Abstract

We simulate and analyze the propagation of truncated temporal Airy pulses in a single mode fiber in the presence of self-phase modulation and anomalous dispersion as a function of the launched Airy power and truncation coefficient. Soliton pulse shedding is observed, where the emergent soliton parameters depend on the launched Airy pulse characteristics. The Soliton temporal position shifts to earlier times with higher launched powers due to an earlier shedding event and with greater energy in the Airy tail due to collisions with the accelerating lobes. In spite of the Airy energy loss to the shed Soliton, the Airy pulse continues to exhibit the unique property of acceleration in time and the main lobe recovers from the energy loss (healing property of Airy waveforms).

© 2011 OSA

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  1. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
    [CrossRef]
  2. 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]
  3. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
    [CrossRef]
  4. 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]
  5. 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]
  6. P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of femtosecond laser Airy beams in water,” Phys. Rev. Lett. 103(12), 123902 (2009).
    [CrossRef] [PubMed]
  7. 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]
  8. 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]
  9. C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with self-healing Airy pulses,” in CLEO:2011—Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPC9.
  10. 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), 043832–043835 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. H. A. Haus, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, “Interaction of soliton with sinusoidal wave packet,” IEEE J. Quantum Electron. 32(6), 917–924 (1996).
    [CrossRef]
  16. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).
  17. 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]

2010 (4)

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. 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), 043832–043835 (2010).
[CrossRef]

2009 (2)

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]

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of femtosecond laser Airy beams in water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[CrossRef] [PubMed]

2008 (3)

1996 (2)

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

N. Belanger and P. A. Belanger, “Bright solitons on a cw background,” Opt. Commun. 124(3-4), 301–308 (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]

1993 (1)

1982 (1)

1979 (1)

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

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]

Arie, A.

Balazs, N. L.

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

Baumgartl, J.

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

Belanger, N.

N. Belanger and P. A. Belanger, “Bright solitons on a cw background,” Opt. Commun. 124(3-4), 301–308 (1996).
[CrossRef]

Belanger, P. A.

N. Belanger and P. A. Belanger, “Bright solitons on a cw background,” Opt. Commun. 124(3-4), 301–308 (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.

Chbat, M. W.

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), 043832–043835 (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.

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]

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), 043832–043835 (2010).
[CrossRef]

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.

Ellenbogen, T.

Gordon, J. P.

Hasegawa, A.

Haus, H. A.

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

Ippen, E. P.

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

Islam, M. N.

Khatri, F. I.

H. A. Haus, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, “Interaction of soliton 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]

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of femtosecond laser Airy beams in water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[CrossRef] [PubMed]

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]

Mazilu, M.

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

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]

Moloney, J.

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of femtosecond laser Airy beams in water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[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]

Papazoglou, D. G.

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]

Polynkin, P.

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of femtosecond laser Airy beams in water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[CrossRef] [PubMed]

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]

Prucnal, P. R.

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]

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]

Siviloglou, G. A.

Soccolich, C. E.

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 soliton with sinusoidal wave packet,” IEEE J. Quantum Electron. 32(6), 917–924 (1996).
[CrossRef]

Tzortzakis, 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]

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), 043832–043835 (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, F. I. Khatri, W. S. Wong, E. P. Ippen, and K. R. Tamura, “Interaction of soliton with sinusoidal wave packet,” IEEE J. Quantum Electron. 32(6), 917–924 (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), 043832–043835 (2010).
[CrossRef]

Am. J. Phys. (1)

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

IEEE J. Quantum Electron. (1)

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

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

Nat. Photonics (2)

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

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]

Opt. Commun. (1)

N. Belanger and P. A. Belanger, “Bright solitons on a cw background,” Opt. Commun. 124(3-4), 301–308 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

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), 043832–043835 (2010).
[CrossRef]

Phys. Rev. Lett. (2)

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of femtosecond laser Airy beams in water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[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]

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]

Science (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]

Other (2)

C. Ament, P. Polynkin, and J. V. Moloney, “Supercontinuum generation with self-healing Airy pulses,” in CLEO:2011—Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPC9.

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

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Figures (12)

Fig. 1
Fig. 1

(a) Intensity distribution as a function of time and propagation distance for truncated Airy pulse in the linear regime (or low launch power). (b) Launched Airy pulse in time (blue solid curve), compared to a soliton pulse (red dashed curve).

Fig. 2
Fig. 2

Intensity distributions as a function of time and propagation distance in the nonlinear propagation regime for: (a) R = 0.8, (b) R = 1.2, and (c) R = 2.

Fig. 3
Fig. 3

(a) Oscillations of soliton width for different launched peak power, (b) soliton oscillations length of period as a function of launched peak power, (c) soliton oscillations modulation depth as a function of launched peak power.

Fig. 4
Fig. 4

(a) Soliton peak time position along propagation distance, (b) mean soliton peak time position as a function of launched power. Note that Airy peak time position at launch is at t = −1. (c) soliton peak phase oscillations along propagation distance for select launched powers.

Fig. 5
Fig. 5

– Airy accelerating tail trajectories in time-distance space(blue) and in intensity-distance space (green) for (a) R = 1, (b) R = 1.3 and (c) R = 2.

Fig. 6
Fig. 6

(a) Airy tail relative energy for the linear and the nonlinear cases, (b) soliton relative energy, (c) soliton relative energy as function of launched power.

Fig. 7
Fig. 7

(a) Launched Airy amplitude for several truncation values, (b)-(c) Intensity distributions as a function of time and propagation distance for: (b) a = 0.01, (c) a = 0.09.

Fig. 8
Fig. 8

Effect of different launched truncation values on oscillations of (a) soliton width and (b) soliton peak phase, (c) soliton peak time position as function of truncation coefficient. Note that Airy peak time position at launch is truncation value dependent, as evidenced by the dashed red line.

Fig. 9
Fig. 9

Airy accelerating wavefront trajectories in time-distance space (blue) and in intensity-distance space (green) for (a) a = 0.01, (b)a = 0.04 and (c)a = 0.08.

Fig. 10
Fig. 10

Examples of energy evolution along propagation distance of (a) the relative energy of the emergent soliton (the soliton energy itself is hardly dependent on truncation coefficient) and (b) accelerating wavefront.

Fig. 11
Fig. 11

(a) Schematic illustration of the sources of temporal shift of the emergent Soliton. (b) Distribution of Soliton mean time position as a function of truncation coefficient and launched power in our investigation range.

Fig. 12
Fig. 12

Intensity distributions as a function of time and propagation distance for R = 4, showing multiple soliton shedding at high launched peak powers.

Equations (5)

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i A z = β 2 2 2 A T 2 ,
i A z = β 2 2 2 A T 2 γ | A | 2 A
P 0 T 0 2 = | β 2 | γ .
i A z = sgn ( β 2 ) 1 2 2 A T 2 | A | 2 A ,
A ( T , z = 0 ) = R K p ( a ) Ai ( T ) Exp ( a T )

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