Fig. 1. Diagram of changing arrangement of liquid crystals by changing applied electric field^[28]

Fig. 2. Output spectra and autocorrelation traces of laser^[30]. (a) Output spectrum with 160 GHz repetition rate and 1561.5 nm wavelength; (c) output spectrum with 160 GHz repetition rate and 1542 nm wavelength; output spectra with (d) 40 GHz repetition rate and (f) 640 GHz repetition rate; output autocorrelation traces of different repetition rates at repetition rate of (b) 160 GHz, (e) 40 GHz, and (g) 640 GHz

Fig. 3. Output for different net dispersion values of 0.4 ps², 0.5 ps², and 0.8 ps^2[31]. (a1)‒(a3) Optical spectra; (b1)‒(b3) FROG spectrograms; (c1)‒(c3) recovered field intensity (solid) and phase (dashed) from FROG

Fig. 4. Cavity outputs controlled by different dispersion scale factor α^［32］. (a) Transmission of SLM and group delay corresponding to different dispersions; (b) pulse spectra before SLM; (c) autocorrelation traces after SLM; (d) FWHM and TBP of pulses after SLM

Fig. 5. Temporal intensity, chirp profiles, and spectral intensity profiles of pulse, with black solid lines corresponding to before SLM, blue solid lines corresponding to after SLM, dashed red lines corresponding to shaping target, and solid green lines corresponding to after gain fiber^[33]. (a) Bright parabolic line; (b) dark parabolic line; (c) flat-top; (d) triangular; (e) saw-tooth

Fig. 6. Typical measured optical spectra (left) and auto correlation traces (right) for output soliton (black), stretch pulse (red), and dissipative soliton (blue)^[34]

Fig. 7. Quaternary encoding based on time separations of soliton molecules^[35]. (a) Measured single-shot spectrum for string (0|3|1|2|0|3);(b) corresponding time separations of six soliton molecule states;"Ψ"in (c) binary and (d) quatermary encoding systems; (e) measured single-shot spectrum for"Ψ"with 36 encoding holograms; (f) corresponding time separations of soliton molecules extracted from encoding sequence with 36 holograms

Fig. 8. Experimental results of synchronized dual-wavelength mode-locked solitons^[37]. (a) Spectrum of pulses, filtering and group delay imparted by SLM; (b) pulse train and radio frequency spectrum of wavepacket; (c) FROG spectrograms; (d) retrieved pulse profile; (e) autocorrelation trace and the sech² fitting line; (f) frequency difference and sub-pulse separation versus imparted group delay dispersion

Fig. 9. Heteronuclear multicolor soliton compound (HMSC) fiber laser^[38]. (a) Experimental setup (WDM: wavelength division multiplexer; EDF: erbium-doped fiber; OC: output coupler; PI-ISO: polarization-insensitive isolator; PPS: programmable pulse shaper; PC: polarization controller; CNT-SA: carbon nanotube saturable absorber); (b) principle and function of PPS

Fig. 10. Properties of HMSC with different amplitudes of concave phase^[38]. (a)‒(c) Spectra, phases, and filtering shapes; (d)‒(f) FROG spectrograms and retrieved pulses

Fig. 11. Principle of operation of pure-quartic soliton laser^[41]. (a) Schematic of erbium doped laser cavity (Er³⁺: erbium-doped fibre; LD: laser diode; FP: in-line fiber polarizer; PC: polarization controller; SLM: spatial light modulator; OC: output coupler); (b)(c) conceptual illustrations of quadratic and quartic dispersive phases imparted by the cavity (dot dash line) and SLM (dotted line), with the net quadratic and quartic phases shown in solid line

Fig. 12. Sideband analysis^[41]. (a) Positions of marked sidebands; (b) fourth power of sideband positions as a function of sideband order; (c) measured optical spectra that correspond to shortest pulse duration recorded for different dispersion, from top to bottom: -20 ps⁴/km, -40 ps⁴/km, -60 ps⁴/km, -80 ps⁴/km, -90 ps⁴/km,-100 ps⁴/km,and -110 ps⁴/km; (d) corresponding fourth power of sideband positions as a function of sideband order

Fig. 13. Stable output with different fourth order dispersions^[45]. (a) Schematic of passively mode-locked fiber laser used for simulations;(b) phase curves; (c) pulse profiles; (d) pulse spectra

Fig. 14. Pulsating regime of pure-quartic soliton^[45]. (a) Evolution in time domain and flow of energy; (b) evolution in spectral domain

Fig. 15. Evolution of pure-quartic soliton with different E_s values. (a) Normalized peak intensity evolution; pulse profiles obtained when (b) E_s is 160 pJ and (c) E_s is 130 pJ, respectively

Fig. 16. Experimentally measured shot-to-shot spectra over 6000 roundtrips under different compensated dispersion of fiber laser^[46]. (a) -0.18 ps/nm; (b) -0.17 ps/nm; (c) -0.15 ps/nm; (d) -0.12 ps/nm

Fig. 17. Control of mode-locking states using SLM^[48]. (a) Optical spectra corresponding to reversible transitions from CW to mode locking. Corresponding spectral filters applied by SLM are shown at top; (b)(c) autocorrelations and optical spectra corresponding to repeatable irreversible transitions; (d) autocorrelation trace of 40 fs long pulses. Inset shows corresponding optical spectrum; (e) autocorrelation traces showing SLM-based pedestal removal. Inset shows corresponding optical spectra. Black (red) lines correspond before (after) filtering; (f) elimination of undesired, characteristic spectral structure for wave-breaking-free laser operating near its stability limit in terms of pulse energy. Autocorrelation trace is shown. Inset shows spectra before filtering (black line) and after filtering (red line) along with filter transmission pattem

Fig. 18. Schematic diagram of genetic multi-dimensional fibre laser using wavefront shaping^[50]

Fig. 19. Mode profile cleaning of multi-dimensional fibre laser with genetic algorithm optimization working in quasi-CW state^[50]. (a) Mode profile before genetic algorithm optimization, recorded by CCD camera; (b) mode profile after genetic algorithm optimization; (c) line profiles of mode patterns; (d) mass factors M² for x and y directions; (e) intensity evolution of targeted area selected for genetic algorithm optimization; (f) corresponding optical power evolution during mode profile optimization

Fig. 20. Wavelength manipulation of multi-dimensional fibre laser with genetic algorithm optimization working in quasi-CW state^[50]. (a) Evolution of wavelength switching; (b) optical spectra before and after wavelength switching;(c) intensity evolution at wavelengths of 1035 nm and 1060 nm; (d) improved evolution process; (e) optical spectra before and after side mode suppression ratio improvement; (f) wavelength tuning of genetic algorithm

Fig. 21. Automatic mode-locking manipulation of multi-dimensional fibre laser with genetic algorithm optimization^[50]. (a) Evolution of cost function value during mode-locking of genetic algorithm; (b) temporal signals before and after mode-locking; (c) optical spectra without and with mode-locking, only one of CW wavelength components has evolved into mode-locking state; (d) RF signals before and after mode-locking; (e) autocorrelation traces of chirped and dechirped pulses; (f) generation of multiple pulses

Fig. 22. Evolutionary algorithm optimized fiber laser ^[51]. (a) Schematic of fiber laser (LC represents liquid-crystal retarder);(b) schematic of homemade pulse shaper containing two gratings (G), two cylindrical lenses (L), and dual-mask SLM in Fourier plane; (c) graph presenting typical spectral transmission induced by pulse shaper for generation of two-soliton molecules