Periodic and Chaotic Exploding Dissipative Solitons

Abstract

This article shows for the first time the existence of periodic exploding dissipative solitons. These non-chaotic explosions appear when higher-order non-linear and dispersive effects are added to the complex cubic–quintic Ginzburg–Landau equation modeling soliton transmission lines. This counter-intuitive phenomenon is the result of period-halving bifurcations leading to order (periodic explosions), followed by period-doubling bifurcations leading to chaos (chaotic explosions). This periodic behavior is persistent even when small amounts of noise are added to the system. Since for ultrashort optical pulses it is necessary to include these higher-order effects, it is conjectured that the predictions can be tested in mode-locked lasers.

Keywords:

• chaotic explosions
• complex cubic–quintic Ginzburg–Landau equations
• periodic explosions

Additional information

Funding

The authors wish to acknowledge the support of FONDECYT (projects 11121228 and 1140139) and Universidad de los Andes through FAI initiatives.

Notes on contributors

Carlos Cartes

Carlos Cartes received his Ph.D. in physics from University of Paris VI in 2008. He is presently an assistant professor at the Universidad de los Andes, Santiago, Chile. His current interests include non-linear optics, chaos in extended systems, and numerical simulations.

Orazio Descalzi

Orazio Descalzi received his Ph.D. in physics from University of Essen, Germany, in 1994. He is presently a full professor and research director at Universidad de los Andes, Santiago, Chile. His current interests include non-linear optics, optical solitons, and chaos.