Transient Evolution and Manipulation Mechanisms of Multi‐Breathing Soliton States in SGS‐Structured Passively Mode‐Locked Fiber Lasers for Encoding Applications

ABSTRACT The modulation of multi‐pulse breathing soliton states is of fundamental importance for elucidating energy competition and intracavity nonlinear balance in nonlinear dissipative systems. In this work, tunable breathing soliton states with pulse numbers ranging from one to ten are realized using the single‐mode fiber–graded‐index few‐mode fiber–single‐mode fiber (SMF–GIFMF–SMF, SGS) structure, and the transient evolution of in‐phase and anti‐phase strong–weak breathing dynamics among multiple pulses is captured. Both experimental observations and numerical simulations demonstrate that phase accumulation induced by multimode interference, together with gain redistribution among interacting pulses, plays a dominant role in the formation of strong–weak breathing states, thereby revealing the underlying phase–gain co‐evolution dynamics in passively mode‐locked fiber lasers. Leveraging the high controllability of breathing soliton states, we further propose an optical encoding scheme comprising 26 distinct state combinations, enabling direct mapping from conventional solitons and multi‐pulse breathing states to alphabetic sequences. The practicality of the scheme is verified through a graphical user interface, offering new insights into the potential of ultrafast fiber lasers for applications in optical communications and optical information processing.