Phase-encoding of loosely bound soliton molecules

Dissipative soliton molecules (DSMs) are of great interest for studying the complexity of nonlinear optical problems as they can map with the matter molecules for making interdisciplinary analogies. In contrast to strongly bound DSMs that have a short time separation between the bound solitons, the complex dynamics and underlying binding mechanism of loosely bound soliton molecules (LBSMs) with orders of magnitude longer time separation remain open questions. To this end, here, we explore real-time spectroscopy using a dispersive temporal interferometer (DTI) to visualize the dynamics of LBSMs in a mode-locked fiber laser and unveil their underlying phase-evolving mechanism. The DTI enables fringe-resolved spectroscopy in real time of the LBSM's evolution by creating duplicates of the LBSM that results in a much closer time separation between the individual solitons of the LBSM. The real-time evolution of the LBSM's phase exhibits a diverging sliding landscape, which is theoretically and experimentally proved to be closely associated with gain dynamics. Based on the understanding of its phase dynamics, we finally demonstrate programmable phase-encoding modulation of the LBSM through gain control. These efforts not only shed light on understanding the mechanism of long-range interactions in LBSMs but also provide an alternative approach for all-optical information processing.