Abstract

A unified theory to construct exact optical rogue wave solutions of (1+1)-dimensional nonlinear Schrodinger equation with varying coefficients is proposed. The dynamics of the first-order optical rogue waves in nonlinear graded-index waveguide amplifiers exhibiting self-focusing or self-defocusing Kerr nonlinearity are also investigated. Moreover, under the suitable parameter condition, the propagation characteristics of the rogue waves in the nonlinear optical media are discussed. The properties of the optical rogue waves, such as width, amplitude, and position, can be controlled in the nonlinear optical media.

© 2013 Chinese Optics Letters

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  1. A. R. Osborne, Nonlinear Ocean Waves (Academic Press, New York, 2009).
  2. N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
  3. A. Ankiewicz, N. Devine, and N. Akhmediev, Phys. Lett. A 373, 3997 (2009).
  4. C. Kharif, E. Pelinovsky, and A. Slunyaev, Rogue Waves in the Ocean, Observation, Theories and Modeling (Springer, New York, 2009).
  5. P. Muller, Ch. Garrett, and A. Osborne, Oceanography 18, 66 (2005).
  6. A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Phys. Rev. X 2, 011015 (2012).
  7. C. Q. Dai, G. Q. Zhou, and J. F. Zhang, Phys. Rev. E 85, 016603 (2012).
  8. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
  9. N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
  10. B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Scientific Reports 2, 463 (2012).
  11. Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).
  12. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Modern Phys. 71, 463 (1999).
  13. Yu. V. Bludov, V. V. Konotop, and N. Akhmedicv, Phys. Rev. A 80, 033610 (2009).
  14. W. P. Zhong, R. H. Xie, M. Bellic, N. Petrovic, G. Chen, and L. Yi, Phys. Rev. A 78, 023821 (2008).
  15. C. Q. Dai, X. G. Wang, and J. F. Zhang, Ann. Phys. 326, 645 (2011).
  16. C. Q. Dai, R. P. Chen, and J. F. Zhang, Soliton Fract. 44, 862 (2011).
  17. S. A. Ponomarenko and G. P. Agrawal, Phys. Rev. Lett. 97, 013901 (2006).
  18. S. A. Ponomarenko and G. P. Agrawal, Opt. Lett. 32, 1659 (2007).
  19. D. H. Peregrine, Soc. Ser. B 25, 16 (1983).
  20. B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010).
  21. K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).
  22. L. Li, X. S. Zhao, and Z. Y. Xu, Phys. Rev. A 78, 063833 (2008).

2012

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Phys. Rev. X 2, 011015 (2012).

C. Q. Dai, G. Q. Zhou, and J. F. Zhang, Phys. Rev. E 85, 016603 (2012).

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Scientific Reports 2, 463 (2012).

2011

Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).

C. Q. Dai, X. G. Wang, and J. F. Zhang, Ann. Phys. 326, 645 (2011).

C. Q. Dai, R. P. Chen, and J. F. Zhang, Soliton Fract. 44, 862 (2011).

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).

2010

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

2009

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

Yu. V. Bludov, V. V. Konotop, and N. Akhmedicv, Phys. Rev. A 80, 033610 (2009).

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

A. Ankiewicz, N. Devine, and N. Akhmediev, Phys. Lett. A 373, 3997 (2009).

2008

W. P. Zhong, R. H. Xie, M. Bellic, N. Petrovic, G. Chen, and L. Yi, Phys. Rev. A 78, 023821 (2008).

L. Li, X. S. Zhao, and Z. Y. Xu, Phys. Rev. A 78, 063833 (2008).

2007

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

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

2006

S. A. Ponomarenko and G. P. Agrawal, Phys. Rev. Lett. 97, 013901 (2006).

2005

P. Muller, Ch. Garrett, and A. Osborne, Oceanography 18, 66 (2005).

1999

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Modern Phys. 71, 463 (1999).

1983

D. H. Peregrine, Soc. Ser. B 25, 16 (1983).

Agrawal, G. P.

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

S. A. Ponomarenko and G. P. Agrawal, Phys. Rev. Lett. 97, 013901 (2006).

Akhmedicv, N.

Yu. V. Bludov, V. V. Konotop, and N. Akhmedicv, Phys. Rev. A 80, 033610 (2009).

Akhmediev, N.

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Phys. Rev. X 2, 011015 (2012).

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Scientific Reports 2, 463 (2012).

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

A. Ankiewicz, N. Devine, and N. Akhmediev, Phys. Lett. A 373, 3997 (2009).

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

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

Ankiewicz, A.

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

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

A. Ankiewicz, N. Devine, and N. Akhmediev, Phys. Lett. A 373, 3997 (2009).

Bellic, M.

W. P. Zhong, R. H. Xie, M. Bellic, N. Petrovic, G. Chen, and L. Yi, Phys. Rev. A 78, 023821 (2008).

Bludov, Yu. V.

Yu. V. Bludov, V. V. Konotop, and N. Akhmedicv, Phys. Rev. A 80, 033610 (2009).

Chabchoub, A.

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Phys. Rev. X 2, 011015 (2012).

Chen, G.

W. P. Zhong, R. H. Xie, M. Bellic, N. Petrovic, G. Chen, and L. Yi, Phys. Rev. A 78, 023821 (2008).

Chen, R. P.

C. Q. Dai, R. P. Chen, and J. F. Zhang, Soliton Fract. 44, 862 (2011).

Dai, C. Q.

C. Q. Dai, G. Q. Zhou, and J. F. Zhang, Phys. Rev. E 85, 016603 (2012).

Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).

C. Q. Dai, R. P. Chen, and J. F. Zhang, Soliton Fract. 44, 862 (2011).

C. Q. Dai, X. G. Wang, and J. F. Zhang, Ann. Phys. 326, 645 (2011).

Dalfovo, F.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Modern Phys. 71, 463 (1999).

Devine, N.

A. Ankiewicz, N. Devine, and N. Akhmediev, Phys. Lett. A 373, 3997 (2009).

Dias, F.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Scientific Reports 2, 463 (2012).

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

Dudley, J. M.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Scientific Reports 2, 463 (2012).

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).

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

Fatome, J.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Scientific Reports 2, 463 (2012).

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).

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

Finot, C.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Scientific Reports 2, 463 (2012).

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).

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

Garrett, Ch.

P. Muller, Ch. Garrett, and A. Osborne, Oceanography 18, 66 (2005).

Genty, G.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Scientific Reports 2, 463 (2012).

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

Giorgini, S.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Modern Phys. 71, 463 (1999).

Hammani, K.

Hoffmann, N.

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Phys. Rev. X 2, 011015 (2012).

Jalali, B.

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

Kibler, B.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Scientific Reports 2, 463 (2012).

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).

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

Konotop, V. V.

Yu. V. Bludov, V. V. Konotop, and N. Akhmedicv, Phys. Rev. A 80, 033610 (2009).

Koonath, P.

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

Li, L.

L. Li, X. S. Zhao, and Z. Y. Xu, Phys. Rev. A 78, 063833 (2008).

Millot, G.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Scientific Reports 2, 463 (2012).

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).

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

Morin, P.

Muller, P.

P. Muller, Ch. Garrett, and A. Osborne, Oceanography 18, 66 (2005).

Onorato, M.

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Phys. Rev. X 2, 011015 (2012).

Osborne, A.

P. Muller, Ch. Garrett, and A. Osborne, Oceanography 18, 66 (2005).

Peregrine, D. H.

D. H. Peregrine, Soc. Ser. B 25, 16 (1983).

Petrovic, N.

W. P. Zhong, R. H. Xie, M. Bellic, N. Petrovic, G. Chen, and L. Yi, Phys. Rev. A 78, 023821 (2008).

Pitaevskii, L. P.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Modern Phys. 71, 463 (1999).

Ponomarenko, S. A.

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

S. A. Ponomarenko and G. P. Agrawal, Phys. Rev. Lett. 97, 013901 (2006).

Ropers, C.

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

Solli, D. R.

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

Stringari, S.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Modern Phys. 71, 463 (1999).

Taki, M.

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

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

Tian, Q.

Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).

Wang, X. G.

C. Q. Dai, X. G. Wang, and J. F. Zhang, Ann. Phys. 326, 645 (2011).

Wetzel, B.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Scientific Reports 2, 463 (2012).

Xie, R. H.

W. P. Zhong, R. H. Xie, M. Bellic, N. Petrovic, G. Chen, and L. Yi, Phys. Rev. A 78, 023821 (2008).

Xu, Z. Y.

L. Li, X. S. Zhao, and Z. Y. Xu, Phys. Rev. A 78, 063833 (2008).

Yang, Q.

Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).

Yi, L.

W. P. Zhong, R. H. Xie, M. Bellic, N. Petrovic, G. Chen, and L. Yi, Phys. Rev. A 78, 023821 (2008).

Zhang, J. F.

C. Q. Dai, G. Q. Zhou, and J. F. Zhang, Phys. Rev. E 85, 016603 (2012).

Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).

C. Q. Dai, R. P. Chen, and J. F. Zhang, Soliton Fract. 44, 862 (2011).

C. Q. Dai, X. G. Wang, and J. F. Zhang, Ann. Phys. 326, 645 (2011).

Zhao, X. S.

L. Li, X. S. Zhao, and Z. Y. Xu, Phys. Rev. A 78, 063833 (2008).

Zhong, W. P.

W. P. Zhong, R. H. Xie, M. Bellic, N. Petrovic, G. Chen, and L. Yi, Phys. Rev. A 78, 023821 (2008).

Zhou, G. Q.

C. Q. Dai, G. Q. Zhou, and J. F. Zhang, Phys. Rev. E 85, 016603 (2012).

Ann. Phys.

C. Q. Dai, X. G. Wang, and J. F. Zhang, Ann. Phys. 326, 645 (2011).

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).

Nature

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

Oceanography

P. Muller, Ch. Garrett, and A. Osborne, Oceanography 18, 66 (2005).

Opt. Commun.

Q. Tian, Q. Yang, C. Q. Dai, and J. F. Zhang, Opt. Commun. 284, 2222 (2011).

Opt. Lett.

Phys. Lett. A

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

A. Ankiewicz, N. Devine, and N. Akhmediev, Phys. Lett. A 373, 3997 (2009).

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

Phys. Rev. A

Yu. V. Bludov, V. V. Konotop, and N. Akhmedicv, Phys. Rev. A 80, 033610 (2009).

W. P. Zhong, R. H. Xie, M. Bellic, N. Petrovic, G. Chen, and L. Yi, Phys. Rev. A 78, 023821 (2008).

L. Li, X. S. Zhao, and Z. Y. Xu, Phys. Rev. A 78, 063833 (2008).

Phys. Rev. E

C. Q. Dai, G. Q. Zhou, and J. F. Zhang, Phys. Rev. E 85, 016603 (2012).

Phys. Rev. Lett.

S. A. Ponomarenko and G. P. Agrawal, Phys. Rev. Lett. 97, 013901 (2006).

Phys. Rev. X

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Phys. Rev. X 2, 011015 (2012).

Rev. Modern Phys.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Modern Phys. 71, 463 (1999).

Scientific Reports

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Scientific Reports 2, 463 (2012).

Soc. Ser. B

D. H. Peregrine, Soc. Ser. B 25, 16 (1983).

Soliton Fract.

C. Q. Dai, R. P. Chen, and J. F. Zhang, Soliton Fract. 44, 862 (2011).

Other

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

C. Kharif, E. Pelinovsky, and A. Slunyaev, Rogue Waves in the Ocean, Observation, Theories and Modeling (Springer, New York, 2009).

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