simulation of spectral evolution with increasing input average power. The laser launch efficiency is taken to be 30%. Fiber length is 44 cm.

Fig. 10.
Fig. 10.

Numerical modelling of the spectral (A,B,C) and temporal evolution (D,E,F) of launched laser pulses in 70 cm PCF for three different power levels (below, at, and above bound state formation; the input power increases stepwise from A to C). G & H: soliton splitting (G) and bound pair formation (H) after 60 cm of propagation. I: the solitons before collision at the distance of 16 cm.

Equations (3)

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A ( z , τ ) z = n 2 i n + 1 β n n ! n A ( z , τ ) τ n α 2 A ( z , τ ) + ( 1 + i ω 0 τ ) ( A ( z , τ ) -∞ R ( t ' ) A ( z , τ t ' ) 2 dt ' )
R ( t ) = ( 1 f R ) δ ( t ) + f R ( q a h a ( t ) + q b h b ( t ) )
h a ( t ) = τ 1 2 + τ 2 2 τ 1 τ 2 2 exp ( t τ 2 ) sin ( t τ 1 ) , h b ( t ) = 2 τ b t τ b 2 exp ( t τ b ) .

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