Fig. 1. The experimental configuration. (a) The ultrafast fiber laser setup. Controlling the SMs in the laser can be done in the EPC-based feedback loop. The spectral information is obtained through the OSA or oscilloscope along with TS-DFT, where the FBG is used as the dispersion medium. WDM, wavelength division multiplexing; TDF, thulium-doped fiber; PDI, polarization-dependent isolator; EPC, electronic polarization controller; OC, optical coupler; FBGA, field-programmable gate array; PC, computer; DAC, digital-to-analog converter; FBG, fiber Bragg grating; Circ, circulator. (b) The flow chart of the EA.

Fig. 2. Spectral shape programming of SMs. (a)–(h) Spectrum programming results of doublet SM. (a), (d) Acquired and standard doublet SM spectrum with NMSE of 0.0051 and 0.0010, respectively. (b), (e) DFT spectra and (c), (f) field autocorrelation trace evolution over consecutive RTs corresponding to (a) and (d), respectively. (g) DFT spectra and (h) field autocorrelation trace evolution of doublet SM deterministic switching (a)–(d). (i)–(p) Spectrum programming results of triplet SM. (i), (l) Acquired and standard triplet SM spectrum with NMSE of 0.0005 and 0.0042, respectively. (j), (m) DFT spectra and (k), (n) field autocorrelation trace evolution over consecutive RTs corresponding to (i) and (l), respectively. (o) DFT spectra and (p) field autocorrelation trace evolution of triplet SM deterministic switching (i)–(l).

Fig. 3. Pulsation SM with and without EA optimization. (a) Sketch of the RF signal under pulsation SM operation, where fr is the cavity repetition rate and the sideband frequency f±1 is a manifestation of SMs with pulsation frequency |f±1−fr|. (b) Evolution of the best merit score over successive generations. RF spectra of SM in (c) with pulsation frequency locking correspond to a single-mode oscillation and in (d) without pulsation frequency locking correspond to unstable multimode oscillation. (e) DFT spectra and (f) field autocorrelation trace evolution of frequency-locked pulsation SM showing a well-defined periodicity. (g) DFT spectra and (h) field autocorrelation trace evolution of frequency-unlocked pulsation SM showing a degraded periodicity.

Fig. 4. Evolutionary algorithm optimization results for doublet SMs with a tunable pulsation ratio. Dynamics of doublet SMs with (a)–(c) small, (d)–(f) moderate, and (g)–(i) large pulsation ratios. (a), (d), and (g) DFT spectral evolution over consecutive cavity RTs. (b), (e), and (h) Field autocorrelation trace evolution over consecutive cavity RTs. (c), (f), and (i) Single-shot spectra of maximal and minimal spectrum extents within a pulsation period.

Fig. 5. Evolutionary algorithm optimization results for (2+2) SMCs with a tunable pulsation ratio. Dynamics of (2+2) SMC with (a)–(e) small, (f)–(j) moderate, and (k)–(o) large pulsation ratio. (a), (f), (k) DFT spectral evolution over consecutive cavity RTs. (b), (c), (g), (h), (l), and (m) Field autocorrelation trace evolution over consecutive cavity RTs. (d), (e), (i), (j), (n), and (o) Single-shot spectra of maximal and minimal spectrum extents within a pulsation period.

Fig. 6. Controllable continuous switching of doublet and triplet SMs. (a)–(h) Controllable switching of doublet SM. (a), (b) Continuous switching of stationary SM with different temporal separations. (c), (d) Continuous switching of SM between pulsation and stationary states. (e), (f) Continuous switching of SM among three states. (g), (h) Continuous switching of SM among four states. (i)–(j) Controllable switching of triplet SM. (k)–(l) Continuous switching of SM between two states with different temporal separations. (a), (c), (e), (g), (i), and (k) DFT spectral evolution over consecutive cavity RTs. (b), (d), (f), (h), (j), and (l) Field autocorrelation trace evolution over consecutive cavity RTs.

Fig. 7. Exemplary multiletter encoding based on the doublet SM of four assembled forms. (a), (d) Successive recording of the encoded DFT streams. The pump power is set at 420 mW, and the EPC is modulated by four different drive voltages. (b), (e) Field autocorrelation trace evolution. (c), (f) ASCII quaternary format codes for each letter, which contain four bits. (g) Visualization of each letter. Each frame is composed of four time slots and represents a single letter.