Efficient Approach for 3D Stationary Optical Solitons in Dissipative Systems

A. Konaté, E. Soro, O. Asseu^*, A. Kamagaté, P. Yoboué

Ecole Supérieure Africaine des Technologies d’Information et de Communication (ESATIC), Abidjan, Cote d’Ivoire.

DOI: 10.4236/jamp.2015.310152                

Abstract

We feature the stationary solutions of the 3D complex cubic-quintic Ginzburg-Landau equation (CGLE). Our approach is based on collective variables approach which helps to obtain a system of variational equations, giving the evolution of the light pulses parameters as a function of the propagation distance. The collective variables approach permits us to obtain, efficiently, a global mapping of the 3D stationary dissipative solitons. In addition it allows describing the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics. Thus it helps to show the impact of dispersion and nonlinear gain on the stationary dynamic.

Keywords

Dissipative Solitons, Dispersion, Nonlinear Gain, Collective Variables Approach, Complex Cubic-Quintic Ginzburg-Landau Equation, (3D) Three-Dimensional Soliton, Spatio-Temporal Pulses

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Saarlos, W.V. and Hhenberg, P.C. (1992) Fronts, Pulse, Sources and Sinks in Generalized Ginzburg-Landau. Physica D, 56, 303-367. http://dx.doi.org/10.1016/0167-2789(92)90175-M
[2]	Akhmediev, N. and Ankiewicz, A. (2003) Solitons around Us: Integrable, Hamiltonian and Dissipative Systems. In: Porsezian, K. and Kurakose, V.C., Eds., Optical Solitons: Theoretical and Experimental Challenges, Springer, Heidelberg.
[3]	Akhmediev, N. and Ankiewicz, A. (2005) Dissipative Solitons. Springer, Heidelberg. http://dx.doi.org/10.1007/b11728
[4]	Rosanov, N.N. (2002) Spatial Hysteresis and Optical Patterns. Springer, Berlin, Chap. 6. http://dx.doi.org/10.1007/978-3-662-04792-7
[5]	Sakaguchi, H. and Malomed, B.A. (2001) Instabilities and Splitting of Pulses in Coupled Ginzburg-Landau Equations. Physica D, 154, 229-239. http://dx.doi.org/10.1016/S0167-2789(01)00243-3
[6]	Akhmediev, N., Soto-Crespo, J.M. and Town, G. (2001) Pulsating Solitons, Chaotic Solitons, Period Doubling, and Pulse Coexistence in Mode-Locked Lasers: CGLE Approach. Physical Review E, 63, Article ID: 056602. http://dx.doi.org/10.1103/PhysRevE.63.056602
[7]	Deissler, R.J. and Brand, H.R. (1994) Periodic, Quasiperiodic, and Chaotic Localized Solutions of the Quintic Complex GinZburg-Landau Equation. Physical Review Letters, 72, 478-481. http://dx.doi.org/10.1103/PhysRevLett.72.478
[8]	Soto-Crespo, J.M., Grelu, M.Ph. and Akhmediev, N. (2004) Bifurcations and Multiple-Period Soliton Pulsations in a Passively Mode-Locked Fiber Laser. Physical Review E, 70, Article ID: 066612. http://dx.doi.org/10.1103/physreve.70.066612
[9]	Kamagaté, A., Grelu, Ph., Tchofo-Dinda, P., Soto-Crespo, J.M. and Akhmediev, N. (2009) Stationary and Pulsating Dissipative Light Bullets from a Collective Variable Approach. Physical Review E, 79, Article ID: 026609. http://dx.doi.org/10.1103/physreve.79.026609
[10]	Haus, H.A., Fujimoto, J.G. and Ippen, E.P. (1995) Structures for Additive Pulse Mode Locking. Journal of the Optical Society of America B, 8, 2068-2076. http://dx.doi.org/10.1364/JOSAB.8.002068
[11]	Moores, J.D. (1993) On the Ginzburg-Landau Laser Mode-Locking Model with Fifth-Odersaturable Absorber Term. Optics Communications, 96, 65-70. http://dx.doi.org/10.1016/0030-4018(93)90524-9
[12]	Soto-Crespo, J.M., Akhmediev, N. and Grelu, P. (2006) Optical Bullets and Double Bullet Complexes in Dissipative Systems. Physical Review E, 74, Article ID: 046612. http://dx.doi.org/10.1103/physreve.74.046612
[13]	Boesch, R., Stancioff, P. and Willis, C.R. (1988) Hamiltonian Equations for Multiple-Collective-Variable Theories of Nonlinear Klein-Gordon Equations: A Projection-Operator Approach. Physical Review B, 38, 6713-6735. http://dx.doi.org/10.1103/PhysRevB.38.6713
[14]	Tchofo-Dinda, P., Moubissi, A.B. and Nakkeeran, K. (2001) Collective Variable Theory for Optical Solitons in Fibers. Physical Review E, 64, Article ID: 016608. http://dx.doi.org/10.1103/physreve.64.016608
[15]	Soto-Crespo, J.M., Akhmediev, N. and Town, G. (2002) Continuous-Wave versus Pulse Regime in Passively Mode-Locked Laser with a Fast Saturable Absorber. Journal of the Optical Society of America B, 19, 234-242. http://dx.doi.org/10.1364/JOSAB.19.000234
[16]	Kamagaté, A. (2010) Propagation des solitons spatio-temporels dans des milieux dissipatifs. Thesis, Universite de Bourgogne, Bourgogne.