Abstract

We report the experimental and numerical observation of step-like behavior of the high-intensity transmission deep inside the bandgap of a 1D photonic crystal. We show this to be a novel manifestation of the quantization of the soliton area, and derive an upper limit for the energy of the transmission steps, which is consistent with measurements and simulations.

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  9. 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(13), 1095–1098 (1980).
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  16. J. Leon and A. Spire, “Gap soliton formation by nonlinear supratransmission in bragg media,” Phys. Lett. A 327(5-6), 474–480 (2004).
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  17. W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58(2), 160–163 (1987).
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  21. G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett. 14(15), 823–825 (1989).
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  25. H. G. Winful, “Pulse-compression in optical fiber filters,” Appl. Phys. Lett. 46(6), 527–529 (1985).
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  26. J. E. Sipe and H. G. Winful, “Nonlinear Schroedinger solitons in a periodic structure,” Opt. Lett. 13(2), 132–133 (1988).
    [CrossRef] [PubMed]
  27. C. Martijn de Sterke and J. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42(1), 550–555 (1990).
    [CrossRef] [PubMed]
  28. D. Taverner, N. G. R. Broderick, D. J. Richardson, R. I. Laming, and M. Ibsen, “Nonlinear self-switching and multiple gap-soliton formation in a fiber Bragg grating,” Opt. Lett. 23(5), 328–330 (1998).
    [CrossRef]
  29. J. T. Mok, I. C. M. Littler, E. Tsoy, and B. J. Eggleton, “Soliton compression and pulse-train generation by use of microchip Q-switched pulses in Bragg gratings,” Opt. Lett. 30(18), 2457–2459 (2005).
    [CrossRef] [PubMed]
  30. E. Golovchenko, E. Dianov, A. Prokhorov, and V. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87–91 (1985).
  31. H. Weber and W. Hodel, “Propagation of subpicosecond pulses and soliton formation in an optical fiber,” Phys. Scr. T23, 200–205 (1988).
    [CrossRef]
  32. S. F. Mingaleev and Y. S. Kivshar, “Self-trapping and stable localized modes in nonlinear photonic crystals,” Phys. Rev. Lett. 86(24), 5474–5477 (2001).
    [CrossRef] [PubMed]
  33. P. Xie, Z.-Q. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasiperiodic photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(2), 026607 (2003).
    [CrossRef] [PubMed]
  34. E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, and A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34(5), 4442–4444 (1986).
    [CrossRef] [PubMed]
  35. A. Grudinin, D. Richardson, and D. Payne, “Energy quantisation in figure eight fibre laser,” Electron. Lett. 28(1), 67–68 (1992).
    [CrossRef]
  36. D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005).
    [CrossRef]
  37. S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18(21), 908–911 (1967).
    [CrossRef]
  38. R. E. Slusher and H. M. Gibbs, “Self-induced transparency in atomic rubidium,” Phys. Rev. A 5(4), 1634–1659 (1972).
    [CrossRef]
  39. H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81(19), 4260–4263 (1998).
    [CrossRef]
  40. R. Landauer, “Spatial variation of currents and fields due to localized scatterers in metallic conduction,” IBM J. Res. Develop. 1(3), 223–231 (1957).
    [CrossRef]
  41. B. van Wees, H. van Houten, C. Beenakker, J. Williamson, L. Kouwenhoven, D. van der Marel, and C. Foxon, “Quantized conductance of point contacts in a two-dimensional electron gas,” Phys. Rev. Lett. 60(9), 848–850 (1988).
    [CrossRef] [PubMed]

2008 (1)

2006 (2)

I. C. M. Littler, T. Grujic, and B. J. Eggleton, “Photothermal effects in fiber Bragg gratings,” Appl. Opt. 45(19), 4679–4685 (2006).
[CrossRef] [PubMed]

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys. 2(11), 775–780 (2006).
[CrossRef]

2005 (2)

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005).
[CrossRef]

J. T. Mok, I. C. M. Littler, E. Tsoy, and B. J. Eggleton, “Soliton compression and pulse-train generation by use of microchip Q-switched pulses in Bragg gratings,” Opt. Lett. 30(18), 2457–2459 (2005).
[CrossRef] [PubMed]

2004 (1)

J. Leon and A. Spire, “Gap soliton formation by nonlinear supratransmission in bragg media,” Phys. Lett. A 327(5-6), 474–480 (2004).
[CrossRef]

2003 (4)

E. A. Ostrovskaya and Y. S. Kivshar, “Matter-wave gap solitons in atomic band-gap structures,” Phys. Rev. Lett. 90(16), 160407 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

A. Sukhorukov, Y. Kivshar, H. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” IEEE J. Quantum Electron. 39(1), 31–50 (2003).
[CrossRef]

P. Xie, Z.-Q. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasiperiodic photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(2), 026607 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

S. F. Mingaleev and Y. S. Kivshar, “Self-trapping and stable localized modes in nonlinear photonic crystals,” Phys. Rev. Lett. 86(24), 5474–5477 (2001).
[CrossRef] [PubMed]

1999 (1)

1998 (2)

D. Taverner, N. G. R. Broderick, D. J. Richardson, R. I. Laming, and M. Ibsen, “Nonlinear self-switching and multiple gap-soliton formation in a fiber Bragg grating,” Opt. Lett. 23(5), 328–330 (1998).
[CrossRef]

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81(19), 4260–4263 (1998).
[CrossRef]

1996 (1)

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76(10), 1627–1630 (1996).
[CrossRef] [PubMed]

1995 (1)

S. Wabnitz, “Pulse self-switching in optical fiber bragg gratings,” Opt. Commun. 114(1-2), 170–180 (1995).
[CrossRef]

1992 (2)

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

A. B. Aceves, C. De Angelis, and S. Wabnitz, “Generation of solitons in a nonlinear periodic medium,” Opt. Lett. 17(22), 1566–1568 (1992).
[CrossRef] [PubMed]

1990 (1)

C. Martijn de Sterke and J. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42(1), 550–555 (1990).
[CrossRef] [PubMed]

1989 (3)

G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett. 14(15), 823–825 (1989).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62(15), 1746–1749 (1989).
[CrossRef] [PubMed]

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141(1-2), 37–42 (1989).
[CrossRef]

1988 (3)

H. Weber and W. Hodel, “Propagation of subpicosecond pulses and soliton formation in an optical fiber,” Phys. Scr. T23, 200–205 (1988).
[CrossRef]

J. E. Sipe and H. G. Winful, “Nonlinear Schroedinger solitons in a periodic structure,” Opt. Lett. 13(2), 132–133 (1988).
[CrossRef] [PubMed]

B. van Wees, H. van Houten, C. Beenakker, J. Williamson, L. Kouwenhoven, D. van der Marel, and C. Foxon, “Quantized conductance of point contacts in a two-dimensional electron gas,” Phys. Rev. Lett. 60(9), 848–850 (1988).
[CrossRef] [PubMed]

1987 (1)

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58(2), 160–163 (1987).
[CrossRef] [PubMed]

1986 (1)

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, and A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34(5), 4442–4444 (1986).
[CrossRef] [PubMed]

1985 (2)

H. G. Winful, “Pulse-compression in optical fiber filters,” Appl. Phys. Lett. 46(6), 527–529 (1985).
[CrossRef]

E. Golovchenko, E. Dianov, A. Prokhorov, and V. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87–91 (1985).

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(13), 1095–1098 (1980).
[CrossRef]

1978 (1)

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32(10), 647–649 (1978).
[CrossRef]

1973 (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. i. anomalous dispersion,” Appl. Phys. Lett. 23(3), 142–144 (1973).
[CrossRef]

1972 (2)

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

R. E. Slusher and H. M. Gibbs, “Self-induced transparency in atomic rubidium,” Phys. Rev. A 5(4), 1634–1659 (1972).
[CrossRef]

1967 (1)

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18(21), 908–911 (1967).
[CrossRef]

1957 (1)

R. Landauer, “Spatial variation of currents and fields due to localized scatterers in metallic conduction,” IBM J. Res. Develop. 1(3), 223–231 (1957).
[CrossRef]

Aceves, A. B.

A. B. Aceves, C. De Angelis, and S. Wabnitz, “Generation of solitons in a nonlinear periodic medium,” Opt. Lett. 17(22), 1566–1568 (1992).
[CrossRef] [PubMed]

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141(1-2), 37–42 (1989).
[CrossRef]

Beenakker, C.

B. van Wees, H. van Houten, C. Beenakker, J. Williamson, L. Kouwenhoven, D. van der Marel, and C. Foxon, “Quantized conductance of point contacts in a two-dimensional electron gas,” Phys. Rev. Lett. 60(9), 848–850 (1988).
[CrossRef] [PubMed]

Boardman, A. D.

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, and A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34(5), 4442–4444 (1986).
[CrossRef] [PubMed]

Boyd, R. W.

Broderick, N. G. R.

Chen, W.

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58(2), 160–163 (1987).
[CrossRef] [PubMed]

Christodoulides, D. N.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62(15), 1746–1749 (1989).
[CrossRef] [PubMed]

De Angelis, C.

de Sterke, C.

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76(10), 1627–1630 (1996).
[CrossRef] [PubMed]

de Sterke, C. M.

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys. 2(11), 775–780 (2006).
[CrossRef]

Dianov, E.

E. Golovchenko, E. Dianov, A. Prokhorov, and V. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87–91 (1985).

Eggleton, B.

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76(10), 1627–1630 (1996).
[CrossRef] [PubMed]

Eggleton, B. J.

Eisenberg, H.

A. Sukhorukov, Y. Kivshar, H. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” IEEE J. Quantum Electron. 39(1), 31–50 (2003).
[CrossRef]

Foxon, C.

B. van Wees, H. van Houten, C. Beenakker, J. Williamson, L. Kouwenhoven, D. van der Marel, and C. Foxon, “Quantized conductance of point contacts in a two-dimensional electron gas,” Phys. Rev. Lett. 60(9), 848–850 (1988).
[CrossRef] [PubMed]

Fu, L.

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32(10), 647–649 (1978).
[CrossRef]

Gibbs, H. M.

R. E. Slusher and H. M. Gibbs, “Self-induced transparency in atomic rubidium,” Phys. Rev. A 5(4), 1634–1659 (1972).
[CrossRef]

Giessen, H.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81(19), 4260–4263 (1998).
[CrossRef]

Glenn, W. H.

Golovchenko, E.

E. Golovchenko, E. Dianov, A. Prokhorov, and V. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87–91 (1985).

Gordon, J. P.

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(13), 1095–1098 (1980).
[CrossRef]

Grudinin, A.

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

Grujic, T.

Grün, M.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81(19), 4260–4263 (1998).
[CrossRef]

Haas, S.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81(19), 4260–4263 (1998).
[CrossRef]

Hahn, E. L.

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18(21), 908–911 (1967).
[CrossRef]

Hasegawa, A.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. i. anomalous dispersion,” Appl. Phys. Lett. 23(3), 142–144 (1973).
[CrossRef]

Heebner, J. E.

Hetterich, M.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81(19), 4260–4263 (1998).
[CrossRef]

Hill, K. O.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32(10), 647–649 (1978).
[CrossRef]

Hodel, W.

H. Weber and W. Hodel, “Propagation of subpicosecond pulses and soliton formation in an optical fiber,” Phys. Scr. T23, 200–205 (1988).
[CrossRef]

Ibsen, M.

Johnson, D. C.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32(10), 647–649 (1978).
[CrossRef]

Joseph, R. I.

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62(15), 1746–1749 (1989).
[CrossRef] [PubMed]

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32(10), 647–649 (1978).
[CrossRef]

Kivshar, Y.

A. Sukhorukov, Y. Kivshar, H. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” IEEE J. Quantum Electron. 39(1), 31–50 (2003).
[CrossRef]

Kivshar, Y. S.

E. A. Ostrovskaya and Y. S. Kivshar, “Matter-wave gap solitons in atomic band-gap structures,” Phys. Rev. Lett. 90(16), 160407 (2003).
[CrossRef] [PubMed]

S. F. Mingaleev and Y. S. Kivshar, “Self-trapping and stable localized modes in nonlinear photonic crystals,” Phys. Rev. Lett. 86(24), 5474–5477 (2001).
[CrossRef] [PubMed]

Klingshirn, C.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81(19), 4260–4263 (1998).
[CrossRef]

Knorr, A.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81(19), 4260–4263 (1998).
[CrossRef]

Koch, S. W.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81(19), 4260–4263 (1998).
[CrossRef]

Kogelnik, H.

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

Kouwenhoven, L.

B. van Wees, H. van Houten, C. Beenakker, J. Williamson, L. Kouwenhoven, D. van der Marel, and C. Foxon, “Quantized conductance of point contacts in a two-dimensional electron gas,” Phys. Rev. Lett. 60(9), 848–850 (1988).
[CrossRef] [PubMed]

Krug, P.

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76(10), 1627–1630 (1996).
[CrossRef] [PubMed]

Kuhl, J.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81(19), 4260–4263 (1998).
[CrossRef]

Laming, R. I.

Lamont, M. R. E.

Landauer, R.

R. Landauer, “Spatial variation of currents and fields due to localized scatterers in metallic conduction,” IBM J. Res. Develop. 1(3), 223–231 (1957).
[CrossRef]

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

Leon, J.

J. Leon and A. Spire, “Gap soliton formation by nonlinear supratransmission in bragg media,” Phys. Lett. A 327(5-6), 474–480 (2004).
[CrossRef]

Linden, S.

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81(19), 4260–4263 (1998).
[CrossRef]

Littler, I. C. M.

Liu, A. Q.

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005).
[CrossRef]

Mägi, E. C.

Martijn de Sterke, C.

McCall, S. L.

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18(21), 908–911 (1967).
[CrossRef]

Meltz, G.

Mills, D. L.

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58(2), 160–163 (1987).
[CrossRef] [PubMed]

Mingaleev, S. F.

S. F. Mingaleev and Y. S. Kivshar, “Self-trapping and stable localized modes in nonlinear photonic crystals,” Phys. Rev. Lett. 86(24), 5474–5477 (2001).
[CrossRef] [PubMed]

Mok, J. T.

Mollenauer, L. F.

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(13), 1095–1098 (1980).
[CrossRef]

Moloney, J. V.

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, and A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34(5), 4442–4444 (1986).
[CrossRef] [PubMed]

Morey, W. W.

Ostrovskaya, E. A.

E. A. Ostrovskaya and Y. S. Kivshar, “Matter-wave gap solitons in atomic band-gap structures,” Phys. Rev. Lett. 90(16), 160407 (2003).
[CrossRef] [PubMed]

Payne, D.

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

Pereira, S.

Prokhorov, A.

E. Golovchenko, E. Dianov, A. Prokhorov, and V. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87–91 (1985).

Richardson, D.

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

Richardson, D. J.

Roelens, M. A. F.

Seaton, C. T.

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, and A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34(5), 4442–4444 (1986).
[CrossRef] [PubMed]

Serkin, V.

E. Golovchenko, E. Dianov, A. Prokhorov, and V. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87–91 (1985).

Shank, C. V.

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

Silberberg, Y.

A. Sukhorukov, Y. Kivshar, H. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” IEEE J. Quantum Electron. 39(1), 31–50 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

Sipe, J.

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76(10), 1627–1630 (1996).
[CrossRef] [PubMed]

C. Martijn de Sterke and J. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42(1), 550–555 (1990).
[CrossRef] [PubMed]

Sipe, J. E.

Slusher, R.

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76(10), 1627–1630 (1996).
[CrossRef] [PubMed]

Slusher, R. E.

Spire, A.

J. Leon and A. Spire, “Gap soliton formation by nonlinear supratransmission in bragg media,” Phys. Lett. A 327(5-6), 474–480 (2004).
[CrossRef]

Stegeman, G. I.

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, and A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34(5), 4442–4444 (1986).
[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(13), 1095–1098 (1980).
[CrossRef]

Sukhorukov, A.

A. Sukhorukov, Y. Kivshar, H. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” IEEE J. Quantum Electron. 39(1), 31–50 (2003).
[CrossRef]

Tang, D. Y.

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005).
[CrossRef]

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. i. anomalous dispersion,” Appl. Phys. Lett. 23(3), 142–144 (1973).
[CrossRef]

Taverner, D.

Tsoy, E.

van der Marel, D.

B. van Wees, H. van Houten, C. Beenakker, J. Williamson, L. Kouwenhoven, D. van der Marel, and C. Foxon, “Quantized conductance of point contacts in a two-dimensional electron gas,” Phys. Rev. Lett. 60(9), 848–850 (1988).
[CrossRef] [PubMed]

van Houten, H.

B. van Wees, H. van Houten, C. Beenakker, J. Williamson, L. Kouwenhoven, D. van der Marel, and C. Foxon, “Quantized conductance of point contacts in a two-dimensional electron gas,” Phys. Rev. Lett. 60(9), 848–850 (1988).
[CrossRef] [PubMed]

van Wees, B.

B. van Wees, H. van Houten, C. Beenakker, J. Williamson, L. Kouwenhoven, D. van der Marel, and C. Foxon, “Quantized conductance of point contacts in a two-dimensional electron gas,” Phys. Rev. Lett. 60(9), 848–850 (1988).
[CrossRef] [PubMed]

Wabnitz, S.

S. Wabnitz, “Pulse self-switching in optical fiber bragg gratings,” Opt. Commun. 114(1-2), 170–180 (1995).
[CrossRef]

A. B. Aceves, C. De Angelis, and S. Wabnitz, “Generation of solitons in a nonlinear periodic medium,” Opt. Lett. 17(22), 1566–1568 (1992).
[CrossRef] [PubMed]

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141(1-2), 37–42 (1989).
[CrossRef]

Weber, H.

H. Weber and W. Hodel, “Propagation of subpicosecond pulses and soliton formation in an optical fiber,” Phys. Scr. T23, 200–205 (1988).
[CrossRef]

Williamson, J.

B. van Wees, H. van Houten, C. Beenakker, J. Williamson, L. Kouwenhoven, D. van der Marel, and C. Foxon, “Quantized conductance of point contacts in a two-dimensional electron gas,” Phys. Rev. Lett. 60(9), 848–850 (1988).
[CrossRef] [PubMed]

Winful, H. G.

J. E. Sipe and H. G. Winful, “Nonlinear Schroedinger solitons in a periodic structure,” Opt. Lett. 13(2), 132–133 (1988).
[CrossRef] [PubMed]

H. G. Winful, “Pulse-compression in optical fiber filters,” Appl. Phys. Lett. 46(6), 527–529 (1985).
[CrossRef]

Wright, E. M.

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, and A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34(5), 4442–4444 (1986).
[CrossRef] [PubMed]

Xie, P.

P. Xie, Z.-Q. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasiperiodic photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(2), 026607 (2003).
[CrossRef] [PubMed]

Yeom, D.-I.

Zhang, X.

P. Xie, Z.-Q. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasiperiodic photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(2), 026607 (2003).
[CrossRef] [PubMed]

Zhang, Z.-Q.

P. Xie, Z.-Q. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasiperiodic photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(2), 026607 (2003).
[CrossRef] [PubMed]

Zhao, B.

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005).
[CrossRef]

Zhao, L. M.

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. i. anomalous dispersion,” Appl. Phys. Lett. 23(3), 142–144 (1973).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32(10), 647–649 (1978).
[CrossRef]

H. G. Winful, “Pulse-compression in optical fiber filters,” Appl. Phys. Lett. 46(6), 527–529 (1985).
[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]

IBM J. Res. Develop. (1)

R. Landauer, “Spatial variation of currents and fields due to localized scatterers in metallic conduction,” IBM J. Res. Develop. 1(3), 223–231 (1957).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Sukhorukov, Y. Kivshar, H. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” IEEE J. Quantum Electron. 39(1), 31–50 (2003).
[CrossRef]

J. Appl. Phys. (1)

H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43(5), 2327–2335 (1972).
[CrossRef]

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

JETP Lett. (1)

E. Golovchenko, E. Dianov, A. Prokhorov, and V. Serkin, “Decay of optical solitons,” JETP Lett. 42, 87–91 (1985).

Nat. Phys. (1)

J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys. 2(11), 775–780 (2006).
[CrossRef]

Nature (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. Wabnitz, “Pulse self-switching in optical fiber bragg gratings,” Opt. Commun. 114(1-2), 170–180 (1995).
[CrossRef]

Opt. Lett. (7)

Phys. Lett. A (2)

J. Leon and A. Spire, “Gap soliton formation by nonlinear supratransmission in bragg media,” Phys. Lett. A 327(5-6), 474–480 (2004).
[CrossRef]

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141(1-2), 37–42 (1989).
[CrossRef]

Phys. Rev. A (4)

C. Martijn de Sterke and J. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42(1), 550–555 (1990).
[CrossRef] [PubMed]

E. M. Wright, G. I. Stegeman, C. T. Seaton, J. V. Moloney, and A. D. Boardman, “Multisoliton emission from a nonlinear waveguide,” Phys. Rev. A 34(5), 4442–4444 (1986).
[CrossRef] [PubMed]

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005).
[CrossRef]

R. E. Slusher and H. M. Gibbs, “Self-induced transparency in atomic rubidium,” Phys. Rev. A 5(4), 1634–1659 (1972).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

P. Xie, Z.-Q. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasiperiodic photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(2), 026607 (2003).
[CrossRef] [PubMed]

Phys. Rev. Lett. (9)

S. F. Mingaleev and Y. S. Kivshar, “Self-trapping and stable localized modes in nonlinear photonic crystals,” Phys. Rev. Lett. 86(24), 5474–5477 (2001).
[CrossRef] [PubMed]

H. Giessen, A. Knorr, S. Haas, S. W. Koch, S. Linden, J. Kuhl, M. Hetterich, M. Grün, and C. Klingshirn, “Self-induced transmission on a free exciton resonance in a semiconductor,” Phys. Rev. Lett. 81(19), 4260–4263 (1998).
[CrossRef]

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18(21), 908–911 (1967).
[CrossRef]

B. van Wees, H. van Houten, C. Beenakker, J. Williamson, L. Kouwenhoven, D. van der Marel, and C. Foxon, “Quantized conductance of point contacts in a two-dimensional electron gas,” Phys. Rev. Lett. 60(9), 848–850 (1988).
[CrossRef] [PubMed]

W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58(2), 160–163 (1987).
[CrossRef] [PubMed]

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76(10), 1627–1630 (1996).
[CrossRef] [PubMed]

E. A. Ostrovskaya and Y. S. Kivshar, “Matter-wave gap solitons in atomic band-gap structures,” Phys. Rev. Lett. 90(16), 160407 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62(15), 1746–1749 (1989).
[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(13), 1095–1098 (1980).
[CrossRef]

Phys. Scr. (1)

H. Weber and W. Hodel, “Propagation of subpicosecond pulses and soliton formation in an optical fiber,” Phys. Scr. T23, 200–205 (1988).
[CrossRef]

Other (4)

C. M. de Sterke, and J. E. Sipe, in Progress in Optics XXXIII (Elsevier, Amsterdam, 1994), vol. XXXIII Chap. III.

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

T. Dauxois, and M. Peyard, Physics of Solitons (Cambrdige University Press, 2006).

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

Supplementary Material (2)

» Media 1: AVI (3761 KB)     
» Media 2: AVI (3087 KB)     

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Figures (7)

Fig. 1
Fig. 1

(a) Effect of a positive Kerr nonlinearity in a simple cw-model on the measurement of the transmission versus detuning (lower scale) and wavelength (upper scale). A fixed laser wavelength, tuned just inside the grating’s upper band edge, is reflected al low intensities and might be expected to be transmitted at high intensities. (b) Schematic of the experimental setup. Laser pulses coupled into the FBG and the transmission is measured with a power meter. Time-resolved transmission is measured with a fast sampling oscilloscope. Longitudinal strain applied to the FBG can be used to tune the grating with respect to the laser.

Fig. 2
Fig. 2

(a) Measured and (b) calculated low- and high-intensity transmission spectra near the upper band edge for different incident pulse energies.

Fig. 4
Fig. 4

(a) Measured, and (b) calculated time resolved transmission spectra near the upper the band edge. Each vertical slice represents the optical power P(t) at the end of the grating for a given detuning. In (b), the calculated transmission spectrum has been overlaid. Input energy E = 2.5 µJ. Different positions on the detuning axes are caused by backlash of the strain stage.

Fig. 3
Fig. 3

Measured time-resolved transmission for different detunings near the upper band edge where gap solitons can form. Input energy E = 2.5 µJ.

Fig. 5
Fig. 5

Calculated transmission curves (output energy vs. input energy) close to the upper band edge for different detunings and grating strengths.

Fig. 6
Fig. 6

(a) Evolution of the normalized soliton area [see Eq. (3)] as a function of the time, for a single transmitted soliton for Ein = 6 µJ (blue, δ = 0.67) and a triplet of transmitted solitons, at the edge of the transition from two to three solitons (red, δ = 0.81). (b) Power distribution inside the FBG for δ = 0.67, t ≈1.2 ns (Media 1). (c) Power distribution inside the FBG for δ = 0.81, t ≈1.0 ns (Media 2).

Fig. 7
Fig. 7

Normalized pulse area F = c n P ( t ) 1 / 2 d t [see Eq. (3)] as a function of the detuning. The pulse area is determined experimentally from the intensity of the light at the end of the FBG. Data is inferred from the measurement presented in Fig. 4 (a).

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

+ i A + z + i n c A + t + δ A + + κ ( z ) A + γ ( | A + | 2 + 2 | A | 2 ) A + = 0 i A z + i n c A t + δ A + κ ( z ) A + + γ ( | A | 2 + 2 | A + | 2 ) A = 0
i u t + 1 2 ω 2 u ξ 2 + A u | u | 2 = 0 ,
F = 0 L P ( z ) d z , F 0 = π 2 / ( 3 κ γ ) ,
E 0 4 n 3 α γ c < 4 n 3 γ c 1.3   μJ .

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