Fig. 1. Schemes of Fourier transform，inverse scattering transform and nonlinear Fourier transform^[40]. (a) Fourier transform；(b) inverse scattering transform；(c) nonlinear Fourier transform

Fig. 2. Nonlinear spectrum of optical signal^[43]

Fig. 3. Nonlinear frequency division multiplexing (NFDM) system^[52]. (a) Block diagram of NFDM transmission system；(b) pre-compensation signal；(c)-(e) comparison of OFDM and NFDM transmission performance under different constellations

Fig. 4. Relationship between the ratio of discrete spectral energy to total pulse energy and chirp parameters C and product of Aτ ^[74]

Fig. 5. Evolution of non-steady state soliton pulse^[74]. (a) Evolution of pulse；(b)-(c) evolution of discrete eigenvalues and continuous spectrum；(d) evolution of total energy，discrete spectrum energy and their ratio

Fig. 6. Evolution of steady-state soliton pulse^[74]. (a) Evolution of pulse；(b)-(c) evolution of discrete eigenvalues and continuous spectrum；(d) evolution of total energy，discrete spectrum energy and their ratio

Fig. 7. NFT characterization and reconstruction of single soliton pulse^[76]. (a) Continuous wave background；(b) evolution of dissipative soliton；(c) discrete eigenvalues；(d) pulse evolution reconstructed from discrete eigenvalues；(e) ratio of discrete spectrum energy to total pulse energy

Fig. 8. NFT reconstruction of three soliton pulses^[76]. (a) Original pulse evolution；(b) pulse evolution obtained by NFT reconstruction

Fig. 9. Experimental setup of dissipative soliton full-field information collection^[78]

Fig. 10. Eigenvalue distribution of unstable soliton^[78]. (a)-(b) Eigenvalue distribution correspond to different states in breath cycle；(c)-(d) eigenvalue distribution correspond to double soliton and three-soliton cases

Fig. 11. Calculation process of nonlinear spectrum of mode-locked fiber laser^[35]. (a) Experimental setup；(b) full-field reconstruction of mode-locked pulse obtained from single-sided spectrum；(c) relationship between time domain and nonlinear domain；(d) eigenvalue of pulse

Fig. 12. Real-time NFT data evolution obtained from measurement of fibre laser field^[35]. (a)(e) Real-time spatio-temporal dynamics of laser evolution obtained from full-field measurements；(b)(c)(f)(g) instantaneous NFT spectra obtained in different round trips；(d)(h) real-time evolution of imaginary parts of two largest discrete eigenvalues

Fig. 13. Temporal profile and eigenvalue of a theoretical soliton and a mode-locked laser pulse^[33]. (a) Temporal profile of a theoretical soliton；(b) eigenvalue of a theoretical soliton；(c) temporal profile arising in a mode-locked laser pulse；(d) eigenvalue distribution of a mode-locked laser pulse

Fig. 14. Temporal profiles and optical spectra of laser pulse，filtered soliton and theoretical soliton^[33]. (a)Temporal profiles；(b) optical spectra

Fig. 15. NFT data evolution obtained from double pulses under unstable (a)-(d) and stable (e)-(l) states^[34]. (a)(e)(i) Real-time spatial-temporal dynamics of laser evolution from full-field measurements；(b)(f)(j) evolution of imaginary parts of eigenvalues；(c)(g)(k) temporal profiles of laser pulse；(d)(h)(l) temporal profiles with soliton distillation