Abstract

We study optical rogue waves (RWs) in a nonlinear graded-index waveguide with variable coefficients. An exact RW solution on Gaussian background beam is presented, in contrast to the previous studies about RWs, on plane wave background. It is shown that the characteristics of RWs are maintained on Gaussian background beam and that the beam’s width is even a bit smaller than the RWs scale. These results may raise the possibility of related experiments and potential applications in nonlinear optics.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Akhmediev and E. Pelinovsky, Eur. Phys. J. Spec. Top. 185, 1 (2010).
    [CrossRef]
  2. M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, Phys. Rep. 528, 47 (2013).
    [CrossRef]
  3. C. Kharif and E. Pelinovsky, Eur. J. Mech. B/Fluids 22, 603 (2003).
    [CrossRef]
  4. A. R. Osborne, Nonlinear Ocean Waves (Academic, 2009).
  5. E. Pelinovsky and C. Kharif, Extreme Ocean Waves (Springer, 2008).
  6. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
    [CrossRef]
  7. B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
    [CrossRef]
  8. A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, Phys. Rev. Lett. 106, 204502 (2011).
    [CrossRef]
  9. H. Bailung, S. K. Sharma, and Y. Nakamura, Phys. Rev. Lett. 107, 255005 (2011).
    [CrossRef]
  10. A. R. Osborne, Mar. Struct. 14, 275 (2001).
  11. N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
    [CrossRef]
  12. J. M. Dudley, G. Genty, and B. J. Eggleton, Opt. Express 16, 3644 (2008).
    [CrossRef]
  13. J. Fatome, B. Kibler, and C. Finot, Opt. Lett. 38, 1663 (2013).
    [CrossRef]
  14. Yu. V. Bludov, V. V. Konotop, and N. Akhmediev, Opt. Lett. 34, 3015 (2009).
    [CrossRef]
  15. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. E 80, 026601 (2009).
    [CrossRef]
  16. N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 541 (2011).
    [CrossRef]
  17. Y. Ohta and J. Yang, Proc. J. Soc. A 468, 1716 (2012).
    [CrossRef]
  18. B. L. Guo, L. M. Ling, and Q. P. Liu, Phys. Rev. E 85, 026607 (2012).
    [CrossRef]
  19. D. H. Peregrine, J. Aust. Math. Soc. Ser. B 25, 16 (1983).
    [CrossRef]
  20. J. S. He, H. R. Zhang, L. H. Wang, K. Porsezian, and A. S. Fokas, Phys. Rev. E 87, 052914 (2013).
    [CrossRef]
  21. L. C. Zhao, Ann. Phys. 329, 73 (2013).
    [CrossRef]
  22. P. Dubard, P. Gaillard, C. Klein, and V. B. Matveev, Eur. J. Phys. Spec. Top. 185, 247 (2010).
    [CrossRef]
  23. N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, J. Opt. 15, 060201 (2013).
    [CrossRef]
  24. Yu. S. Kivshar and B. L. Davies, Phys. Rep. 298, 81 (1998).
    [CrossRef]
  25. V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, Phys. Rev. Lett. 98, 074102 (2007).
    [CrossRef]
  26. S. A. Ponomarenko and G. P. Agrawal, Opt. Lett. 32, 1659 (2007).
    [CrossRef]
  27. J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and V. V. Konotop, Phys. Rev. Lett. 100, 164102 (2008).
    [CrossRef]
  28. G. Y. Yang, L. Li, and S. T. Jia, Phys. Rev. E 85, 046608 (2012).
    [CrossRef]
  29. J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
    [CrossRef]
  30. B. L. Guo and L. M. Ling, Chin. Phys. Lett. 28, 110202 (2011).
    [CrossRef]
  31. L. C. Zhao and J. Liu, J. Opt. Soc. Am. B 29, 3119 (2012).
    [CrossRef]
  32. F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
    [CrossRef]
  33. L. C. Zhao and J. Liu, Phys. Rev. E 87, 013201 (2013).
    [CrossRef]
  34. F. Baronio, M. Conforti, A. Degasperis, and S. Lombardo, Phys. Rev. Lett. 111, 114101 (2013).
    [CrossRef]
  35. C. Liu, Z. Y. Yang, L. C. Zhao, W. L. Yang, and R. H. Yue, Chin. Phys. Lett. 30, 040304 (2013).
    [CrossRef]

2013

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, Phys. Rep. 528, 47 (2013).
[CrossRef]

J. S. He, H. R. Zhang, L. H. Wang, K. Porsezian, and A. S. Fokas, Phys. Rev. E 87, 052914 (2013).
[CrossRef]

L. C. Zhao, Ann. Phys. 329, 73 (2013).
[CrossRef]

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, J. Opt. 15, 060201 (2013).
[CrossRef]

L. C. Zhao and J. Liu, Phys. Rev. E 87, 013201 (2013).
[CrossRef]

F. Baronio, M. Conforti, A. Degasperis, and S. Lombardo, Phys. Rev. Lett. 111, 114101 (2013).
[CrossRef]

C. Liu, Z. Y. Yang, L. C. Zhao, W. L. Yang, and R. H. Yue, Chin. Phys. Lett. 30, 040304 (2013).
[CrossRef]

J. Fatome, B. Kibler, and C. Finot, Opt. Lett. 38, 1663 (2013).
[CrossRef]

2012

L. C. Zhao and J. Liu, J. Opt. Soc. Am. B 29, 3119 (2012).
[CrossRef]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
[CrossRef]

G. Y. Yang, L. Li, and S. T. Jia, Phys. Rev. E 85, 046608 (2012).
[CrossRef]

Y. Ohta and J. Yang, Proc. J. Soc. A 468, 1716 (2012).
[CrossRef]

B. L. Guo, L. M. Ling, and Q. P. Liu, Phys. Rev. E 85, 026607 (2012).
[CrossRef]

2011

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 541 (2011).
[CrossRef]

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, Phys. Rev. Lett. 106, 204502 (2011).
[CrossRef]

H. Bailung, S. K. Sharma, and Y. Nakamura, Phys. Rev. Lett. 107, 255005 (2011).
[CrossRef]

B. L. Guo and L. M. Ling, Chin. Phys. Lett. 28, 110202 (2011).
[CrossRef]

2010

N. Akhmediev and E. Pelinovsky, Eur. Phys. J. Spec. Top. 185, 1 (2010).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

P. Dubard, P. Gaillard, C. Klein, and V. B. Matveev, Eur. J. Phys. Spec. Top. 185, 247 (2010).
[CrossRef]

2009

N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. E 80, 026601 (2009).
[CrossRef]

Yu. V. Bludov, V. V. Konotop, and N. Akhmediev, Opt. Lett. 34, 3015 (2009).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

2008

J. M. Dudley, G. Genty, and B. J. Eggleton, Opt. Express 16, 3644 (2008).
[CrossRef]

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and V. V. Konotop, Phys. Rev. Lett. 100, 164102 (2008).
[CrossRef]

2007

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, Phys. Rev. Lett. 98, 074102 (2007).
[CrossRef]

S. A. Ponomarenko and G. P. Agrawal, Opt. Lett. 32, 1659 (2007).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

2003

C. Kharif and E. Pelinovsky, Eur. J. Mech. B/Fluids 22, 603 (2003).
[CrossRef]

2001

A. R. Osborne, Mar. Struct. 14, 275 (2001).

1998

Yu. S. Kivshar and B. L. Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

1983

D. H. Peregrine, J. Aust. Math. Soc. Ser. B 25, 16 (1983).
[CrossRef]

Agrawal, G. P.

Akhmediev, N.

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, J. Opt. 15, 060201 (2013).
[CrossRef]

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, Phys. Rev. Lett. 106, 204502 (2011).
[CrossRef]

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 541 (2011).
[CrossRef]

N. Akhmediev and E. Pelinovsky, Eur. Phys. J. Spec. Top. 185, 1 (2010).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
[CrossRef]

Yu. V. Bludov, V. V. Konotop, and N. Akhmediev, Opt. Lett. 34, 3015 (2009).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. E 80, 026601 (2009).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

Ankiewicz, A.

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 541 (2011).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. E 80, 026601 (2009).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
[CrossRef]

Arecchi, F. T.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, Phys. Rep. 528, 47 (2013).
[CrossRef]

Bailung, H.

H. Bailung, S. K. Sharma, and Y. Nakamura, Phys. Rev. Lett. 107, 255005 (2011).
[CrossRef]

Baronio, F.

F. Baronio, M. Conforti, A. Degasperis, and S. Lombardo, Phys. Rev. Lett. 111, 114101 (2013).
[CrossRef]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
[CrossRef]

Belmonte-Beitia, J.

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and V. V. Konotop, Phys. Rev. Lett. 100, 164102 (2008).
[CrossRef]

Belyaeva, T. L.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, Phys. Rev. Lett. 98, 074102 (2007).
[CrossRef]

Bludov, Yu. V.

Bortolozzo, U.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, Phys. Rep. 528, 47 (2013).
[CrossRef]

Chabchoub, A.

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, Phys. Rev. Lett. 106, 204502 (2011).
[CrossRef]

Conforti, M.

F. Baronio, M. Conforti, A. Degasperis, and S. Lombardo, Phys. Rev. Lett. 111, 114101 (2013).
[CrossRef]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
[CrossRef]

Davies, B. L.

Yu. S. Kivshar and B. L. Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

Degasperis, A.

F. Baronio, M. Conforti, A. Degasperis, and S. Lombardo, Phys. Rev. Lett. 111, 114101 (2013).
[CrossRef]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
[CrossRef]

Dias, F.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

Dubard, P.

P. Dubard, P. Gaillard, C. Klein, and V. B. Matveev, Eur. J. Phys. Spec. Top. 185, 247 (2010).
[CrossRef]

Dudley, J. M.

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, J. Opt. 15, 060201 (2013).
[CrossRef]

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 541 (2011).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

J. M. Dudley, G. Genty, and B. J. Eggleton, Opt. Express 16, 3644 (2008).
[CrossRef]

Eggleton, B. J.

Fatome, J.

J. Fatome, B. Kibler, and C. Finot, Opt. Lett. 38, 1663 (2013).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Finot, C.

J. Fatome, B. Kibler, and C. Finot, Opt. Lett. 38, 1663 (2013).
[CrossRef]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Fokas, A. S.

J. S. He, H. R. Zhang, L. H. Wang, K. Porsezian, and A. S. Fokas, Phys. Rev. E 87, 052914 (2013).
[CrossRef]

Gaillard, P.

P. Dubard, P. Gaillard, C. Klein, and V. B. Matveev, Eur. J. Phys. Spec. Top. 185, 247 (2010).
[CrossRef]

Genty, G.

Guo, B. L.

B. L. Guo, L. M. Ling, and Q. P. Liu, Phys. Rev. E 85, 026607 (2012).
[CrossRef]

B. L. Guo and L. M. Ling, Chin. Phys. Lett. 28, 110202 (2011).
[CrossRef]

Hasegawa, A.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, Phys. Rev. Lett. 98, 074102 (2007).
[CrossRef]

He, J. S.

J. S. He, H. R. Zhang, L. H. Wang, K. Porsezian, and A. S. Fokas, Phys. Rev. E 87, 052914 (2013).
[CrossRef]

Hoffmann, N. P.

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, Phys. Rev. Lett. 106, 204502 (2011).
[CrossRef]

Jalali, B.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Jia, S. T.

G. Y. Yang, L. Li, and S. T. Jia, Phys. Rev. E 85, 046608 (2012).
[CrossRef]

Kharif, C.

C. Kharif and E. Pelinovsky, Eur. J. Mech. B/Fluids 22, 603 (2003).
[CrossRef]

E. Pelinovsky and C. Kharif, Extreme Ocean Waves (Springer, 2008).

Kibler, B.

Kivshar, Yu. S.

Yu. S. Kivshar and B. L. Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

Klein, C.

P. Dubard, P. Gaillard, C. Klein, and V. B. Matveev, Eur. J. Phys. Spec. Top. 185, 247 (2010).
[CrossRef]

Konotop, V. V.

Yu. V. Bludov, V. V. Konotop, and N. Akhmediev, Opt. Lett. 34, 3015 (2009).
[CrossRef]

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and V. V. Konotop, Phys. Rev. Lett. 100, 164102 (2008).
[CrossRef]

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Li, L.

G. Y. Yang, L. Li, and S. T. Jia, Phys. Rev. E 85, 046608 (2012).
[CrossRef]

Ling, L. M.

B. L. Guo, L. M. Ling, and Q. P. Liu, Phys. Rev. E 85, 026607 (2012).
[CrossRef]

B. L. Guo and L. M. Ling, Chin. Phys. Lett. 28, 110202 (2011).
[CrossRef]

Liu, C.

C. Liu, Z. Y. Yang, L. C. Zhao, W. L. Yang, and R. H. Yue, Chin. Phys. Lett. 30, 040304 (2013).
[CrossRef]

Liu, J.

L. C. Zhao and J. Liu, Phys. Rev. E 87, 013201 (2013).
[CrossRef]

L. C. Zhao and J. Liu, J. Opt. Soc. Am. B 29, 3119 (2012).
[CrossRef]

Liu, Q. P.

B. L. Guo, L. M. Ling, and Q. P. Liu, Phys. Rev. E 85, 026607 (2012).
[CrossRef]

Lombardo, S.

F. Baronio, M. Conforti, A. Degasperis, and S. Lombardo, Phys. Rev. Lett. 111, 114101 (2013).
[CrossRef]

Matveev, V. B.

P. Dubard, P. Gaillard, C. Klein, and V. B. Matveev, Eur. J. Phys. Spec. Top. 185, 247 (2010).
[CrossRef]

Millot, G.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Montina, A.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, Phys. Rep. 528, 47 (2013).
[CrossRef]

Nakamura, Y.

H. Bailung, S. K. Sharma, and Y. Nakamura, Phys. Rev. Lett. 107, 255005 (2011).
[CrossRef]

Ohta, Y.

Y. Ohta and J. Yang, Proc. J. Soc. A 468, 1716 (2012).
[CrossRef]

Onorato, M.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, Phys. Rep. 528, 47 (2013).
[CrossRef]

Osborne, A. R.

A. R. Osborne, Mar. Struct. 14, 275 (2001).

A. R. Osborne, Nonlinear Ocean Waves (Academic, 2009).

Pelinovsky, E.

N. Akhmediev and E. Pelinovsky, Eur. Phys. J. Spec. Top. 185, 1 (2010).
[CrossRef]

C. Kharif and E. Pelinovsky, Eur. J. Mech. B/Fluids 22, 603 (2003).
[CrossRef]

E. Pelinovsky and C. Kharif, Extreme Ocean Waves (Springer, 2008).

Peregrine, D. H.

D. H. Peregrine, J. Aust. Math. Soc. Ser. B 25, 16 (1983).
[CrossRef]

Pérez-García, V. M.

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and V. V. Konotop, Phys. Rev. Lett. 100, 164102 (2008).
[CrossRef]

Ponomarenko, S. A.

Porsezian, K.

J. S. He, H. R. Zhang, L. H. Wang, K. Porsezian, and A. S. Fokas, Phys. Rev. E 87, 052914 (2013).
[CrossRef]

Residori, S.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, Phys. Rep. 528, 47 (2013).
[CrossRef]

Ropers, C.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Serkin, V. N.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, Phys. Rev. Lett. 98, 074102 (2007).
[CrossRef]

Sharma, S. K.

H. Bailung, S. K. Sharma, and Y. Nakamura, Phys. Rev. Lett. 107, 255005 (2011).
[CrossRef]

Solli, D. R.

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, J. Opt. 15, 060201 (2013).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Soto-Crespo, J. M.

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 541 (2011).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. E 80, 026601 (2009).
[CrossRef]

Taki, M.

N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
[CrossRef]

Turitsyn, S. K.

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, J. Opt. 15, 060201 (2013).
[CrossRef]

Vekslerchik, V.

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and V. V. Konotop, Phys. Rev. Lett. 100, 164102 (2008).
[CrossRef]

Wabnitz, S.

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
[CrossRef]

Wang, L. H.

J. S. He, H. R. Zhang, L. H. Wang, K. Porsezian, and A. S. Fokas, Phys. Rev. E 87, 052914 (2013).
[CrossRef]

Yang, G. Y.

G. Y. Yang, L. Li, and S. T. Jia, Phys. Rev. E 85, 046608 (2012).
[CrossRef]

Yang, J.

Y. Ohta and J. Yang, Proc. J. Soc. A 468, 1716 (2012).
[CrossRef]

Yang, W. L.

C. Liu, Z. Y. Yang, L. C. Zhao, W. L. Yang, and R. H. Yue, Chin. Phys. Lett. 30, 040304 (2013).
[CrossRef]

Yang, Z. Y.

C. Liu, Z. Y. Yang, L. C. Zhao, W. L. Yang, and R. H. Yue, Chin. Phys. Lett. 30, 040304 (2013).
[CrossRef]

Yue, R. H.

C. Liu, Z. Y. Yang, L. C. Zhao, W. L. Yang, and R. H. Yue, Chin. Phys. Lett. 30, 040304 (2013).
[CrossRef]

Zhang, H. R.

J. S. He, H. R. Zhang, L. H. Wang, K. Porsezian, and A. S. Fokas, Phys. Rev. E 87, 052914 (2013).
[CrossRef]

Zhao, L. C.

C. Liu, Z. Y. Yang, L. C. Zhao, W. L. Yang, and R. H. Yue, Chin. Phys. Lett. 30, 040304 (2013).
[CrossRef]

L. C. Zhao and J. Liu, Phys. Rev. E 87, 013201 (2013).
[CrossRef]

L. C. Zhao, Ann. Phys. 329, 73 (2013).
[CrossRef]

L. C. Zhao and J. Liu, J. Opt. Soc. Am. B 29, 3119 (2012).
[CrossRef]

Ann. Phys.

L. C. Zhao, Ann. Phys. 329, 73 (2013).
[CrossRef]

Chin. Phys. Lett.

B. L. Guo and L. M. Ling, Chin. Phys. Lett. 28, 110202 (2011).
[CrossRef]

C. Liu, Z. Y. Yang, L. C. Zhao, W. L. Yang, and R. H. Yue, Chin. Phys. Lett. 30, 040304 (2013).
[CrossRef]

Eur. J. Mech. B/Fluids

C. Kharif and E. Pelinovsky, Eur. J. Mech. B/Fluids 22, 603 (2003).
[CrossRef]

Eur. J. Phys. Spec. Top.

P. Dubard, P. Gaillard, C. Klein, and V. B. Matveev, Eur. J. Phys. Spec. Top. 185, 247 (2010).
[CrossRef]

Eur. Phys. J. Spec. Top.

N. Akhmediev and E. Pelinovsky, Eur. Phys. J. Spec. Top. 185, 1 (2010).
[CrossRef]

J. Aust. Math. Soc. Ser. B

D. H. Peregrine, J. Aust. Math. Soc. Ser. B 25, 16 (1983).
[CrossRef]

J. Opt.

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, J. Opt. 15, 060201 (2013).
[CrossRef]

J. Opt. Soc. Am. B

Mar. Struct.

A. R. Osborne, Mar. Struct. 14, 275 (2001).

Nat. Phys.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
[CrossRef]

Nature

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, and J. M. Dudley, Phys. Lett. A 375, 541 (2011).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
[CrossRef]

Phys. Rep.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, Phys. Rep. 528, 47 (2013).
[CrossRef]

Yu. S. Kivshar and B. L. Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

Phys. Rev. E

B. L. Guo, L. M. Ling, and Q. P. Liu, Phys. Rev. E 85, 026607 (2012).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. E 80, 026601 (2009).
[CrossRef]

L. C. Zhao and J. Liu, Phys. Rev. E 87, 013201 (2013).
[CrossRef]

J. S. He, H. R. Zhang, L. H. Wang, K. Porsezian, and A. S. Fokas, Phys. Rev. E 87, 052914 (2013).
[CrossRef]

G. Y. Yang, L. Li, and S. T. Jia, Phys. Rev. E 85, 046608 (2012).
[CrossRef]

Phys. Rev. Lett.

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).
[CrossRef]

F. Baronio, M. Conforti, A. Degasperis, and S. Lombardo, Phys. Rev. Lett. 111, 114101 (2013).
[CrossRef]

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, Phys. Rev. Lett. 106, 204502 (2011).
[CrossRef]

H. Bailung, S. K. Sharma, and Y. Nakamura, Phys. Rev. Lett. 107, 255005 (2011).
[CrossRef]

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, Phys. Rev. Lett. 98, 074102 (2007).
[CrossRef]

J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and V. V. Konotop, Phys. Rev. Lett. 100, 164102 (2008).
[CrossRef]

Proc. J. Soc. A

Y. Ohta and J. Yang, Proc. J. Soc. A 468, 1716 (2012).
[CrossRef]

Other

A. R. Osborne, Nonlinear Ocean Waves (Academic, 2009).

E. Pelinovsky and C. Kharif, Extreme Ocean Waves (Springer, 2008).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) Density plot of fundamental RW |u| on a Gaussian background beam. (b) Profile of |u| at the central position z=0 (blue solid line), and the Gaussian background beam (red dashed line). It is shown that the maximum peak value of the RW is still nine times the maximum value of the Gaussian background beam. The parameter b=6.

Fig. 2.
Fig. 2.

(a) Density modulation on the Gaussian background beam with b=6. The black dashed line corresponds to the Gaussian background beam density distribution, and the red solid line corresponds to the Gaussian background beam with modulated signal. (b) The phase modulation form on the background.

Fig. 3.
Fig. 3.

(a) Density plot of the second-order RW |u| on the Gaussian background beam. (b) The profile of |u| at the central position z=0 (blue solid line), and the Gaussian background beam (red dashed line). It is shown that the maximum peak value is still 25 times of the maximum value of the Gaussian background beam. The parameter b=6.

Fig. 4.
Fig. 4.

Density plot of RW |u| on a narrower-width Gaussian background beam. Namely the width of the background beam is a bit smaller than the scale of RW. It is shown that the maximum peak value is still nine times the maximum value of the Gaussian background beam. The parameter b=2.

Fig. 5.
Fig. 5.

Numerical simulation of the optical RW |u| on Gaussian background beam from solution (3) with parameter b=6.

Equations (5)

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

n=n0+n1(ζ,χ)+g(ζ,χ)I(ζ,χ),
iuζ+12k0f(ζ,χ)2uχ2+k0n0n1(ζ,χ)u+k0n0g(ζ,χ)|u|2u+ik0n0γ(ζ,χ)u=0,
u0(z,x)=exp[x22b2+iz],
u(z,x)=(14+8iz1+4X2+4z2)exp[x22b2+iz],
u=(1+4X2+396)2+64001+4X2+400·exp[x22b2+iθi10],

Metrics