Vol. 55

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2017-02-22

Transitional Behaviors of CQGLE Solitons Across Boundaries on a Phase Plane

By Huai-Ming Chang and Jean-Fu Kiang
Progress In Electromagnetics Research M, Vol. 55, 1-12, 2017
doi:10.2528/PIERM16112203

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.

Citation


Huai-Ming Chang and Jean-Fu Kiang, "Transitional Behaviors of CQGLE Solitons Across Boundaries on a Phase Plane," Progress In Electromagnetics Research M, Vol. 55, 1-12, 2017.
doi:10.2528/PIERM16112203
http://www.jpier.org/PIERM/pier.php?paper=16112203

References


    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

    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

    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

    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

    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

    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

    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

    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.

    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

    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

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

    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

    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

    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

    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

    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

    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