Observation of the “invisible” pulsation of soliton molecules in a bidirectional ultrafast fiber laser

Abstract

A novel optical soliton dynamics phenomenon, called “invisible” pulsation, has gradually attracted extensive interest in recent years, which can only be identified effectively with the help of real-time spectroscopy technique, i.e., dispersive Fourier transformation (DFT). In this paper, based on a new bidirectional passively mode-locked fiber laser (MLFL), the “invisible” pulsation dynamics of soliton molecules (SMs) is systematically studied. It is indicated that the spectral center intensity, pulse peak power and relative phase of SMs are periodically changed during the “invisible” pulsation, while the temporal separation inside the SMs is constant. The degree of spectral distortion is positively correlated with the pulse peak power, which verifies that self-phase modulation (SPM) is the inducement of spectral distortion. Finally, the universality of the SMs “invisible” pulsation is further experimentally verified. We believe our work is not only conducive to the development of compact and reliable bidirectional ultrafast light sources, but also of great significance to enrich the study of nonlinear dynamics.

Pure-high-even-order dispersion bound solitons complexes in ultra-fast fiber lasers

“…Consequently, these dispersive waves present themselves as Kelly sidebands, which invariably share intra-cavity energy with solitons 53 . Studies have confirmed that these Kelly sidebands, which correspond to temporal oscillatory tails, play a crucial role in the generation of bound solitons within mode-locked fiber lasers 43 , 44 and oscillate in sync with pulsating bound soliton pairs, suggesting that the energy transfer between sidebands and solitons could result in various bound states 59 . The spectrum of PHEOD solitons exhibits a series of sidebands induced by high-even-order dispersion.…”

“…In other words, various relative phases and separations can be retrieved from the shot-to-shot spectrum, depicting the energy flow between each constituent facilitated by gain dynamics and soliton interactions 59 . Figure 6 provides the build-up of stationary PHEOD bound soliton pair and stationary PHEOD bound tri-soliton.…”

“…7e–h demonstrate that separations remain nearly constant during the spectrum variation, while relative phases exhibit periodic oscillations with periods of 25 RTs, 16 RTs, 22 RTs, and 58 RTs, respectively. Phase oscillation implies a weak bond between PHEOD solitons, and the relative intensity between PHEOD solitons undergoes an oscillation process concurrent with the phase oscillation 59 , 60 .

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Pure-high-even-order dispersion bound solitons complexes in ultra-fast fiber lasers

“…For bound solitons containing more than two solitons, under certain conditions, the information concerning the ∆φ and τ between solitons can be retrieved through the methods of spectrum interferometry 23,46 . In other words, various relative phases and separations can be retrieved from the shot-to-shot spectrum, depicting the energy flow between each constituent facilitated by gain dynamics and soliton interactions 47 . Figure 6 By integrating spectra across the entire spectrum band, we obtained periodic energy evolutions with oscillation periods of 13 RTs, 8 RTs, 11 RTs, and 27 RTs, as depicted by white curves.…”

“…The results demonstrate that separations remain nearly constant during the spectrum variation, while relative phases exhibit periodic oscillations with periods of 25 RTs, 16 RTs, 22 RTs, and 58 RTs, respectively. Phase oscillation implies a weak bond between PHEOD solitons, and the relative intensity between PHEOD solitons undergoes an oscillation process concurrent with the phase oscillation 47,50 . It is noteworthy that the oscillation period of the relative phase is precisely an integral multiple of the energy evolution period 50 .…”