Orbital-angular-momentum-resolved diagnostics for tracking internal phase evolution in multi-bound solitons

The generation of multi-bound solitons is a fascinating subject of investigation in many conservative and dissipative systems, such as photonics, fluid mechanics, Bose-Einstein condensates, and so on. In this study, we demonstrate the successful extraction of phase dynamics between solitons in bound multiple solitons with up to seven constituents in a mode-locked Er laser system. By mapping the internal phase motions of multi-bound solitons to the spatial phase movement of cylindrical vector beams using orbital angular momentum (OAM)-based diagnostics, different categories of internal pulsations are revealed. We show that bound state of four solitons exhibits linear drifting relative phase evolution dynamics; while for bound multiple solitons with constituents from five to seven pulses, stationary relative phase dynamics are observed. These findings highlight the possibility of the OAM-based method access to the internal motion of multi-soliton molecules with more freedom of degrees and fuel the analogy with research on chemistry molecule complex.