Fig. 1. Pulse evolution process in GMN amplifier. (a) Seed pulse profile; (b) Self-similar pulse profile; (c) Pulse profile beyond the self-similar range; (d) GMN output pulse profile (Temporal intensity is solid blue line, instantaneous frequency is dashed red line) ^[26]

Fig. 2. Gain spectrum of Yb-doped fiber for varying levels of relative inversion

Fig. 3. Evolution process of pulse spectrum in GMN amplifier. (a)-(f) show the spectral evolution of the pulse (blue line) and the dynamic gain spectrum (red line); (g)-(l) The time domain evolution of the pulse ^[26]

Fig. 4. The correlation of STD and pump power. (a) Output energy and beam quality M² vary with pump power; (b)-(e) Output mode-resolved pulses at distinct pump power; (f) STD process in the GMN amplifier ^[27]

Fig. 5. The effect of SRS and GR on STD. (a) The variation curves of beam quality M² with pump power for the case with SRS and GR, the case without GR, and the case without SRS, respectively; (b) The walk-off between fundamental mode and higher-order mode vs pump power for the case with and without GR, respectively; (c) The energy distribution of various modes along fiber for the case with SRS and the case without SRS; (d) The energy distribution of various modes along fiber for the case with GR and the case without GR ^[27]

Fig. 6. Evolution of GMN in Yb-doped fiber amplifier with core diameter 10 μm. (a) Output pulse spectral profile; (b) Pulse peak power changes with gain fiber length

Fig. 7. GMN evolution under different pump wavelengths. (a) Spectral profile; (b) Pulse trace before compression; (c) Pulse trace after compression

Fig. 8. GMN evolution under different pumping configurations. (a) Spectral evolution under counter-pump and co-pump configurations; (b) Ratio of compressed pulse duration to transform-limit (top) and fraction of energy contained in the main peak (bottom) (The data of bidirectional pumping and reverse pumping in the figure are represented by blue and red lines, respectively) ^[28]

Fig. 9. GMN evolution with different pump powers under three pumping configurations. (a) Spectral profile; (b) Pulse trace before compression; (c) Pulse trace after compression

Fig. 10. Experimental evidence of a nonlinear attractor. (a) Output spectra of GMN amplifier under different seed pulse energies; (b) The corresponding compressed pulse trace in Fig.(a); (c) Output spectra of GMN amplifiers at different seed bandwidths (inset: seed spectrum); (d) The corresponding compressed pulse trace in Fig.(c) ^[26]

Fig. 11. GMN evolution under different seed pre-chirps. (a) Compressed pulse duration (top), the ratio between the transformation limit pulse duration and the corresponding compressed pulse duration (bottom); (b) The output spectrum profile of different seed pre-chirps; (c) Red line: compressed pulse trace, black line: transform-limit pulse trace ^[29]

Fig. 12. GMN amplification system based on Mamyshev oscillator ^[31]

Fig. 13. Schematic diagram of the GMN amplification system ^[33]

Fig. 14. Schematic of the all-fiber-structure GMN amplification system ^[34]

Fig. 15. Schematic diagram of the ultra-low repetition rate GMN amplification system ^[37]

Fig. 16. Schematic diagram of the all-fiber-integrated GMN amplification system ^[39]

Fig. 17. Schematic diagram of the birefringence phase-matched fiber OPCPA ^[40]

Fig. 18. Schematic diagram of OPA experiment system ^[41]

Fig. 19. Schematic diagram of all-fiber-integrated supercontinuum light source