Abstract

We explore dispersive and rectangular similariton solutions to the generalized nonlinear Schrödinger equation with varying dispersion, nonlinearity, gain, and source. The obtained similariton solutions are approximate but nevertheless highly accurate. As an application, we delineate the nonlinear compression of these similaritons for a dispersion-decreasing management profile. Also, for a periodic distributed amplification system, we demonstrate the formation of bound-state similaritons.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).
  2. V. N. Serkin and A. Hasegawa, “Soliton management in the nonlinear Schrödinger equation model with varying dispersion, nonlinearity, and gain,” JETP Lett. 72, 89–92 (2000).
  3. V. N. Serkin and T. L. Belyaeva, “Optimal control of optical soliton parameters: the Lax representation in the problem of soliton management,” Qunatum Elec. 32, 1007–1015 (2001).
  4. V. N. Serkin and T. L. Belyaeva, “High energy optical Schrödinger solitons,” JETP Lett. 74, 573–577 (2001).
  5. V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Comment on ‘Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 92, 199401 (2004).
  6. V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous solitons in external potentials,” Phys. Rev. Lett. 98, 074102 (2007).
  7. V. N. Serkin and A. Hasegawa, “Exactly integrable nonlinear Schrödinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion,” IEEE J. Sel. Top. Quantum Electron. 8, 418–431 (2002).
  8. V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).
  9. V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E 71, 056619 (2005).
  10. J. F. Wang, L. Li, Z. H. Li, G. S. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression and propagation of pulse trains under higher-order effects,” Opt. Commun. 263, 328–336 (2006).
  11. S. A. Ponomarenko and G. P. Agrawal, “Interaction of chirped and chirp-free similaritons in fiber amplifiers,” Opt. Express 15, 2963–2973 (2007).
  12. S. A. Ponomarenko and G. P. Agrawal, “Optical similaritons in nonlinear waveguides,” Opt. Lett. 32, 1659–1661 (2007).
  13. J. F. Wang, L. Li, and S. T. Jia, “Nonlinear tunneling of optical similaritons in nonlinear waveguides,” J. Opt. Soc. Am. B 25, 1254–1260 (2008).
  14. V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, “Self-similar propagation of parabolic pulses in normal-dispersion fiber amplifiers,” J. Opt. Soc. Am. B 19, 461–469 (2002).
  15. F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
  16. J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).
  17. L. Wu, J. F. Zhang, L. Li, Q. Tian, and K. Porsezian, “Similaritons in nonlinear optical systems,” Opt. Express 16, 6352–6360 (2008).
  18. V. I. Kruglov, C. Aguergaray, N. G. Broderick, and J. D. Harvey, “Dispersive and rectangular similariton generation in fiber amplifiers and lasers,” Phys. Rev. A 85, 061803(R) (2012).
  19. K. Porsezian, A. Hasegawa, V. N. Serkin, T. L. Belyaeva, and R. Ganapathy, “Dispersion and nonlinear management for femtosecond optical solitons,” Phys. Lett. A 361, 504–508 (2007).
  20. V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons,” J. Mod. Opt. 57, 1456–1472 (2010).
  21. B. A. Malomed, I. M. Skinner, P. L. Chu, and G. D. Peng, “Symmetric and asymmetric solitons in twin-core nonlinear optical fibers,” Phys. Rev. E 53, 4084–4091 (1996).
  22. M. Liu and P. Shum, “Generalized coupled nonlinear equations for the analysis of asymmetric two-core fiber coupler,” Opt. Express 11, 116–119 (2003).
  23. G. Cohen, “Soliton interaction with an external traveling wave,” Phys. Rev. E 61, 874–879 (2000).
  24. B. A. Malomed, “Bound solitons in a nonlinear optical coupler,” Phys. Rev. E 51, R864–R866 (1995).
  25. T. Soloman Raju, P. K. Panigrahi, and K. Porsezian, “Nonlinear compression of solitary waves in asymmetric twin-core fibers,” Phys. Rev. E 71, 026608 (2005).
  26. T. Soloman Raju, P. K. Panigrahi, and K. Porsezian, “Self-similar propagation and compression of chirped self-similar waves in asymmetric twin-core fibers with nonlinear gain,” Phys. Rev. E 72, 046612 (2005).
  27. T. Soloman Raju and P. K. Panigrahi, “Self-similar propagation in a graded-index nonlinear-fiber amplifier with an external source,” Phys. Rev. A 81, 043820 (2010).
  28. T. Soloman Raju and P. K. Panigrahi, “Optical similaritons in a tapered graded-index nonlinear-fiber amplifier with an external source,” Phys. Rev. A 84, 033807 (2011).
  29. P. G. Drazin and R. S. Johnson, Solitons: An Introduction(Cambridge University, 1988).
  30. F. Calogero and A. Degasperis, Spectral Transform and Solitons (North-Holland, 1982).
  31. R. Y. Hao, L. Li, Z. H. Li, R. C. Yang, and G. S. Zhou, “A new way to exact quasi-soliton solutions and soliton interaction for the cubic-quintic nonlinear Schrödinger equation with variable coefficients,” Opt. Commun. 245, 383–390 (2005).

2012 (1)

V. I. Kruglov, C. Aguergaray, N. G. Broderick, and J. D. Harvey, “Dispersive and rectangular similariton generation in fiber amplifiers and lasers,” Phys. Rev. A 85, 061803(R) (2012).

2011 (1)

T. Soloman Raju and P. K. Panigrahi, “Optical similaritons in a tapered graded-index nonlinear-fiber amplifier with an external source,” Phys. Rev. A 84, 033807 (2011).

2010 (2)

T. Soloman Raju and P. K. Panigrahi, “Self-similar propagation in a graded-index nonlinear-fiber amplifier with an external source,” Phys. Rev. A 81, 043820 (2010).

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons,” J. Mod. Opt. 57, 1456–1472 (2010).

2008 (2)

2007 (5)

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).

S. A. Ponomarenko and G. P. Agrawal, “Interaction of chirped and chirp-free similaritons in fiber amplifiers,” Opt. Express 15, 2963–2973 (2007).

S. A. Ponomarenko and G. P. Agrawal, “Optical similaritons in nonlinear waveguides,” Opt. Lett. 32, 1659–1661 (2007).

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous solitons in external potentials,” Phys. Rev. Lett. 98, 074102 (2007).

K. Porsezian, A. Hasegawa, V. N. Serkin, T. L. Belyaeva, and R. Ganapathy, “Dispersion and nonlinear management for femtosecond optical solitons,” Phys. Lett. A 361, 504–508 (2007).

2006 (1)

J. F. Wang, L. Li, Z. H. Li, G. S. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression and propagation of pulse trains under higher-order effects,” Opt. Commun. 263, 328–336 (2006).

2005 (4)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E 71, 056619 (2005).

T. Soloman Raju, P. K. Panigrahi, and K. Porsezian, “Nonlinear compression of solitary waves in asymmetric twin-core fibers,” Phys. Rev. E 71, 026608 (2005).

T. Soloman Raju, P. K. Panigrahi, and K. Porsezian, “Self-similar propagation and compression of chirped self-similar waves in asymmetric twin-core fibers with nonlinear gain,” Phys. Rev. E 72, 046612 (2005).

R. Y. Hao, L. Li, Z. H. Li, R. C. Yang, and G. S. Zhou, “A new way to exact quasi-soliton solutions and soliton interaction for the cubic-quintic nonlinear Schrödinger equation with variable coefficients,” Opt. Commun. 245, 383–390 (2005).

2004 (2)

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Comment on ‘Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 92, 199401 (2004).

2003 (2)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).

M. Liu and P. Shum, “Generalized coupled nonlinear equations for the analysis of asymmetric two-core fiber coupler,” Opt. Express 11, 116–119 (2003).

2002 (2)

V. N. Serkin and A. Hasegawa, “Exactly integrable nonlinear Schrödinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion,” IEEE J. Sel. Top. Quantum Electron. 8, 418–431 (2002).

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, “Self-similar propagation of parabolic pulses in normal-dispersion fiber amplifiers,” J. Opt. Soc. Am. B 19, 461–469 (2002).

2001 (2)

V. N. Serkin and T. L. Belyaeva, “Optimal control of optical soliton parameters: the Lax representation in the problem of soliton management,” Qunatum Elec. 32, 1007–1015 (2001).

V. N. Serkin and T. L. Belyaeva, “High energy optical Schrödinger solitons,” JETP Lett. 74, 573–577 (2001).

2000 (3)

V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).

V. N. Serkin and A. Hasegawa, “Soliton management in the nonlinear Schrödinger equation model with varying dispersion, nonlinearity, and gain,” JETP Lett. 72, 89–92 (2000).

G. Cohen, “Soliton interaction with an external traveling wave,” Phys. Rev. E 61, 874–879 (2000).

1996 (1)

B. A. Malomed, I. M. Skinner, P. L. Chu, and G. D. Peng, “Symmetric and asymmetric solitons in twin-core nonlinear optical fibers,” Phys. Rev. E 53, 4084–4091 (1996).

1995 (1)

B. A. Malomed, “Bound solitons in a nonlinear optical coupler,” Phys. Rev. E 51, R864–R866 (1995).

Agrawal, G. P.

Aguergaray, C.

V. I. Kruglov, C. Aguergaray, N. G. Broderick, and J. D. Harvey, “Dispersive and rectangular similariton generation in fiber amplifiers and lasers,” Phys. Rev. A 85, 061803(R) (2012).

Belyaeva, T. L.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons,” J. Mod. Opt. 57, 1456–1472 (2010).

K. Porsezian, A. Hasegawa, V. N. Serkin, T. L. Belyaeva, and R. Ganapathy, “Dispersion and nonlinear management for femtosecond optical solitons,” Phys. Lett. A 361, 504–508 (2007).

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous solitons in external potentials,” Phys. Rev. Lett. 98, 074102 (2007).

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Comment on ‘Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 92, 199401 (2004).

V. N. Serkin and T. L. Belyaeva, “Optimal control of optical soliton parameters: the Lax representation in the problem of soliton management,” Qunatum Elec. 32, 1007–1015 (2001).

V. N. Serkin and T. L. Belyaeva, “High energy optical Schrödinger solitons,” JETP Lett. 74, 573–577 (2001).

Broderick, N. G.

V. I. Kruglov, C. Aguergaray, N. G. Broderick, and J. D. Harvey, “Dispersive and rectangular similariton generation in fiber amplifiers and lasers,” Phys. Rev. A 85, 061803(R) (2012).

Buckley, J. R.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).

Calogero, F.

F. Calogero and A. Degasperis, Spectral Transform and Solitons (North-Holland, 1982).

Chu, P. L.

B. A. Malomed, I. M. Skinner, P. L. Chu, and G. D. Peng, “Symmetric and asymmetric solitons in twin-core nonlinear optical fibers,” Phys. Rev. E 53, 4084–4091 (1996).

Clark, W. G.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).

Cohen, G.

G. Cohen, “Soliton interaction with an external traveling wave,” Phys. Rev. E 61, 874–879 (2000).

Degasperis, A.

F. Calogero and A. Degasperis, Spectral Transform and Solitons (North-Holland, 1982).

Drazin, P. G.

P. G. Drazin and R. S. Johnson, Solitons: An Introduction(Cambridge University, 1988).

Dudley, J. M.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, “Self-similar propagation of parabolic pulses in normal-dispersion fiber amplifiers,” J. Opt. Soc. Am. B 19, 461–469 (2002).

Finot, C.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).

Ganapathy, R.

K. Porsezian, A. Hasegawa, V. N. Serkin, T. L. Belyaeva, and R. Ganapathy, “Dispersion and nonlinear management for femtosecond optical solitons,” Phys. Lett. A 361, 504–508 (2007).

Hao, R. Y.

R. Y. Hao, L. Li, Z. H. Li, R. C. Yang, and G. S. Zhou, “A new way to exact quasi-soliton solutions and soliton interaction for the cubic-quintic nonlinear Schrödinger equation with variable coefficients,” Opt. Commun. 245, 383–390 (2005).

Harvey, J. D.

V. I. Kruglov, C. Aguergaray, N. G. Broderick, and J. D. Harvey, “Dispersive and rectangular similariton generation in fiber amplifiers and lasers,” Phys. Rev. A 85, 061803(R) (2012).

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E 71, 056619 (2005).

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, “Self-similar propagation of parabolic pulses in normal-dispersion fiber amplifiers,” J. Opt. Soc. Am. B 19, 461–469 (2002).

Hasegawa, A.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons,” J. Mod. Opt. 57, 1456–1472 (2010).

K. Porsezian, A. Hasegawa, V. N. Serkin, T. L. Belyaeva, and R. Ganapathy, “Dispersion and nonlinear management for femtosecond optical solitons,” Phys. Lett. A 361, 504–508 (2007).

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous solitons in external potentials,” Phys. Rev. Lett. 98, 074102 (2007).

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Comment on ‘Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 92, 199401 (2004).

V. N. Serkin and A. Hasegawa, “Exactly integrable nonlinear Schrödinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion,” IEEE J. Sel. Top. Quantum Electron. 8, 418–431 (2002).

V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).

V. N. Serkin and A. Hasegawa, “Soliton management in the nonlinear Schrödinger equation model with varying dispersion, nonlinearity, and gain,” JETP Lett. 72, 89–92 (2000).

Ilday, F. Ö.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).

Jia, S. T.

Johnson, R. S.

P. G. Drazin and R. S. Johnson, Solitons: An Introduction(Cambridge University, 1988).

Kruglov, V. I.

V. I. Kruglov, C. Aguergaray, N. G. Broderick, and J. D. Harvey, “Dispersive and rectangular similariton generation in fiber amplifiers and lasers,” Phys. Rev. A 85, 061803(R) (2012).

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E 71, 056619 (2005).

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, “Self-similar propagation of parabolic pulses in normal-dispersion fiber amplifiers,” J. Opt. Soc. Am. B 19, 461–469 (2002).

Li, L.

J. F. Wang, L. Li, and S. T. Jia, “Nonlinear tunneling of optical similaritons in nonlinear waveguides,” J. Opt. Soc. Am. B 25, 1254–1260 (2008).

L. Wu, J. F. Zhang, L. Li, Q. Tian, and K. Porsezian, “Similaritons in nonlinear optical systems,” Opt. Express 16, 6352–6360 (2008).

J. F. Wang, L. Li, Z. H. Li, G. S. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression and propagation of pulse trains under higher-order effects,” Opt. Commun. 263, 328–336 (2006).

R. Y. Hao, L. Li, Z. H. Li, R. C. Yang, and G. S. Zhou, “A new way to exact quasi-soliton solutions and soliton interaction for the cubic-quintic nonlinear Schrödinger equation with variable coefficients,” Opt. Commun. 245, 383–390 (2005).

Li, Z. H.

J. F. Wang, L. Li, Z. H. Li, G. S. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression and propagation of pulse trains under higher-order effects,” Opt. Commun. 263, 328–336 (2006).

R. Y. Hao, L. Li, Z. H. Li, R. C. Yang, and G. S. Zhou, “A new way to exact quasi-soliton solutions and soliton interaction for the cubic-quintic nonlinear Schrödinger equation with variable coefficients,” Opt. Commun. 245, 383–390 (2005).

Liu, M.

Malomed, B. A.

J. F. Wang, L. Li, Z. H. Li, G. S. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression and propagation of pulse trains under higher-order effects,” Opt. Commun. 263, 328–336 (2006).

B. A. Malomed, I. M. Skinner, P. L. Chu, and G. D. Peng, “Symmetric and asymmetric solitons in twin-core nonlinear optical fibers,” Phys. Rev. E 53, 4084–4091 (1996).

B. A. Malomed, “Bound solitons in a nonlinear optical coupler,” Phys. Rev. E 51, R864–R866 (1995).

Mihalache, D.

J. F. Wang, L. Li, Z. H. Li, G. S. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression and propagation of pulse trains under higher-order effects,” Opt. Commun. 263, 328–336 (2006).

Millot, G.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).

Panigrahi, P. K.

T. Soloman Raju and P. K. Panigrahi, “Optical similaritons in a tapered graded-index nonlinear-fiber amplifier with an external source,” Phys. Rev. A 84, 033807 (2011).

T. Soloman Raju and P. K. Panigrahi, “Self-similar propagation in a graded-index nonlinear-fiber amplifier with an external source,” Phys. Rev. A 81, 043820 (2010).

T. Soloman Raju, P. K. Panigrahi, and K. Porsezian, “Self-similar propagation and compression of chirped self-similar waves in asymmetric twin-core fibers with nonlinear gain,” Phys. Rev. E 72, 046612 (2005).

T. Soloman Raju, P. K. Panigrahi, and K. Porsezian, “Nonlinear compression of solitary waves in asymmetric twin-core fibers,” Phys. Rev. E 71, 026608 (2005).

Peacock, A. C.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E 71, 056619 (2005).

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, “Self-similar propagation of parabolic pulses in normal-dispersion fiber amplifiers,” J. Opt. Soc. Am. B 19, 461–469 (2002).

Peng, G. D.

B. A. Malomed, I. M. Skinner, P. L. Chu, and G. D. Peng, “Symmetric and asymmetric solitons in twin-core nonlinear optical fibers,” Phys. Rev. E 53, 4084–4091 (1996).

Ponomarenko, S. A.

Porsezian, K.

L. Wu, J. F. Zhang, L. Li, Q. Tian, and K. Porsezian, “Similaritons in nonlinear optical systems,” Opt. Express 16, 6352–6360 (2008).

K. Porsezian, A. Hasegawa, V. N. Serkin, T. L. Belyaeva, and R. Ganapathy, “Dispersion and nonlinear management for femtosecond optical solitons,” Phys. Lett. A 361, 504–508 (2007).

T. Soloman Raju, P. K. Panigrahi, and K. Porsezian, “Nonlinear compression of solitary waves in asymmetric twin-core fibers,” Phys. Rev. E 71, 026608 (2005).

T. Soloman Raju, P. K. Panigrahi, and K. Porsezian, “Self-similar propagation and compression of chirped self-similar waves in asymmetric twin-core fibers with nonlinear gain,” Phys. Rev. E 72, 046612 (2005).

Raju, T. Soloman

T. Soloman Raju and P. K. Panigrahi, “Optical similaritons in a tapered graded-index nonlinear-fiber amplifier with an external source,” Phys. Rev. A 84, 033807 (2011).

T. Soloman Raju and P. K. Panigrahi, “Self-similar propagation in a graded-index nonlinear-fiber amplifier with an external source,” Phys. Rev. A 81, 043820 (2010).

T. Soloman Raju, P. K. Panigrahi, and K. Porsezian, “Self-similar propagation and compression of chirped self-similar waves in asymmetric twin-core fibers with nonlinear gain,” Phys. Rev. E 72, 046612 (2005).

T. Soloman Raju, P. K. Panigrahi, and K. Porsezian, “Nonlinear compression of solitary waves in asymmetric twin-core fibers,” Phys. Rev. E 71, 026608 (2005).

Richardson, D. J.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).

Serkin, V. N.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons,” J. Mod. Opt. 57, 1456–1472 (2010).

K. Porsezian, A. Hasegawa, V. N. Serkin, T. L. Belyaeva, and R. Ganapathy, “Dispersion and nonlinear management for femtosecond optical solitons,” Phys. Lett. A 361, 504–508 (2007).

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous solitons in external potentials,” Phys. Rev. Lett. 98, 074102 (2007).

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Comment on ‘Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 92, 199401 (2004).

V. N. Serkin and A. Hasegawa, “Exactly integrable nonlinear Schrödinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion,” IEEE J. Sel. Top. Quantum Electron. 8, 418–431 (2002).

V. N. Serkin and T. L. Belyaeva, “High energy optical Schrödinger solitons,” JETP Lett. 74, 573–577 (2001).

V. N. Serkin and T. L. Belyaeva, “Optimal control of optical soliton parameters: the Lax representation in the problem of soliton management,” Qunatum Elec. 32, 1007–1015 (2001).

V. N. Serkin and A. Hasegawa, “Soliton management in the nonlinear Schrödinger equation model with varying dispersion, nonlinearity, and gain,” JETP Lett. 72, 89–92 (2000).

V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).

Shum, P.

Skinner, I. M.

B. A. Malomed, I. M. Skinner, P. L. Chu, and G. D. Peng, “Symmetric and asymmetric solitons in twin-core nonlinear optical fibers,” Phys. Rev. E 53, 4084–4091 (1996).

Tian, Q.

Wang, J. F.

J. F. Wang, L. Li, and S. T. Jia, “Nonlinear tunneling of optical similaritons in nonlinear waveguides,” J. Opt. Soc. Am. B 25, 1254–1260 (2008).

J. F. Wang, L. Li, Z. H. Li, G. S. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression and propagation of pulse trains under higher-order effects,” Opt. Commun. 263, 328–336 (2006).

Wise, F. W.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).

Wu, L.

Yang, R. C.

R. Y. Hao, L. Li, Z. H. Li, R. C. Yang, and G. S. Zhou, “A new way to exact quasi-soliton solutions and soliton interaction for the cubic-quintic nonlinear Schrödinger equation with variable coefficients,” Opt. Commun. 245, 383–390 (2005).

Zhang, J. F.

Zhou, G. S.

J. F. Wang, L. Li, Z. H. Li, G. S. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression and propagation of pulse trains under higher-order effects,” Opt. Commun. 263, 328–336 (2006).

R. Y. Hao, L. Li, Z. H. Li, R. C. Yang, and G. S. Zhou, “A new way to exact quasi-soliton solutions and soliton interaction for the cubic-quintic nonlinear Schrödinger equation with variable coefficients,” Opt. Commun. 245, 383–390 (2005).

IEEE J. Sel. Top. Quantum Electron. (1)

V. N. Serkin and A. Hasegawa, “Exactly integrable nonlinear Schrödinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion,” IEEE J. Sel. Top. Quantum Electron. 8, 418–431 (2002).

J. Mod. Opt. (1)

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons,” J. Mod. Opt. 57, 1456–1472 (2010).

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

JETP Lett. (2)

V. N. Serkin and A. Hasegawa, “Soliton management in the nonlinear Schrödinger equation model with varying dispersion, nonlinearity, and gain,” JETP Lett. 72, 89–92 (2000).

V. N. Serkin and T. L. Belyaeva, “High energy optical Schrödinger solitons,” JETP Lett. 74, 573–577 (2001).

Nat. Phys. (1)

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007).

Opt. Commun. (2)

J. F. Wang, L. Li, Z. H. Li, G. S. Zhou, D. Mihalache, and B. A. Malomed, “Generation, compression and propagation of pulse trains under higher-order effects,” Opt. Commun. 263, 328–336 (2006).

R. Y. Hao, L. Li, Z. H. Li, R. C. Yang, and G. S. Zhou, “A new way to exact quasi-soliton solutions and soliton interaction for the cubic-quintic nonlinear Schrödinger equation with variable coefficients,” Opt. Commun. 245, 383–390 (2005).

Opt. Express (3)

Opt. Lett. (1)

Phys. Lett. A (1)

K. Porsezian, A. Hasegawa, V. N. Serkin, T. L. Belyaeva, and R. Ganapathy, “Dispersion and nonlinear management for femtosecond optical solitons,” Phys. Lett. A 361, 504–508 (2007).

Phys. Rev. A (3)

T. Soloman Raju and P. K. Panigrahi, “Self-similar propagation in a graded-index nonlinear-fiber amplifier with an external source,” Phys. Rev. A 81, 043820 (2010).

T. Soloman Raju and P. K. Panigrahi, “Optical similaritons in a tapered graded-index nonlinear-fiber amplifier with an external source,” Phys. Rev. A 84, 033807 (2011).

V. I. Kruglov, C. Aguergaray, N. G. Broderick, and J. D. Harvey, “Dispersive and rectangular similariton generation in fiber amplifiers and lasers,” Phys. Rev. A 85, 061803(R) (2012).

Phys. Rev. E (6)

B. A. Malomed, I. M. Skinner, P. L. Chu, and G. D. Peng, “Symmetric and asymmetric solitons in twin-core nonlinear optical fibers,” Phys. Rev. E 53, 4084–4091 (1996).

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E 71, 056619 (2005).

G. Cohen, “Soliton interaction with an external traveling wave,” Phys. Rev. E 61, 874–879 (2000).

B. A. Malomed, “Bound solitons in a nonlinear optical coupler,” Phys. Rev. E 51, R864–R866 (1995).

T. Soloman Raju, P. K. Panigrahi, and K. Porsezian, “Nonlinear compression of solitary waves in asymmetric twin-core fibers,” Phys. Rev. E 71, 026608 (2005).

T. Soloman Raju, P. K. Panigrahi, and K. Porsezian, “Self-similar propagation and compression of chirped self-similar waves in asymmetric twin-core fibers with nonlinear gain,” Phys. Rev. E 72, 046612 (2005).

Phys. Rev. Lett. (5)

V. N. Serkin and A. Hasegawa, “Novel soliton solutions of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Comment on ‘Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 92, 199401 (2004).

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous solitons in external potentials,” Phys. Rev. Lett. 98, 074102 (2007).

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).

Qunatum Elec. (1)

V. N. Serkin and T. L. Belyaeva, “Optimal control of optical soliton parameters: the Lax representation in the problem of soliton management,” Qunatum Elec. 32, 1007–1015 (2001).

Other (2)

P. G. Drazin and R. S. Johnson, Solitons: An Introduction(Cambridge University, 1988).

F. Calogero and A. Degasperis, Spectral Transform and Solitons (North-Holland, 1982).

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 (6)

Fig. 1.
Fig. 1.

Evolution of super-Gaussian similariton for dispersion-decreasing fiber.

Fig. 2.
Fig. 2.

Evolution of super-Gaussian similariton for periodic varying GVD parameter.

Fig. 3.
Fig. 3.

Evolution of RS for dispersion-decreasing fiber.

Fig. 4.
Fig. 4.

Evolution of RS for periodic varying GVD parameter.

Fig. 5.
Fig. 5.

Evolution of DS when perturbation is introduced. It indicates stable evolution.

Fig. 6.
Fig. 6.

Evolution of RS when perturbation is introduced. It indicates stable evolution.

Equations (22)

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

iψz=β(z)2ψττγ(z)|ψ|2ψ+ig(z)2ψ+ε(z)eiΦ(z,τ).
ψ(z,τ)=P(z,τ)exp[iΦ(z,τ)],
Pz=β(z)2[2PτΦτ+PΦττ]+g(z)2P,
PΦz=β(z)2[PττP(Φτ)2]γ(z)P3+ε(z).
P(z,τ)=exp(12G(z))Q(z)R(T),
Φ(z,τ)=ϕ(z)+C(z)(ττc)2,
dQ(z)dz=β(z)C(z)Q(z),
dΓ(z)dz=2β(z)C(z)Γ(z),
dC(z)dz=2β(z)C(z)2,
dϕ(z)dz=γ(z)eG(z)Q(z)2R(T)2β(z)2Γ(z)2R(T)d2R(T)dT2ε(z)Q(z)R(T).
C(z)=C01+η(z),η(z)=2C00zβ(z)dz.
Q(z)=[1+η(z)]1/2,Γ(z)=1+η(z).
P020zγ(z)eG(z)dz1+η(z)1,0z|β(z)|dz2w(z)21,0zε(z)dz[1+η(z)]1/21,
ψ(z,τ)=exp(12G(z))Γ(z)F(τΓ(z))exp(iϕ0+iC0τ2Γ(z)),
ψ(z,τ)=exp(12g0z)Γ(z)F(TΓ(z))exp(iϕ0+iC0τ2Γ(z)),
Ω(z,τ)=2C0τ1+2C0β0α(exp(αz)1).
β(z)=β0cos(αz)exp(σz),
I˜(x)=1+exp(λ/2)1+exp[λ|x|λ/2],
P(z,τ)=P0exp(12G(z))[1+exp(λ/2)]1+η(z){1+exp[λ|ττ0(z)|/w(z)λ/2]},
τ0(z)=τ0[1+η(z)],w(z)=w0[1+η(z)].
Φ(z,τ)=ϕ0+P020zγ(z)eG(z)dz1+η(z)+C0τ21+η(z).
β(z)=β0cos(αz)exp(σz),

Metrics