Abstract

We investigate numerically the interactions of two in-phase and out-of-phase Airy beams and nonlinear (NL) accelerating beams in Kerr and saturable NL media, in one transverse dimension. We find that bound and unbound soliton pairs, as well as single solitons, can form in such interactions. If the interval between two incident beams is large relative to the width of their first lobes, the generated soliton pairs just propagate individually and do not interact. However, if the interval is comparable to the widths of the maximum lobes, the pairs interact and display varied behavior. In the in-phase case, they attract each other and exhibit stable bound, oscillating, and unbound states, after shedding some radiation initially. In the out-of-phase case, they repel each other and, after an initial interaction, fly away as individual solitons. While the incident beams display acceleration, the solitons or soliton pairs generated from those beams do not.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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M. A. Bandres and B. M. Rodrguez-Lara, New J. Phys. 15, 013054 (2013).
[CrossRef]

M. A. Bandres, M. A. Alonso, I. Kaminer, and M. Segev, Opt. Express 21, 13917 (2013).
[CrossRef]

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, Phys. Rev. A 87, 043637 (2013).
[CrossRef]

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, Opt. Lett. 38, 2416 (2013).
[CrossRef]

2012 (7)

M. A. Alonso and M. A. Bandres, Opt. Lett. 37, 5175 (2012).
[CrossRef]

I. Kaminer, J. Nemirovsky, and M. Segev, Opt. Express 20, 18827 (2012).
[CrossRef]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
[CrossRef]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

2011 (4)

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Y. Fattal, A. Rudnick, and D. M. Marom, Opt. Express 19, 17298 (2011).
[CrossRef]

A. Rudnick and D. M. Marom, Opt. Express 19, 25570 (2011).
[CrossRef]

2010 (4)

2009 (3)

2008 (2)

2007 (2)

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

2003 (1)

Z. Bouchal, Czech J. Phys. 53, 537 (2003).
[CrossRef]

1987 (1)

1979 (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Abdollahpour, D.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Aleahmad, P.

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

Alonso, M. A.

Arie, A.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Balazs, N. L.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Bandres, M. A.

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Berry, M. V.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Bouchal, Z.

Z. Bouchal, Czech J. Phys. 53, 537 (2003).
[CrossRef]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Cannan, D.

Chen, Z.

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Christodoulides, D. N.

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, Opt. Lett. 35, 4045 (2010).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Cottrell, D. M.

Couairon, A.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Davis, J. A.

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dolev, I.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

Durnin, J.

Efremidis, N. K.

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, Phys. Rev. A 87, 043637 (2013).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, Opt. Lett. 35, 4045 (2010).
[CrossRef]

Ellenbogen, T.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Faccio, D.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Fattal, Y.

Fuerschbach, K.

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Hazard, T. M.

Hu, Y.

Kaminer, I.

M. A. Bandres, M. A. Alonso, I. Kaminer, and M. Segev, Opt. Express 21, 13917 (2013).
[CrossRef]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

I. Kaminer, J. Nemirovsky, and M. Segev, Opt. Express 20, 18827 (2012).
[CrossRef]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

Królikowski, W.

Li, P.

Li, T.

Liu, S.

Lotti, A.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Lu, K.

Marom, D. M.

Maucher, F.

Mills, M. S.

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

Miri, M.-A.

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

Morandotti, R.

Nemirovsky, J.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

I. Kaminer, J. Nemirovsky, and M. Segev, Opt. Express 20, 18827 (2012).
[CrossRef]

Paltoglou, V.

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, Phys. Rev. A 87, 043637 (2013).
[CrossRef]

Panagiotopoulos, P.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Papazoglou, D. G.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Pour, A. G.

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Rodrguez-Lara, B. M.

M. A. Bandres and B. M. Rodrguez-Lara, New J. Phys. 15, 013054 (2013).
[CrossRef]

Rolland, J. P.

Rudnick, A.

Salandrino, A.

Segev, M.

M. A. Bandres, M. A. Alonso, I. Kaminer, and M. Segev, Opt. Express 21, 13917 (2013).
[CrossRef]

I. Kaminer, J. Nemirovsky, and M. Segev, Opt. Express 20, 18827 (2012).
[CrossRef]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

Shapira, A.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

Siviloglou, G. A.

Skupin, S.

Thompson, K. P.

Tzortzakis, S.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Vo, S.

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

von Klitzing, W.

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, Phys. Rev. A 87, 043637 (2013).
[CrossRef]

Wang, M.

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Zhang, P.

Zhang, X.

Zhang, Y.

Zhao, J.

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Czech J. Phys. (1)

Z. Bouchal, Czech J. Phys. 53, 537 (2003).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nat. Photonics (2)

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

New J. Phys. (1)

M. A. Bandres and B. M. Rodrguez-Lara, New J. Phys. 15, 013054 (2013).
[CrossRef]

Opt. Express (5)

Opt. Lett. (9)

Phys. Rev. A (3)

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, Phys. Rev. A 87, 043637 (2013).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

Phys. Rev. Lett. (5)

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Soliton formation in the interaction of two (a1)–(h1) in-phase and (a2)–(h2) out-of-phase incident Airy beams, in Kerr medium; (i1), (i2) maximum intensities of beams in (b)–(f) versus propagation distance.

Fig. 2.
Fig. 2.

Intensities of two interacting in-phase (top row) and out-of-phase (bottom row) Airy beams in the medium with saturable nonlinearity.

Fig. 3.
Fig. 3.

(a) Nonlinear accelerating modes, according to Eq. (6). Kerr and saturable cases share the left and bottom axes, while the strong Kerr case uses the top and right ones. (b) Propagating Kerr and (c) truncated Kerr solutions, obtained for α=10; (d) propagating strong Kerr and (e) truncated strong Kerr solutions, obtained for α=108; (f1)–(i1) interacting in-phase truncated Kerr solutions, shifted by B=2, 1, 0, and 1, respectively; (f2)–(i2) same as (f1)–(i1), but for the out-of-phase case; (f3)–(i3) same as (f1)–(i1), but for the in-phase truncated strong Kerr solutions; (f4)–(i4) same as (f3)–(i3), but for the out-of-phase case.

Equations (6)

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

iψz+122ψx2+δnψ=0,
ψ(x,z)=Ai(xz2/4+iaz)exp[i(6a2z12iax+6iaz2+6xzz3)/12],
ψ(x)=A·Ai[±(xB)]exp[±a(xB)],
ψ(x)=A{Ai[(xB)]exp[a(xB)]+exp(ilπ)Ai[(x+B)]exp[a(x+B)]},
iψziz2ψx+122ψx2+δnψ=0.
2ux2+2δnuxu=0.

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