Breathing pulses, as a unique nonlinear pulse phenomenon, play a key role in laser performance optimization, nonlinear optical processes, and complex signal transmission. Unlike stable solitons, the energy of breathing pulses fluctuates periodically over time, exhibiting periodic changes in both pulse frequency and amplitude. Through appropriate nonlinear effects, lasers can generate stable breathing pulses, achieving a mode-locked state that demonstrates a periodic "breathing" pattern. Based on this, a fiber laser incorporating a saturable absorber as the mode-locking element was designed and built, and stable breathing states were successfully observed at lower pump power levels. High-speed detection techniques and time-stretched dispersive Fourier transform (TS-DFT) technology were used to time-amplify and spectrally analyze the rapid pulses, while monitoring the evolution of the breathing pulse in both time and frequency domains. Experimental results indicate that changes in pump power significantly affect the periodic modulation induced by additional oscillations, thereby controlling the breathing ratio and ultimately leading to the formation of a stable soliton. When the pump power is between 470 mW and 480 mW, the formation of the breathing pulse was first observed, with a breathing ratio of up to 4.5. As the pump power increases, the breathing effect gradually diminishes, and at 510 mW, it completely disappears, with the breathing ratio dropping to 1.
These results confirm the critical role of pump power in controlling the breathing pulse state and its transition, demonstrating the potential for controlling pump power in ultrafast laser technology and nonlinear optics. The breathing pulse phenomenon, as a periodic pulse behavior, reflects the complex dynamical characteristics between nonlinear optical effects and cavity parameters. When combined with the natural synchronization system formed between the breathing frequency and the cavity frequency (determined by the cavity length), the periodic change of the breathing pulse becomes a crucial factor for controlling laser output. By adjusting parameters such as the laser’s nonlinearity and dissipation, the characteristics of the breathing pulse and breathing ratio can be precisely controlled, thus achieving precise control of the laser output. The periodic oscillatory characteristics of the breathing pulse inside the laser cavity lead to the non-uniform distribution of pulses, a feature that demonstrates enormous potential in pulse shaping, ultrashort pulse generation, and precise frequency comb control. Additionally, the presence of the breathing pulse may impact the stability and energy conversion efficiency of the laser, offering new perspectives for laser design and optimization.