volume | PIER Journals

Abstract

Soliton solutions of a cubic-quintic Ginzburg-Landau equation (CQGLE) are computed and analyzed on a parametric plane, specifically across the transitional zones that separate regions associated with different types of solitons. The transformations of behaviors in these transitional zones between stationary and pulsating regions are characterized by the total pulse energy and its maximum value. It is also found that the initial pulse waveform has little effect on bifurcation and the valid range of initial amplitude.

1. Grelu, Ph. and N. Akhmediev, "Dissipative solitons for mode-locked lasers," Nature Photonics, Vol. 6, 84-90, 2012.
doi:10.1038/nphoton.2011.345 Google Scholar

2. Akhmediev, N., J. M. Soto-Crespo, and G. Town, "Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg-Landau equation approach," Phys. Rev. E, Vol. 63, 056602, 2001.
doi:10.1103/PhysRevE.63.056602 Google Scholar

3. Soto-Crespo, J. M., N. Akhmediev, and A. Ankiewicz, "Pulsating, creeping, and erupting solitons in dissipative systems," Phys. Rev. Lett., Vol. 85, 2937, 2000.
doi:10.1103/PhysRevLett.85.2937 Google Scholar

4. Chang, W., J. M. Soto-Crespo, P. Vouzas, and N. Akhmediev, "Extreme amplitude spikes in a laser model described by the complex Ginzburg-Landau equation," Opt. Lett., Vol. 40, No. 13, 2949, 2015.
doi:10.1364/OL.40.002949 Google Scholar

5. Triki, H., F. Azzouzi, and P. Grelu, "Multipole solitary wave solutions of the higher-order nonlinear Schrödinger equation with quintic non-Kerr terms," Opt. Commun., Vol. 309, 71-79, 2013.
doi:10.1016/j.optcom.2013.06.039 Google Scholar

6. Zakeri, G. A. and E. Yomba, "Dissipative solitons in a generalized coupled cubic-quintic Ginzburg-Landau equations," J. Phys. Soc. Japan, Vol. 82, 084002, 2013.
doi:10.7566/JPSJ.82.084002 Google Scholar

7. Saha, M. and A. K. Sarma, "Solitary wave solutions and modulation instability analysis of the nonlinear Schrödinger equation with higher order dispersion and nonlinear terms," Commun. Nonlinear Sci. Num. Simu., Vol. 18, 2420-2425, 2013.
doi:10.1016/j.cnsns.2012.12.028 Google Scholar

8. Triki, H., F. Azzouzi, and P. Grelu, "An efficient split-step compact finite difference method for cubic-quintic complex Ginzburg-Landau equations," Computer Phys. Commun., Vol. 184, 1511-1521, 2013. Google Scholar

9. Green, P. D., D. Milovic, D. A. Lott, and A. Biswas, "Optical solitons with higher order dispersion by semi-inverse variational principle," Progress In Electromagnetics Research, Vol. 102, 337-350, 2010.
doi:10.2528/PIER10011910 Google Scholar

10. Runge, A. F. J., N. G. R. Broderick, and M. Erkintalo, "Observation of soliton explosions in a passively mode-locked fiber laser," Optica, Vol. 2, 36-39, 2015.
doi:10.1364/OPTICA.2.000036 Google Scholar

11. Cartes, C. and O. Descalzi, "Periodic exploding dissipative solitons," Phys. Rev. A, Vol. 93, 031801, 2016.
doi:10.1103/PhysRevA.93.031801 Google Scholar

12. Chang, W., J. M. Soto-Crespo, P. Vouzas, and N. Akhmediev, "Extreme soliton pulsations in dissipative systems," Phys. Rev. E, Vol. 92, 022926, 2015.
doi:10.1103/PhysRevE.92.022926 Google Scholar

13. Soto-Crespo, J. M., M. Grapinet, P. Grelu, and N. Akhmediev, "Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser," Phys. Rev. E, Vol. 70, 066612, 2004.
doi:10.1103/PhysRevE.70.066612 Google Scholar

14. Akhmediev, N., J. M. Soto-Crespo, M. Grapinet, and P. Grelu, "Dissipative soliton pulsations with periods beyond the laser cavity round trip time," J. Nonlinear Optical Phys. Materials, Vol. 14, No. 2, 177-194, 2005.
doi:10.1142/S0218863505002645 Google Scholar

15. Tsoy, E. N. and N. Akhmediev, "Bifurcations from stationary to pulsating solitons in the cubic-quintic complex Ginzburg-Landau equation," Phys. Lett. A, Vol. 343, 417-422, 2005.
doi:10.1016/j.physleta.2005.05.102 Google Scholar

16. Chang, W., A. Ankiewicz, N. Akhmediev, and J. M. Soto-Crespo, "Creeping solitons in dissipative systems and their bifurcations," Phys. Rev. E, Vol. 76, 016607, 2007.
doi:10.1103/PhysRevE.76.016607 Google Scholar

17. Weiner, A. M., Ultrafast Optics, John Wiley, 2009.
doi:10.1002/9780470473467

18. Agrawal, G. P., Nonlinear Fiber Optics, Academic Press, 2012.

19. Soto-Crespo, J. M., N. Akhmediev, and G. Town, "Continuous-wave versus pulse regime in a passively mode-locked laser with a fast saturable absorber," J. Opt. Soc. Am. B, Vol. 1, 234-242, 2002.
doi:10.1364/JOSAB.19.000234 Google Scholar

Dr. Huai-Ming Chang

Prof. Jean-Fu Kiang