Dissipative soliton molecules with independently evolving or flipping phases in mode-locked fiber lasers

Abstract

We numerically demonstrate the existence of a discrete family of robust dissipative soliton bound state solutions ͑soliton molecules͒ in a mode-locked fiber laser with an instantaneous saturable absorber in the normal dispersion domain. For a certain domain of the small-signal gain, we obtain a robust first-level bound state with almost constant separation where the phase of the two pulses evolves independently. Moreover, their phase difference can evolve either periodically or chaotically depending on the small-signal gain. Interestingly, higher level bound states exhibit a fundamentally different dynamics. They represent oscillating solutions with a phase difference alternating between zero and. We identify the crucial role of the linear gain saturation for the existence of these robust molecules independently of their level.

Soliton Molecules and Multisoliton States in Ultrafast Fibre Lasers: Intrinsic Complexes in Dissipative Systems

“…More generally, bound states can manifest themselves with many types, e.g., variant parameters of phase difference and temporal displacement, which have been widely found and discussed. To name a few, vibrating solitons [83,84] exhibit change of both pulse separation and phase difference within a small range, oscillating bound states [85] possess a periodic oscillation of temporal separation or phase difference or pulse amplitude and bound states with independently evolving phase [5,86] or flipping phase [86] are additionally available. Furthermore, presence of soliton molecules together with a single soliton [20], harmonic mode-locking of two-soliton bound states [33], bound states of two pulse groups (each group is composed of two bound solitons, or say twin-pulse as mentioned before) [87], bunching of soliton molecules, etc.…”

Observation of soliton molecules with independently evolving phase in a mode-locked fiber laser

“…The numerically obtained circular evolution trajectory on the phase plane is a consequence of the infinitely growing phase difference at an almost constant peak separation. The phase is growing because of slightly different amplitudes of the leading and trailing pulses according to the mechanism explained in [6]. Unfortunately this difference of amplitudes cannot be recognized in both the experimental and the simulated autocorrelation functions for its smallness, but it can be clearly seen from the simulated propagation of the soliton molecule in Fig.…”

“…Usually such molecules consist of two pulses and are characterized by the peak-to-peak separation and the phase difference between both pulses. Theoretically, a few kinds of stable scalar soliton molecules have been discovered in mode-locked fiber lasers, namely, molecules with an invariant phase [1,2], or molecules which are slightly vibrating or shaking around a stationary state [2,3], and molecules with an independently evolving phase [4][5][6][7] and such with a flipping phase [6]. Experimentally, only soliton molecules with an invariant phase [5,[8][9][10], with a rotating phase [5], and vibrating molecules [11] have been reported to date.…”

Breathing solitary-pulse pairs in a linearly coupled system

“…(4)], higher-order harmonics, generated by the cubic nonlinearity, couple to the continuous spectrum, initiating decay of the SP. To explore the effect of the nonlinearity in a systematic way, we computed the correlator CO 2π/K0 , using the numerical solutions of the full system (9). The results, shown in Fig.…”

“…(10) with numerical solutions for the SP pairs produced by simulations of the full system (9) demonstrate that the strong nonlinearity tends to gradually destroy the solitons. In Fig.…”