Fig. 1. The finite energy Airy beam's self-accelerating intensity profile and schematic diagram of weak diffraction and self-healing properties. (a) Self-accelerating intensity profile; (b) schematic diagram of weak diffraction and self-healing properties

Fig. 2. The time-domain and frequency-domain evolution diagrams of the decelerated FEAP pumped into the fiber.（a）Time-domain evolution diagram；（b）frequency-domain evolution diagram

Fig. 3. The output pulse shape when the decelerated FEAP peak power changes in the range of 1000‒2500 W

Fig. 4. The output spectra when the decelerated FEAP peak power changes in the range of 1000‒2500 W

Fig. 5. Signal to noise ratio and coherence of decelerated FEAP spectra with different peak power. (a) Signal to noise ratio; (b) coherence

Fig. 6. The time-domain evolution of decelerated FEAP under five different initial chirps. (a) C = -2; (b) C = -0.3; (c) C = 0; (d) C = 0.5; (e) C = 2

Fig. 7. Signal to noise ratio and coherence of decelerated FEAP spectra with different initial chirps. (a) Signal to noise ratio; (b) coherence

Fig. 8. Statistical figure of output soliton peak power when the pulse width is 370 fs

Fig. 9. The maximum value of the peak power of the output soliton, the number of twice the average value, the number of more than twice the average value, and the proportion of the trailing region in the overall range of the peak power of the output soliton for 500 simulations with different pulse widths

Fig. 10. Signal to noise ratio and coherence of decelerated FEAP spectra with different pulse widths. (a) Signal to noise ratio; (b) coherence

Fig. 11. The maximum value of the peak power of the output soliton, the number of twice the average value, the number of more than twice the average value, and the proportion of the trailing region in the overall range of the peak power of the output soliton for 500 simulations with different truncation coefficients

Fig. 12. Signal to noise ratio and coherence of decelerated FEAP spectra with different truncation coefficients. (a) Signal to noise ratio; (b) coherence

Fig. 13. The maximum value of the peak power of the output soliton, the number of twice the average value, the number of more than twice the average value, and the proportion of the trailing region in the overall range of the peak power of the output soliton for 500 simulations with different distribution factors

Fig. 14. Gaussian fitting curves of peak power of output solitons under different distribution factors. (a) Without trailing; (b) with trailing

Fig. 15. Signal to noise ratio and coherence of decelerated FEAP spectra with different distribution factors. (a) Signal to noise ratio; (b) coherence

Fig. 16. The results of promoting the generation of RWs. (a) MOPSO optimization results, illustrated by the corresponding decelerated FEAP waveform; (b) simulation results under optimal parameters

Fig. 17. The results of suppressing the generation of RWs. (a) MOPSO optimization results, illustrated by the corresponding decelerated FEAP waveform; (b) simulation results under optimal parameters