Dispersive time delay interferometer (DTI) technology enables single-shot ultrashort time measurement, providing a new method for studying the temporal dynamics of solitons in mode-locked fiber lasers. Using this technology, we investigate the complete temporal dynamics of steady-state and breathing-state dissipative solitons in a passive mode-locked fiber laser based on carbon nanotubes during their buildup and extinction processes. Our findings show that during both processes, steady-state and breathing-state dissipative solitons exhibit transient decay breathing behavior in the time domain. Furthermore, the duration of this transient decay breathing behavior is influenced by the pump power. Specifically, during the buildup process, a lower pump power results in a longer duration, while during the extinction process, a higher pump power leads to a longer duration. These results are significant for a deeper understanding of soliton generation and evolution, as well as for the design, optimization, and intelligent control of passive mode-locked fiber lasers.

We conduct real-time measurements of the complete temporal dynamics evolution of steady-state and breathing dissipative solitons in a passively mode-locked fiber laser under normal dispersion using the DTI technique. By adjusting the pump power, we achieve stable outputs of steady-state and breathing dissipative solitons and use the DTI technique to characterize their temporal dynamics. We measure the buildup and extinction processes of these solitons in real-time by controlling the pump power. During these processes, the pulses exhibit transient oscillatory breathing behavior in the time domain, and the time-domain position of the pulses correlates closely with the pump power. These temporal dynamics are crucial for the design optimization and intelligent control of mode-locked fiber lasers.

By varying the pump power, we observe the buildup of steady-state and breathing dissipative solitons, which occurs in three stages: relaxation oscillation (RO), decaying breathing (DB), and stable mode-locking. During the extinction process, steady-state dissipative solitons, due to their higher pump power and longer pump shutdown time, show more pronounced transient decaying breathing. In contrast, breathing dissipative solitons, with stable output at lower pump power and shorter pump shutdown time, exhibit less pronounced transient decaying breathing. The soliton’s temporal position changes in real-time due to gain losses. We also record the process of dissipative and breathing dissipative solitons gradually disappearing from a stable state, which also occurs in three stages: stable mode-locking, decaying breathing, and relaxation oscillation. During the extinction process, the steady-state dissipative soliton, due to its higher pump power and longer pump shutdown time, can experience multiple successive accumulations of mode-switching induced by the subsequent pump power, which makes its transient decaying breathing process more pronounced. In contrast, the breathing dissipative soliton, operating at a lower pump power with a shorter pump shutdown time, does not receive sufficient gain from the subsequent pump power to repeatedly meet the threshold condition. As a result, its transient decaying breathing process is less pronounced. Throughout the extinction process of both types of solitons, gain loss significantly influences the real-time changes in their temporal positions.

Both steady-state and breathing dissipative solitons in passive mode-locked fiber lasers exhibit transient oscillatory breathing behavior during their buildup and extinction processes. The duration of this behavior is influenced by the pump power. Specifically, higher pulse energy causes the pulse to appear earlier in the time domain, while lower energy causes it to appear later. An increase in gain or decrease in loss typically increases pulse energy, moving the pulse forward in the time domain, while a decrease in gain or increase in loss decreases pulse energy, moving the pulse backward. The temporal position of solitons is mainly influenced by refractive index and gain-loss effects. Precise control of gain-loss is crucial for designing and optimizing fiber lasers and for understanding and regulating soliton characteristics, including temporal position, pulse width, and spectral shape, thereby improving fiber laser performance and expanding their applications.