Chaotic internal dynamics of dissipative optical soliton molecules

Abstract

When a laser cavity supports the propagation of several ultrashort pulses, these pulses interact and can form compact bound states called soliton molecules. Soliton molecules are fascinating objects of nonlinear science, which present striking analogies with their matter molecules counterparts. The soliton pair, composed of two identical pulses, constitutes the chief soliton molecule of fundamental interest. The relative timing and phase between the two propagating pulses are the most salient internal degrees of freedom of the soliton molecule. These two internal degrees of freedom allow self-oscillating soliton molecules, which have indeed been repeatedly observed, whereas the lowdimensional chaotic dynamics of a soliton-pair molecule remains elusive, noting that it would require at least three degrees of freedom. We here report the observation of chaotic soliton-pair molecules within an ultrafast fiber laser, by means of a direct measurement of the relative optical pulse separation with sub-femtosecond precision in real time. Moreover, we demonstrate an all-optical control of the chaotic dynamics followed by the soliton molecule, by injecting a modulated optical signal that resynchronizes the internal periodic vibration of soliton molecule.

Chaos and synchronization within soliton molecules

“…The relative timing and phase between the copropagating pulses are the most salient internal degrees of freedom of the soliton molecule. Among a wide range of possible pulsation types, optical soliton molecules can exhibit vibrational internal motions, akin to matter molecules (1,2,3) . For temporal soliton molecules, this means that the relative timings between the traveling pulses that make up the molecule will oscillate.…”

“…These features led us to experimentally discover, in the case of a 2-soliton molecule, also called a soliton pair, the existence of chaotic internal dynamics (3) . We reached chaotic dynamics following the typical period-2 bifurcation cascades that are ubiquitous in nonlinear physics and dissipative soliton dynamics (4) .…”

Dynamical Systems of Oscillating Ultrashort Pulse Pairs

“…When pumped beyond the soliton-energy threshold, a cascade of instabilities leads to laser waveforms with two or more solitons, which are subject to a complex variety of interaction mechanisms [2]. Compared with single-soliton operation, multisoliton waveforms can exhibit a much richer and more versatile dynamics: Even the simplest multisoliton waveform, the soliton pair molecule, can be stationary, undergo regular oscillations [3], and even exhibit chaos [4].…”