Vol. 55
Latest Volume
All Volumes
PIERM 126 [2024] PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2017-02-22
Transitional Behaviors of CQGLE Solitons Across Boundaries on a Phase Plane
By
Progress In Electromagnetics Research M, Vol. 55, 1-12, 2017
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
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