Fig. 1. Schematic of the experimental setup. (a) Illustration of an SMF. (b) The fiber ring laser configuration. EDF, erbium-doped fiber; DCF, dispersion compensation fiber; SMF, single-mode fiber; ISO, polarization-independent isolator; WDM, wavelength division multiplexer; OC, output coupler; BS, beam splitter; PD, photodetector; PC, polarization controller; OSC, oscilloscope; OSA, optical spectrum analyzer. (c)–(e) Schematic illustration on different states of the dark and anti-dark soliton molecules.

Fig. 2. Summary of theoretical predictions on various vector soliton solutions based on the CNLSEs or higher-order CNLSEs in different dispersion regions I to VI. Horizontal axis indicates magnitude of GVD (light to dark color corresponds to weak to strong GVD dispersion; red, normal GVD; blue, anomalous dispersion). Atomic representations of the cubic dispersion supported soliton molecules. Red-shaded circle: atomic representation for a dark soliton formed in the normal GVD regime; light red-shaded circle: atomic representation for an anti-dark soliton formed in the near ZGVD regime. Stripe notation: the intramolecular bond between orthogonally polarized solitons. Spring notations: the intermolecular bond between solitons with same polarization and different wavelengths.

Fig. 3. A state of vector dark soliton emission. (a), (b) Evolutions of the polarization-resolved dark solitons with the cavity round trips. (c) Polarization-resolved laser emissions. (d) The corresponding optical spectra of (a) and (b).

Fig. 4. A state of vector dark–anti-dark soliton emission. (a), (b) Evolutions of vector dark and anti-dark solitons. (c) Polarization-resolved laser emissions. (d) The corresponding optical spectra of (c).

Fig. 5. A state of coexistence of vector dark and vector anti-dark solitons. (a) Polarization-resolved laser emissions. (b) The optical spectra of (a).

Fig. 6. A state of vector dark–anti-dark solitons and the coexistence of vector dark, anti-dark, and vector dark–anti-dark solitons. Yellow shaded area: vector dark–anti-dark solitons, dark (anti-dark) solitons polarized along the vertical (horizontal) axis.

Fig. 7. A state of “pure” vector anti-dark soliton emission. (a), (c) Evolution of anti-dark solitons along two orthogonal polarization axes, respectively. (b) Polarization-resolved laser emissions. (d) The optical spectra of (a) and (c).

Fig. 8. (a) A state of coherently coupled vector anti-dark soliton emission. (b) Experimentally measured autocorrelation trace.

Fig. 9. A state of coexistence of vector dark and vector anti-dark soliton molecules. (a) Polarization-resolved laser emissions. (b) Corresponding optical spectra of (a). (c) Schematic illustration of the central wavelengths of vector dark and anti-dark solitons in normal dispersion regime. λ0, position of ZGVD point; λ1,u, wavelength of the dark and anti-dark solitons formed along horizontal axis; λ1,v, wavelength of the dark and anti-dark solitons formed along vertical axis.

Fig. 10. A state of laser emission where only the vector anti-dark soliton molecules are detectable.