Abstract

We investigate and analyze temporal soliton interactions with a dispersive truncated Airy pulse traveling in a nonlinear fiber at the same center wavelength (or frequency), via split step Fourier numerical simulation. Truncated Airy pulses, which remain self-similar during propagation and have a ballistic trajectory in the retarded time frame, can interact with a nearby soliton by its accelerating wavefront property. We find by tracking the fundamental parameters of the emergent soliton—time position, amplitude, phase and frequency—that they alter due to the primary collision with the Airy main lobe and the continuous co-propagation with the dispersed Airy background. These interactions are found to resemble coherent interactions when the initial time separation is small and incoherent at others. This is due to spectral content repositioning within the Airy pulse, changing the nature of interaction from coherent to incoherent. Following the collision, the soliton intensity oscillates as it relaxes. The initial parameters of the Airy pulse such as initial phase, amplitude and time position are varied to better understand the nature of the interactions.

© 2011 OSA

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    [CrossRef]
  3. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
    [CrossRef] [PubMed]
  6. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
    [CrossRef] [PubMed]
  7. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
    [CrossRef] [PubMed]
  8. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
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  9. A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  13. G. P. Agrawal and M. J. Potasek, “Nonlinear pulse distortion in single-mode optical fibers at the zero-dispersion wavelength,” Phys. Rev. A 33(3), 1765–1776 (1986).
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    [CrossRef] [PubMed]
  15. D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
    [CrossRef] [PubMed]
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  30. 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(3), 362–367 (1991).
    [CrossRef]
  31. A. Hasegawa and Y. Kodama, “Amplification and reshaping of optical solitons in a glass fiber-I,” Opt. Lett. 7(6), 285–287 (1982).
    [CrossRef] [PubMed]
  32. H. A. Haus, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, “Interaction of Solitons with Sinusoidal Wave Packet,” IEEE J. Quantum Electron. 32(6), 917–924 (1996).
    [CrossRef]
  33. H. A. Haus, W. S. Wong, and F. I. Khatri, “Continuum generation by perturbation of Soliton,” J. Opt. Soc. Am. B 14(2), 304–313 (1997).
    [CrossRef]
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  35. H. J. Shin, “Soliton scattering from a finite cnoidal wave train in a fiber,” Phys. Rev. E 63(2), 026606 (2001).
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    [CrossRef] [PubMed]
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  38. E. A. Kuznetson and A. V. Mikhailov, “Relaxation oscillations of solitons,” Pis'ma Z. Eksp. Teor. Fiz. 60, 466–470 (1994).
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  42. T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
    [CrossRef] [PubMed]
  43. C. Yeh and L. Bergman, “Pulse shepherding in nonlinear fiber optics,” J. Appl. Phys. 80(6), 3174–3178 (1996).
    [CrossRef]

2011 (4)

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[CrossRef] [PubMed]

A. Bahabad, M. M. Murnane, and H. C. Kapteyn, “Manipulating nonlinear optical processes with acceperating light beams,” Phys. Rev. A 84(3), 033819 (2011).
[CrossRef]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[CrossRef] [PubMed]

Y. Fattal, A. Rudnick, and D. M. Marom, “Soliton shedding from Airy pulses in Kerr media,” Opt. Express 19(18), 17298–17307 (2011).
[CrossRef] [PubMed]

2010 (6)

I. Dolev, T. Ellenbogen, and A. Arie, “Switching the acceleration direction of Airy beams by a nonlinear optical process,” Opt. Lett. 35(10), 1581–1583 (2010).
[CrossRef] [PubMed]

A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
[CrossRef] [PubMed]

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photon. (2010).

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[CrossRef] [PubMed]

R.-P. Chen, C.-F. Yin, X.-X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A 82(4), 043832 (2010).
[CrossRef]

2009 (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

2008 (4)

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[CrossRef]

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[CrossRef] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[CrossRef] [PubMed]

2007 (2)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[CrossRef] [PubMed]

2003 (2)

2001 (1)

H. J. Shin, “Soliton scattering from a finite cnoidal wave train in a fiber,” Phys. Rev. E 63(2), 026606 (2001).
[CrossRef] [PubMed]

1999 (3)

A. V. Buryak and V. V. Steblina, “Soliton collisions in bulk quadratic media: comprehensive analytical and numerical study,” J. Opt. Soc. Am. B 16(2), 245–255 (1999).
[CrossRef]

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

Q. H. Park and H. J. Shin, “Parametric Control of Soliton Light Traffic by cw Traffic Light,” Phys. Rev. Lett. 82(22), 4432–4435 (1999).
[CrossRef]

1997 (1)

1996 (3)

C. Yeh and L. Bergman, “Pulse shepherding in nonlinear fiber optics,” J. Appl. Phys. 80(6), 3174–3178 (1996).
[CrossRef]

H. A. Haus, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, “Interaction of Solitons with Sinusoidal Wave Packet,” IEEE J. Quantum Electron. 32(6), 917–924 (1996).
[CrossRef]

H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68(2), 423–444 (1996).
[CrossRef]

1995 (1)

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87(1-4), 201–215 (1995).
[CrossRef]

1994 (1)

E. A. Kuznetson and A. V. Mikhailov, “Relaxation oscillations of solitons,” Pis'ma Z. Eksp. Teor. Fiz. 60, 466–470 (1994).

1991 (1)

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(3), 362–367 (1991).
[CrossRef]

1987 (3)

1986 (1)

G. P. Agrawal and M. J. Potasek, “Nonlinear pulse distortion in single-mode optical fibers at the zero-dispersion wavelength,” Phys. Rev. A 33(3), 1765–1776 (1986).
[CrossRef] [PubMed]

1983 (1)

1982 (1)

1979 (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[CrossRef]

1974 (1)

J. Satsuma and N. Yajima, “Initial Value Problems of One-Dimensional Self-Modulation of Nonlinear Waves in Dispersive Media,” Suppl. Prog. Theor. Phys. 55,284-306 (1974).

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 (1)

V. E. Zakharov and A. B. Shabat, “Exact Theory Of Two-Dimensional Self-Focusing and One-Dimensional Self-Modulation Of Waves in Nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[CrossRef] [PubMed]

Agrawal, G. P.

G. P. Agrawal and M. J. Potasek, “Nonlinear pulse distortion in single-mode optical fibers at the zero-dispersion wavelength,” Phys. Rev. A 33(3), 1765–1776 (1986).
[CrossRef] [PubMed]

Arie, A.

Bahabad, A.

A. Bahabad, M. M. Murnane, and H. C. Kapteyn, “Manipulating nonlinear optical processes with acceperating light beams,” Phys. Rev. A 84(3), 033819 (2011).
[CrossRef]

Balazs, N. L.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[CrossRef]

Barthélémy, A.

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[CrossRef]

Bergman, L.

C. Yeh and L. Bergman, “Pulse shepherding in nonlinear fiber optics,” J. Appl. Phys. 80(6), 3174–3178 (1996).
[CrossRef]

Berry, M. V.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[CrossRef]

Broky, J.

Buryak, A. V.

Chen, R.-P.

R.-P. Chen, C.-F. Yin, X.-X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A 82(4), 043832 (2010).
[CrossRef]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

Christodoulides, D. N.

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[CrossRef] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[CrossRef] [PubMed]

A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
[CrossRef] [PubMed]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[CrossRef] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[CrossRef] [PubMed]

Chu, X.-X.

R.-P. Chen, C.-F. Yin, X.-X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A 82(4), 043832 (2010).
[CrossRef]

Couderc, V.

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[CrossRef]

Dogariu, A.

Dolev, I.

Durnin, J.

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Efremidis, N. K.

Ellenbogen, T.

Evangelides, S. G.

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(3), 362–367 (1991).
[CrossRef]

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photon. (2010).

Fattal, Y.

Gordon, J. P.

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(3), 362–367 (1991).
[CrossRef]

J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8(11), 596–598 (1983).
[CrossRef] [PubMed]

Hasegawa, A.

A. Hasegawa and Y. Kodama, “Amplification and reshaping of optical solitons in a glass fiber-I,” Opt. Lett. 7(6), 285–287 (1982).
[CrossRef] [PubMed]

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]

Haus, H. A.

H. A. Haus, W. S. Wong, and F. I. Khatri, “Continuum generation by perturbation of Soliton,” J. Opt. Soc. Am. B 14(2), 304–313 (1997).
[CrossRef]

H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68(2), 423–444 (1996).
[CrossRef]

H. A. Haus, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, “Interaction of Solitons with Sinusoidal Wave Packet,” IEEE J. Quantum Electron. 32(6), 917–924 (1996).
[CrossRef]

Hill, S.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[CrossRef] [PubMed]

Ippen, E. P.

H. A. Haus, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, “Interaction of Solitons with Sinusoidal Wave Packet,” IEEE J. Quantum Electron. 32(6), 917–924 (1996).
[CrossRef]

Kaminer, I.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[CrossRef] [PubMed]

Kapteyn, H. C.

A. Bahabad, M. M. Murnane, and H. C. Kapteyn, “Manipulating nonlinear optical processes with acceperating light beams,” Phys. Rev. A 84(3), 033819 (2011).
[CrossRef]

Khatri, F. I.

H. A. Haus, W. S. Wong, and F. I. Khatri, “Continuum generation by perturbation of Soliton,” J. Opt. Soc. Am. B 14(2), 304–313 (1997).
[CrossRef]

H. A. Haus, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, “Interaction of Solitons with Sinusoidal Wave Packet,” IEEE J. Quantum Electron. 32(6), 917–924 (1996).
[CrossRef]

Kodama, Y.

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

König, F.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[CrossRef] [PubMed]

Kuklewicz, C.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[CrossRef] [PubMed]

Kuznetson, E. A.

E. A. Kuznetson and A. V. Mikhailov, “Relaxation oscillations of solitons,” Pis'ma Z. Eksp. Teor. Fiz. 60, 466–470 (1994).

Kuznetsov, E. A.

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87(1-4), 201–215 (1995).
[CrossRef]

Leonhardt, U.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[CrossRef] [PubMed]

Marom, D. M.

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Mikhailov, A. V.

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87(1-4), 201–215 (1995).
[CrossRef]

E. A. Kuznetson and A. V. Mikhailov, “Relaxation oscillations of solitons,” Pis'ma Z. Eksp. Teor. Fiz. 60, 466–470 (1994).

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(3), 362–367 (1991).
[CrossRef]

F. M. Mitschke and L. F. Mollenauer, “Experimental observation of interaction forces between solitons in optical fibers,” Opt. Lett. 12(5), 355–357 (1987).
[CrossRef] [PubMed]

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Murnane, M. M.

A. Bahabad, M. M. Murnane, and H. C. Kapteyn, “Manipulating nonlinear optical processes with acceperating light beams,” Phys. Rev. A 84(3), 033819 (2011).
[CrossRef]

Papazoglou, D. G.

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[CrossRef] [PubMed]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[CrossRef] [PubMed]

Park, Q. H.

Q. H. Park and H. J. Shin, “Parametric Control of Soliton Light Traffic by cw Traffic Light,” Phys. Rev. Lett. 82(22), 4432–4435 (1999).
[CrossRef]

Philbin, T. G.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[CrossRef] [PubMed]

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Potasek, M. J.

G. P. Agrawal and M. J. Potasek, “Nonlinear pulse distortion in single-mode optical fibers at the zero-dispersion wavelength,” Phys. Rev. A 33(3), 1765–1776 (1986).
[CrossRef] [PubMed]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

Robertson, S.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[CrossRef] [PubMed]

Rohrbach, A.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photon. (2010).

Rudnick, A.

Salandrino, A.

Satsuma, J.

J. Satsuma and N. Yajima, “Initial Value Problems of One-Dimensional Self-Modulation of Nonlinear Waves in Dispersive Media,” Suppl. Prog. Theor. Phys. 55,284-306 (1974).

Segev, M.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[CrossRef] [PubMed]

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, “Exact Theory Of Two-Dimensional Self-Focusing and One-Dimensional Self-Modulation Of Waves in Nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

Shimokhin, I. A.

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87(1-4), 201–215 (1995).
[CrossRef]

Shin, H. J.

H. J. Shin, “Interaction of a soliton with a continuous wave packet,” Phys. Rev. E 67(1), 017602 (2003).
[CrossRef] [PubMed]

H. J. Shin, “Soliton scattering from a finite cnoidal wave train in a fiber,” Phys. Rev. E 63(2), 026606 (2001).
[CrossRef] [PubMed]

Q. H. Park and H. J. Shin, “Parametric Control of Soliton Light Traffic by cw Traffic Light,” Phys. Rev. Lett. 82(22), 4432–4435 (1999).
[CrossRef]

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photon. (2010).

Simos, C.

Siviloglou, G. A.

Steblina, V. V.

Stegeman, G. I.

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[CrossRef] [PubMed]

Tamura, K. R.

H. A. Haus, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, “Interaction of Solitons with Sinusoidal Wave Packet,” IEEE J. Quantum Electron. 32(6), 917–924 (1996).
[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]

Tzortzakis, S.

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[CrossRef] [PubMed]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[CrossRef] [PubMed]

Wang, H.

R.-P. Chen, C.-F. Yin, X.-X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A 82(4), 043832 (2010).
[CrossRef]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

Wong, W. S.

H. A. Haus, W. S. Wong, and F. I. Khatri, “Continuum generation by perturbation of Soliton,” J. Opt. Soc. Am. B 14(2), 304–313 (1997).
[CrossRef]

H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68(2), 423–444 (1996).
[CrossRef]

H. A. Haus, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, “Interaction of Solitons with Sinusoidal Wave Packet,” IEEE J. Quantum Electron. 32(6), 917–924 (1996).
[CrossRef]

Yajima, N.

J. Satsuma and N. Yajima, “Initial Value Problems of One-Dimensional Self-Modulation of Nonlinear Waves in Dispersive Media,” Suppl. Prog. Theor. Phys. 55,284-306 (1974).

Yeh, C.

C. Yeh and L. Bergman, “Pulse shepherding in nonlinear fiber optics,” J. Appl. Phys. 80(6), 3174–3178 (1996).
[CrossRef]

Yin, C.-F.

R.-P. Chen, C.-F. Yin, X.-X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A 82(4), 043832 (2010).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, “Exact Theory Of Two-Dimensional Self-Focusing and One-Dimensional Self-Modulation Of Waves in Nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[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. 23(3), 142–144 (1973).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, “Interaction of Solitons with Sinusoidal Wave Packet,” IEEE J. Quantum Electron. 32(6), 917–924 (1996).
[CrossRef]

J. Appl. Phys. (1)

C. Yeh and L. Bergman, “Pulse shepherding in nonlinear fiber optics,” J. Appl. Phys. 80(6), 3174–3178 (1996).
[CrossRef]

J. Lightwave Technol. (1)

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(3), 362–367 (1991).
[CrossRef]

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

J. Opt. Soc. Am. B (3)

Nat. Photon. (1)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photon. (2010).

Nat. Photonics (2)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (8)

Phys. Rev. A (3)

G. P. Agrawal and M. J. Potasek, “Nonlinear pulse distortion in single-mode optical fibers at the zero-dispersion wavelength,” Phys. Rev. A 33(3), 1765–1776 (1986).
[CrossRef] [PubMed]

R.-P. Chen, C.-F. Yin, X.-X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A 82(4), 043832 (2010).
[CrossRef]

A. Bahabad, M. M. Murnane, and H. C. Kapteyn, “Manipulating nonlinear optical processes with acceperating light beams,” Phys. Rev. A 84(3), 033819 (2011).
[CrossRef]

Phys. Rev. E (2)

H. J. Shin, “Soliton scattering from a finite cnoidal wave train in a fiber,” Phys. Rev. E 63(2), 026606 (2001).
[CrossRef] [PubMed]

H. J. Shin, “Interaction of a soliton with a continuous wave packet,” Phys. Rev. E 67(1), 017602 (2003).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

Q. H. Park and H. J. Shin, “Parametric Control of Soliton Light Traffic by cw Traffic Light,” Phys. Rev. Lett. 82(22), 4432–4435 (1999).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. 106(21), 213903 (2011).
[CrossRef] [PubMed]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[CrossRef] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[CrossRef] [PubMed]

Physica D (1)

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87(1-4), 201–215 (1995).
[CrossRef]

Pis'ma Z. Eksp. Teor. Fiz. (1)

E. A. Kuznetson and A. V. Mikhailov, “Relaxation oscillations of solitons,” Pis'ma Z. Eksp. Teor. Fiz. 60, 466–470 (1994).

Rev. Mod. Phys. (1)

H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68(2), 423–444 (1996).
[CrossRef]

Science (3)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[CrossRef] [PubMed]

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

V. E. Zakharov and A. B. Shabat, “Exact Theory Of Two-Dimensional Self-Focusing and One-Dimensional Self-Modulation Of Waves in Nonlinear media,” Sov. Phys. JETP 34, 62–69 (1972).

Suppl. Prog. Theor. Phys. (1)

J. Satsuma and N. Yajima, “Initial Value Problems of One-Dimensional Self-Modulation of Nonlinear Waves in Dispersive Media,” Suppl. Prog. Theor. Phys. 55,284-306 (1974).

Other (3)

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).

J. R. Taylor, Optical Solitons Theory and Experiment (Cambridge Univ. Press, 1992).

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

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Figures (10)

Fig. 1
Fig. 1

Intensity plots for nonlinear propagation of (a) a weak truncated Airy pulse (a = 0.005), and (b) a normalized Soliton both to 20 Ld. Insets show launched intensity distributions.

Fig. 2
Fig. 2

Exemplary initial launch conditions composed of both the Airy (a = 0.005, 8% intensity at collision, τ0 = −6) and the normalized Soliton. (a) linear scale, (b) dB scale (the variation in dip values is an artifact of the sampling).

Fig. 3
Fig. 3

Airy-Soliton interactions with an initial separation of 10 and intensity ratio of 8% at collision for two phases. (a) θ = −π, (b) θ = 0

Fig. 4
Fig. 4

Airy-Soliton interaction with τ0 = −6 and 8% intensity ratio showing a permanent frequency change when (a) θ = −π/2, and (b) θ = π/2 over 157 Ld units (100 soliton periods).

Fig. 5
Fig. 5

Spectrogram of the Airy pulse at three selected distances for two initial separations; upper row: τ0 = −6, lower row: τ0 = −10. Left column: launch condition, center column: at collision distance (5.29 Ld units and 6.63, respectively), right column: at distance where Airy wavefront is at a temporal shift of twice the initial time separation (7.49 Ld units and 9.38, respectively). Green ellipse denotes the Soliton extent over time and frequency.

Fig. 6
Fig. 6

Soliton intensity oscillations. (a) Intensity oscillation (intensity ratio of 8% and τ0 = −6). Also shown envelope fit of the form 1/ z , (b) Mean intensity of the oscillations with a sinusoidal fit, (c) dependence with respect to the Airy's initial phase for all the time separations (intensity ratio of 8%), (d) Mean intensity for all separations with at 8% intensity ratio for the θ = 0, (with a second order polynomial fit; behavior predominantly linear) .

Fig. 7
Fig. 7

Soliton time shift for all initial separations with an 8% intensity ratio for selected phases. (a) τ0 = −6, (b) τ0 = −8, (c) t0 = −10. Note that the scale of the time shift is not identical in all three cases.

Fig. 8
Fig. 8

(a) Soliton frequency change with respect to amplitude at θ = π/2, (b) Sinusoidal fit with respect to Airy phase for amplitudes with τ0 = −6 of the frequency change.

Fig. 9
Fig. 9

Estimated time shift form, (a) Time shift with respect to Airy's initial amplitude for all initial time separations (θ = 0), Time shift with respect to Airy's initial phase and amplitude with τ0 = −10 and a sinusoidal fit profile .

Fig. 10
Fig. 10

Phase difference along the Airy propagation for select Airy initial phases with an intensity ratio of 8% (a) τ0 = −6, (b) τ0 = −8, (c) τ0 = −10.

Equations (5)

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

i u ξ + 1 2 2 u τ 2 +|u | 2 u=0
u A ( ξ,τ )=Airy[ τ ( ξ 2 ) 2 iaξ ]exp[ aτ a ξ 2 2 ]exp[ i( + ξ 3 12 ( a 2 +τ )ξ 2 ) ]
u S ( ξ,τ )=sech(τ)exp( iξ/2 )
u(ξ=0,τ)=sech( τ )+rAiry(τ τ 0 )exp(a( τ τ 0 ))exp( iθ )
ξ= 4( τ Soliton τ 0 + τ peak offset )

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