## Self-accelerating optical beams in highly nonlocal nonlinear media |

Optics Express, Vol. 19, Issue 24, pp. 23706-23715 (2011)

http://dx.doi.org/10.1364/OE.19.023706

Acrobat PDF (1379 KB)

### Abstract

We find self-accelerating beams in highly nonlocal nonlinear optical media, and show that their propagation dynamics is strongly affected by boundary conditions. Specifically for the thermal optical nonlinearity, the boundary conditions have a strong impact on the beam trajectory: they can increase the acceleration during propagation, or even cause beam bending in a direction opposite to the initial trajectory. Under strong self-focusing, the accelerating beam decomposes into a localized self-trapped beam propagating on an oscillatory trajectory and a second beam which accelerates in a different direction. We augment this study by investigating the effects caused by a finite aperture and by a nonlinear range of a finite extent.

© 2011 OSA

## 1. Introduction

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

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

3. 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]

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

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. 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]

7. 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]

7. 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]

7. 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]

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

11. J. A. Giannini and R. I. Joseph, “The role of the second Painleve transcendent in nonlinear optics,” Phys. Lett. A **141**(8-9), 417–419 (1989). [CrossRef]

12. 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]

13. A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A **84**(2), 021807 (2011). [CrossRef]

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

14. F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. **13**(8), 284–286 (1968). [CrossRef]

15. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. **95**(21), 213904 (2005). [CrossRef] [PubMed]

16. E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A **48**(1), 611–622 (1993). [CrossRef] [PubMed]

17. C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. **91**(7), 073901 (2003). [CrossRef] [PubMed]

18. E. A. Ultanir, D. Michaelis, F. Lederer, and G. I. Stegeman, “Stable spatial solitons in semiconductor optical amplifiers,” Opt. Lett. **28**(4), 251–253 (2003). [CrossRef] [PubMed]

15. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. **95**(21), 213904 (2005). [CrossRef] [PubMed]

19. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Boundary force effects exerted on solitons in highly nonlinear media,” Opt. Lett. **32**(2), 154–156 (2007). [CrossRef] [PubMed]

20. C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. **2**(11), 769–774 (2006). [CrossRef]

## 2. Accelerating self-trapped (propagation-invariant) solutions

15. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. **95**(21), 213904 (2005). [CrossRef] [PubMed]

19. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Boundary force effects exerted on solitons in highly nonlinear media,” Opt. Lett. **32**(2), 154–156 (2007). [CrossRef] [PubMed]

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

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

21. E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. **106**(21), 213902 (2011). [CrossRef] [PubMed]

## 3. Propagation dynamics of accelerating self-trapped beams

**95**(21), 213904 (2005). [CrossRef] [PubMed]

19. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Boundary force effects exerted on solitons in highly nonlinear media,” Opt. Lett. **32**(2), 154–156 (2007). [CrossRef] [PubMed]

20. C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. **2**(11), 769–774 (2006). [CrossRef]

22. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Nonlocal surface-wave solitons,” Phys. Rev. Lett. **98**(21), 213901 (2007). [CrossRef] [PubMed]

**32**(2), 154–156 (2007). [CrossRef] [PubMed]

**95**(21), 213904 (2005). [CrossRef] [PubMed]

**32**(2), 154–156 (2007). [CrossRef] [PubMed]

20. C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. **2**(11), 769–774 (2006). [CrossRef]

22. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Nonlocal surface-wave solitons,” Phys. Rev. Lett. **98**(21), 213901 (2007). [CrossRef] [PubMed]

**32**(2), 154–156 (2007). [CrossRef] [PubMed]

21. E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. **106**(21), 213902 (2011). [CrossRef] [PubMed]

23. G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science **286**(5444), 1518–1523 (1999). [CrossRef] [PubMed]

**32**(2), 154–156 (2007). [CrossRef] [PubMed]

## 4. Accelerating self-trapped beams carrying finite power

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

3. 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]

**106**(21), 213903 (2011). [CrossRef] [PubMed]

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

3. 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]

**106**(21), 213903 (2011). [CrossRef] [PubMed]

*a*in Fig. 1).

## 5. Accelerating self-trapped beams in nonlinear media with a finite range of nonlocality

16. E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A **48**(1), 611–622 (1993). [CrossRef] [PubMed]

17. C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. **91**(7), 073901 (2003). [CrossRef] [PubMed]

18. E. A. Ultanir, D. Michaelis, F. Lederer, and G. I. Stegeman, “Stable spatial solitons in semiconductor optical amplifiers,” Opt. Lett. **28**(4), 251–253 (2003). [CrossRef] [PubMed]

24. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. **68**(7), 923–926 (1992). [CrossRef] [PubMed]

26. W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. **80**(15), 3240–3243 (1998). [CrossRef]

27. J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **66**(6), 066615 (2002). [CrossRef] [PubMed]

**106**(21), 213903 (2011). [CrossRef] [PubMed]

## 6. Conclusion

## Acknowledgments

## References and links

1. | M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. |

2. | G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. |

3. | G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. |

4. | J. Baumgartl, M. Mazilu, and K. Dholakia, “Optical mediated particle clearing using Airy wavepackets,” Nat. Photonics |

5. | P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science |

6. | A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics |

7. | D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. |

8. | Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett. |

9. | R.-P. Chen, C.-F. Yin, X.-X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A |

10. | I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett. |

11. | J. A. Giannini and R. I. Joseph, “The role of the second Painleve transcendent in nonlinear optics,” Phys. Lett. A |

12. | Y. Fattal, A. Rudnick, and D. M. Marom, “Soliton shedding from Airy pulses in Kerr media,” Opt. Express |

13. | A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A |

14. | F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett. |

15. | C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. |

16. | E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A |

17. | C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. |

18. | E. A. Ultanir, D. Michaelis, F. Lederer, and G. I. Stegeman, “Stable spatial solitons in semiconductor optical amplifiers,” Opt. Lett. |

19. | B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Boundary force effects exerted on solitons in highly nonlinear media,” Opt. Lett. |

20. | C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys. |

21. | E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. |

22. | B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Nonlocal surface-wave solitons,” Phys. Rev. Lett. |

23. | G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science |

24. | M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. |

25. | M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. |

26. | W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. |

27. | J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

**OCIS Codes**

(190.0190) Nonlinear optics : Nonlinear optics

(190.6135) Nonlinear optics : Spatial solitons

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: September 9, 2011

Revised Manuscript: October 23, 2011

Manuscript Accepted: October 24, 2011

Published: November 7, 2011

**Citation**

Rivka Bekenstein and Mordechai Segev, "Self-accelerating optical beams in highly nonlocal nonlinear media," Opt. Express **19**, 23706-23715 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-23706

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### References

- M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979). [CrossRef]
- 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]
- J. Baumgartl, M. Mazilu, and K. Dholakia, “Optical mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008). [CrossRef]
- P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009). [CrossRef] [PubMed]
- A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics4(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]
- Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, “Persistence and breakdown of Airy beams driven by an initial nonlinearity,” Opt. Lett.35(23), 3952–3954 (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. A82, 043832 (2010).
- I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106(21), 213903 (2011). [CrossRef] [PubMed]
- J. A. Giannini and R. I. Joseph, “The role of the second Painleve transcendent in nonlinear optics,” Phys. Lett. A141(8-9), 417–419 (1989). [CrossRef]
- Y. Fattal, A. Rudnick, and D. M. Marom, “Soliton shedding from Airy pulses in Kerr media,” Opt. Express19(18), 17298–17307 (2011). [CrossRef] [PubMed]
- A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011). [CrossRef]
- F. W. Dabby and J. R. Whinnery, “Thermal self-focusing of laser beams in lead glasses,” Appl. Phys. Lett.13(8), 284–286 (1968). [CrossRef]
- C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett.95(21), 213904 (2005). [CrossRef] [PubMed]
- E. Braun, L. P. Faucheux, and A. Libchaber, “Strong self-focusing in nematic liquid crystals,” Phys. Rev. A48(1), 611–622 (1993). [CrossRef] [PubMed]
- C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett.91(7), 073901 (2003). [CrossRef] [PubMed]
- E. A. Ultanir, D. Michaelis, F. Lederer, and G. I. Stegeman, “Stable spatial solitons in semiconductor optical amplifiers,” Opt. Lett.28(4), 251–253 (2003). [CrossRef] [PubMed]
- B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Boundary force effects exerted on solitons in highly nonlinear media,” Opt. Lett.32(2), 154–156 (2007). [CrossRef] [PubMed]
- C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nat. Phys.2(11), 769–774 (2006). [CrossRef]
- E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett.106(21), 213902 (2011). [CrossRef] [PubMed]
- B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, “Nonlocal surface-wave solitons,” Phys. Rev. Lett.98(21), 213901 (2007). [CrossRef] [PubMed]
- G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science286(5444), 1518–1523 (1999). [CrossRef] [PubMed]
- M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett.68(7), 923–926 (1992). [CrossRef] [PubMed]
- M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett.73(24), 3211–3214 (1994). [CrossRef] [PubMed]
- W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett.80(15), 3240–3243 (1998). [CrossRef]
- J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.66(6), 066615 (2002). [CrossRef] [PubMed]

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