Abstract

We present shape-preserving self-accelerating beams of Maxwell's equations with optical nonlinearities. Such beams are exact solutions to Maxwell's equations with Kerr or saturable nonlinearity. The nonlinearity contributes to self-trapping and causes backscattering. Those effects, together with diffraction effects, work to maintain shape-preserving acceleration of the beam on a circular trajectory. The backscattered beam is found to be a key issue in the dynamics of such highly non-paraxial nonlinear beams. To study that, we develop two new techniques: projection operator separating the forward and backward waves, and reverse simulation. Finally, we discuss the possibility that such beams would reflect themselves through the nonlinear effect, to complete a 'U' shaped trajectory.

© 2012 OSA

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  1. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32(8), 979–981 (2007).
    [CrossRef] [PubMed]
  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]
  3. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
    [CrossRef]
  4. 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]
  5. I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-Accelerating Self-Trapped Optical Beams,” Phys. Rev. Lett.106(21), 213903 (2011).
    [CrossRef] [PubMed]
  6. 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]
  7. R. Bekenstein and M. Segev, “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express19(24), 23706–23715 (2011).
    [CrossRef] [PubMed]
  8. I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental Observation of Self-Accelerating Beams in Quadratic Nonlinear Media,” Phys. Rev. Lett.108(11), 113903 (2012).
    [CrossRef] [PubMed]
  9. 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]
  10. R. Chen, C. Yin, X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A82(4), 043832 (2010).
    [CrossRef]
  11. Y. Fattal, A. Rudnick, and D. M. Marom, “Soliton shedding from Airy pulses in Kerr media,” Opt. Express19(18), 17298–17307 (2011).
    [CrossRef] [PubMed]
  12. Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” to appear in Opt. Lett. (2012).
  13. J. A. Giannini and R. I. Joseph, “The role of the second Painlevé transcendent in nonlinear optics,” Phys. Lett. A141(8-9), 417–419 (1989).
    [CrossRef]
  14. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979).
    [CrossRef]
  15. A. V. Novitsky and D. V. Novitsky, “Nonparaxial Airy beams: role of evanescent waves,” Opt. Lett.34(21), 3430–3432 (2009).
    [CrossRef] [PubMed]
  16. L. Carretero, P. Acebal, S. Blaya, C. García, A. Fimia, R. Madrigal, and A. Murciano, “Nonparaxial diffraction analysis of Airy and SAiry beams,” Opt. Express17(25), 22432–22441 (2009).
    [CrossRef] [PubMed]
  17. A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
    [CrossRef] [PubMed]
  18. 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]
  19. L. Froehly, F. Courvoisier, A. Mathis, M. Jacquot, L. Furfaro, R. Giust, P. A. Lacourt, and J. M. Dudley, “Arbitrary accelerating micron-scale caustic beams in two and three dimensions,” Opt. Express19(17), 16455–16465 (2011).
    [CrossRef] [PubMed]
  20. I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting Accelerating Wave Packets of Maxwell’s Equations,” Phys. Rev. Lett.108(16), 163901 (2012).
    [CrossRef] [PubMed]
  21. F. Courvoisier, A. Mathis, L. Froehly, R. Giust, L. Furfaro, P. A. Lacourt, M. Jacquot, and J. M. Dudley, “Sending femtosecond pulses in circles: highly nonparaxial accelerating beams,” Opt. Lett.37(10), 1736–1738 (2012).
    [CrossRef] [PubMed]
  22. I. Kaminer, R. Bekenstein, and M. Segev, CLEO: QELS-Fundamental Science, OSA Technical Digest (Optical Society of America, 2012), paper QM3E.3. The presentation included experimental results.
  23. This concept of nonlinear accelerating beams of Maxwell's equations was first proposed in Nonlinear Photonics Topical Meeting, paper NTu3C.7, submitted 27/02/2012.
  24. O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear Waves in Subwavelength Waveguide Arrays: Evanescent Bands and the “Phoenix Soliton”,” Phys. Rev. Lett.102(16), 163902 (2009).
    [CrossRef] [PubMed]
  25. M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett.93(15), 153902 (2004).
    [CrossRef] [PubMed]
  26. G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science286(5444), 1518–1523 (1999).
    [CrossRef] [PubMed]
  27. I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, “Causality effects on accelerating light pulses,” Opt. Express19(23), 23132–23139 (2011).
    [CrossRef] [PubMed]
  28. G. Fibich and S. Tsynkov, “High-order two-way artificial boundary conditions for nonlinear wave propagation with backscattering,” J. Comput. Phys.171(2), 632–677 (2001).
    [CrossRef]
  29. G. Fibich, “Small Beam Nonparaxiality Arrests Self-Focusing of Optical Beams,” Phys. Rev. Lett.76(23), 4356–4359 (1996).
    [CrossRef] [PubMed]
  30. M. D. Feit and I. A. Fleck., “Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams,” J. Opt. Soc. Am. B5(3), 633–640 (1988).
    [CrossRef]
  31. H. E. Hemandez-Figueroa, “Nonlinear nonparaxial beam-propagation method,” Electron. Lett.30(4), 352–353 (1994).
    [CrossRef]
  32. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Does the nonlinear Schrödinger equation correctly describe beam propagation?” Opt. Lett.18(6), 411–413 (1993).
    [CrossRef] [PubMed]
  33. P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Propagation properties of non-paraxial spatial solitons,” J. Mod. Opt.47, 1877–1886 (2000).
  34. O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, “Collisions between Optical Spatial Solitons Propagating in Opposite Directions,” Phys. Rev. Lett.89(13), 133901 (2002).
    [CrossRef] [PubMed]

2012

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental Observation of Self-Accelerating Beams in Quadratic Nonlinear Media,” Phys. Rev. Lett.108(11), 113903 (2012).
[CrossRef] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting Accelerating Wave Packets of Maxwell’s Equations,” Phys. Rev. Lett.108(16), 163901 (2012).
[CrossRef] [PubMed]

F. Courvoisier, A. Mathis, L. Froehly, R. Giust, L. Furfaro, P. A. Lacourt, M. Jacquot, and J. M. Dudley, “Sending femtosecond pulses in circles: highly nonparaxial accelerating beams,” Opt. Lett.37(10), 1736–1738 (2012).
[CrossRef] [PubMed]

2011

Y. Fattal, A. Rudnick, and D. M. Marom, “Soliton shedding from Airy pulses in Kerr media,” Opt. Express19(18), 17298–17307 (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. 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]

R. Bekenstein and M. Segev, “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express19(24), 23706–23715 (2011).
[CrossRef] [PubMed]

I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, “Causality effects on accelerating light pulses,” Opt. Express19(23), 23132–23139 (2011).
[CrossRef] [PubMed]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

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]

L. Froehly, F. Courvoisier, A. Mathis, M. Jacquot, L. Furfaro, R. Giust, P. A. Lacourt, and J. M. Dudley, “Arbitrary accelerating micron-scale caustic beams in two and three dimensions,” Opt. Express19(17), 16455–16465 (2011).
[CrossRef] [PubMed]

2010

2009

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. V. Novitsky and D. V. Novitsky, “Nonparaxial Airy beams: role of evanescent waves,” Opt. Lett.34(21), 3430–3432 (2009).
[CrossRef] [PubMed]

L. Carretero, P. Acebal, S. Blaya, C. García, A. Fimia, R. Madrigal, and A. Murciano, “Nonparaxial diffraction analysis of Airy and SAiry beams,” Opt. Express17(25), 22432–22441 (2009).
[CrossRef] [PubMed]

O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear Waves in Subwavelength Waveguide Arrays: Evanescent Bands and the “Phoenix Soliton”,” Phys. Rev. Lett.102(16), 163902 (2009).
[CrossRef] [PubMed]

2008

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

2007

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]

2004

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett.93(15), 153902 (2004).
[CrossRef] [PubMed]

2002

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, “Collisions between Optical Spatial Solitons Propagating in Opposite Directions,” Phys. Rev. Lett.89(13), 133901 (2002).
[CrossRef] [PubMed]

2001

G. Fibich and S. Tsynkov, “High-order two-way artificial boundary conditions for nonlinear wave propagation with backscattering,” J. Comput. Phys.171(2), 632–677 (2001).
[CrossRef]

2000

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Propagation properties of non-paraxial spatial solitons,” J. Mod. Opt.47, 1877–1886 (2000).

1999

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

1996

G. Fibich, “Small Beam Nonparaxiality Arrests Self-Focusing of Optical Beams,” Phys. Rev. Lett.76(23), 4356–4359 (1996).
[CrossRef] [PubMed]

1994

H. E. Hemandez-Figueroa, “Nonlinear nonparaxial beam-propagation method,” Electron. Lett.30(4), 352–353 (1994).
[CrossRef]

1993

1989

J. A. Giannini and R. I. Joseph, “The role of the second Painlevé transcendent in nonlinear optics,” Phys. Lett. A141(8-9), 417–419 (1989).
[CrossRef]

1988

1979

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

Abdollahpour, D.

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]

Acebal, P.

Akhmediev, N.

Ankiewicz, A.

Arie, A.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental Observation of Self-Accelerating Beams in Quadratic Nonlinear Media,” Phys. Rev. Lett.108(11), 113903 (2012).
[CrossRef] [PubMed]

Balazs, N. L.

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

Bartal, G.

O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear Waves in Subwavelength Waveguide Arrays: Evanescent Bands and the “Phoenix Soliton”,” Phys. Rev. Lett.102(16), 163902 (2009).
[CrossRef] [PubMed]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting Accelerating Wave Packets of Maxwell’s Equations,” Phys. Rev. Lett.108(16), 163901 (2012).
[CrossRef] [PubMed]

R. Bekenstein and M. Segev, “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express19(24), 23706–23715 (2011).
[CrossRef] [PubMed]

Berry, M. V.

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

Blaya, S.

Broky, J.

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]

Carmon, T.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, “Collisions between Optical Spatial Solitons Propagating in Opposite Directions,” Phys. Rev. Lett.89(13), 133901 (2002).
[CrossRef] [PubMed]

Carretero, L.

Chamorro-Posada, P.

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Propagation properties of non-paraxial spatial solitons,” J. Mod. Opt.47, 1877–1886 (2000).

Chen, R.

R. Chen, C. Yin, X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A82(4), 043832 (2010).
[CrossRef]

Chen, Z.

Christodoulides, D. N.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-Accelerating Self-Trapped Optical Beams,” Phys. Rev. Lett.106(21), 213903 (2011).
[CrossRef] [PubMed]

I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, “Causality effects on accelerating light pulses,” Opt. Express19(23), 23132–23139 (2011).
[CrossRef] [PubMed]

O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear Waves in Subwavelength Waveguide Arrays: Evanescent Bands and the “Phoenix Soliton”,” Phys. Rev. Lett.102(16), 163902 (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,” Science324(5924), 229–232 (2009).
[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.

R. Chen, C. Yin, X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A82(4), 043832 (2010).
[CrossRef]

Cohen, O.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, “Collisions between Optical Spatial Solitons Propagating in Opposite Directions,” Phys. Rev. Lett.89(13), 133901 (2002).
[CrossRef] [PubMed]

Couairon, A.

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]

Courvoisier, F.

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

Dogariu, A.

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]

Dolev, I.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental Observation of Self-Accelerating Beams in Quadratic Nonlinear Media,” Phys. Rev. Lett.108(11), 113903 (2012).
[CrossRef] [PubMed]

Dubietis, A.

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett.93(15), 153902 (2004).
[CrossRef] [PubMed]

Dudley, J. M.

Faccio, D.

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]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett.93(15), 153902 (2004).
[CrossRef] [PubMed]

Fattal, Y.

Feit, M. D.

Fibich, G.

G. Fibich and S. Tsynkov, “High-order two-way artificial boundary conditions for nonlinear wave propagation with backscattering,” J. Comput. Phys.171(2), 632–677 (2001).
[CrossRef]

G. Fibich, “Small Beam Nonparaxiality Arrests Self-Focusing of Optical Beams,” Phys. Rev. Lett.76(23), 4356–4359 (1996).
[CrossRef] [PubMed]

Fimia, A.

Fleck, I. A.

Fleischer, J. W.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, “Collisions between Optical Spatial Solitons Propagating in Opposite Directions,” Phys. Rev. Lett.89(13), 133901 (2002).
[CrossRef] [PubMed]

Froehly, L.

Furfaro, L.

García, C.

Giannini, J. A.

J. A. Giannini and R. I. Joseph, “The role of the second Painlevé transcendent in nonlinear optics,” Phys. Lett. A141(8-9), 417–419 (1989).
[CrossRef]

Giust, R.

Greenfield, E.

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]

Hemandez-Figueroa, H. E.

H. E. Hemandez-Figueroa, “Nonlinear nonparaxial beam-propagation method,” Electron. Lett.30(4), 352–353 (1994).
[CrossRef]

Hu, Y.

Huang, S.

Jacquot, M.

Janunts, N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

Joseph, R. I.

J. A. Giannini and R. I. Joseph, “The role of the second Painlevé transcendent in nonlinear optics,” Phys. Lett. A141(8-9), 417–419 (1989).
[CrossRef]

Kaminer, I.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental Observation of Self-Accelerating Beams in Quadratic Nonlinear Media,” Phys. Rev. Lett.108(11), 113903 (2012).
[CrossRef] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting Accelerating Wave Packets of Maxwell’s Equations,” Phys. Rev. Lett.108(16), 163901 (2012).
[CrossRef] [PubMed]

I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, “Causality effects on accelerating light pulses,” Opt. Express19(23), 23132–23139 (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]

Kivshar, Y. S.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

Klein, A. E.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

Kolesik, M.

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]

Lacourt, P. A.

Lotti, A.

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]

Lou, C.

Lumer, Y.

Madrigal, R.

Marom, D. M.

Mathis, A.

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

McDonald, G. S.

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Propagation properties of non-paraxial spatial solitons,” J. Mod. Opt.47, 1877–1886 (2000).

Minovich, A.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

Moiseyev, N.

O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear Waves in Subwavelength Waveguide Arrays: Evanescent Bands and the “Phoenix Soliton”,” Phys. Rev. Lett.102(16), 163902 (2009).
[CrossRef] [PubMed]

Moloney, J. V.

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I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting Accelerating Wave Packets of Maxwell’s Equations,” Phys. Rev. Lett.108(16), 163901 (2012).
[CrossRef] [PubMed]

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A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

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P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Propagation properties of non-paraxial spatial solitons,” J. Mod. Opt.47, 1877–1886 (2000).

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O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, “Collisions between Optical Spatial Solitons Propagating in Opposite Directions,” Phys. Rev. Lett.89(13), 133901 (2002).
[CrossRef] [PubMed]

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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]

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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]

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M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett.93(15), 153902 (2004).
[CrossRef] [PubMed]

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O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear Waves in Subwavelength Waveguide Arrays: Evanescent Bands and the “Phoenix Soliton”,” Phys. Rev. Lett.102(16), 163902 (2009).
[CrossRef] [PubMed]

Pertsch, T.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

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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]

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M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett.93(15), 153902 (2004).
[CrossRef] [PubMed]

Raz, O.

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]

Rudnick, A.

Segev, M.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental Observation of Self-Accelerating Beams in Quadratic Nonlinear Media,” Phys. Rev. Lett.108(11), 113903 (2012).
[CrossRef] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting Accelerating Wave Packets of Maxwell’s Equations,” Phys. Rev. Lett.108(16), 163901 (2012).
[CrossRef] [PubMed]

I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, “Causality effects on accelerating light pulses,” Opt. Express19(23), 23132–23139 (2011).
[CrossRef] [PubMed]

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]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-Accelerating Self-Trapped Optical Beams,” Phys. Rev. Lett.106(21), 213903 (2011).
[CrossRef] [PubMed]

R. Bekenstein and M. Segev, “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express19(24), 23706–23715 (2011).
[CrossRef] [PubMed]

O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear Waves in Subwavelength Waveguide Arrays: Evanescent Bands and the “Phoenix Soliton”,” Phys. Rev. Lett.102(16), 163902 (2009).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, “Collisions between Optical Spatial Solitons Propagating in Opposite Directions,” Phys. Rev. Lett.89(13), 133901 (2002).
[CrossRef] [PubMed]

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

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I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental Observation of Self-Accelerating Beams in Quadratic Nonlinear Media,” Phys. Rev. Lett.108(11), 113903 (2012).
[CrossRef] [PubMed]

Siviloglou, G. A.

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]

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]

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Stegeman, G. I.

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

Trapani, P.

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett.93(15), 153902 (2004).
[CrossRef] [PubMed]

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G. Fibich and S. Tsynkov, “High-order two-way artificial boundary conditions for nonlinear wave propagation with backscattering,” J. Comput. Phys.171(2), 632–677 (2001).
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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]

Uzdin, R.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, “Collisions between Optical Spatial Solitons Propagating in Opposite Directions,” Phys. Rev. Lett.89(13), 133901 (2002).
[CrossRef] [PubMed]

Walasik, W.

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]

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R. Chen, C. Yin, X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A82(4), 043832 (2010).
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J. Mod. Opt.

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, “Propagation properties of non-paraxial spatial solitons,” J. Mod. Opt.47, 1877–1886 (2000).

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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]

R. Chen, C. Yin, X. Chu, and H. Wang, “Effect of Kerr nonlinearity on an Airy beam,” Phys. Rev. A82(4), 043832 (2010).
[CrossRef]

Phys. Rev. Lett.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

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]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-Accelerating Self-Trapped Optical Beams,” Phys. Rev. Lett.106(21), 213903 (2011).
[CrossRef] [PubMed]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental Observation of Self-Accelerating Beams in Quadratic Nonlinear Media,” Phys. Rev. Lett.108(11), 113903 (2012).
[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]

O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear Waves in Subwavelength Waveguide Arrays: Evanescent Bands and the “Phoenix Soliton”,” Phys. Rev. Lett.102(16), 163902 (2009).
[CrossRef] [PubMed]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett.93(15), 153902 (2004).
[CrossRef] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting Accelerating Wave Packets of Maxwell’s Equations,” Phys. Rev. Lett.108(16), 163901 (2012).
[CrossRef] [PubMed]

G. Fibich, “Small Beam Nonparaxiality Arrests Self-Focusing of Optical Beams,” Phys. Rev. Lett.76(23), 4356–4359 (1996).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, “Collisions between Optical Spatial Solitons Propagating in Opposite Directions,” Phys. Rev. Lett.89(13), 133901 (2002).
[CrossRef] [PubMed]

Science

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

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]

Other

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” to appear in Opt. Lett. (2012).

I. Kaminer, R. Bekenstein, and M. Segev, CLEO: QELS-Fundamental Science, OSA Technical Digest (Optical Society of America, 2012), paper QM3E.3. The presentation included experimental results.

This concept of nonlinear accelerating beams of Maxwell's equations was first proposed in Nonlinear Photonics Topical Meeting, paper NTu3C.7, submitted 27/02/2012.

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Figures (2)

Fig. 1
Fig. 1

Profile of the electric field (a) and amplitude of the Fourier transform (b) of a nonlinear (linear) accelerating beam in blue (red dashed). The edges of the evanescent regime are marked by a black dashed rectangle in (b), emphasizing in the enlarged window that the peak of the Fourier amplitude is at kx>k0. These beams have angular momentum of α = 60 for the nonlinear (blue) and α = 45 for the red (linear). The nonlinear change in the permittivity is εmean = 0.05, on the background of εmax = 1.3; with λ = 1μm.

Fig. 2
Fig. 2

(a) The full self-accelerating self-trapped beam composed of both the forward and backward wavepackets, shows perfect shape-preserving bending of the nonlinear beam. (b) The self-accelerating nonlinear beam for physical boundary conditions at z = 0, showing an approximately shape-preserving bending. (c) The forward propagating part. (d) The backward propagating part. The arrows indicate the direction of propagation. Both panels have α = 160 and εmax = 0.1. All scales are in microns; λ = 1μm.

Equations (3)

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

E xx + E zz + k 0 2 E+ k 0 2 ε( I )E=0.
d 2 d r 2 U+ 1 r d dr U α 2 r 2 U+ k 0 2 U+ k 0 2 ε( U )U=0.
E( x,z z 0 )= i c i + u i ( x ) e i λ i z + i c i u i ( x ) e i λ i z .

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