Fig. 1. Basic description of optical frequency combs. (a) Time-frequency characteristics of optical frequency combs^[15]; (b) optical frequency comb based on mode-locked fiber laser^[15]; (c) optical frequency comb based on on-chip microcavity^[16]

Fig. 2. The mode-locked microcombs under different second-order dispersion conditions. (a) The bright soliton microcomb in an anomalous dispersion microcavity^[15]; (b) the dark pulse microcomb in a normal dispersion microcavity^[16]

Fig. 3. The dispersion wave induced by the high-order dispersion in the anomalous dispersion microcavity^[40]. (a) The integrated dispersion profile and the principle of the dispersion wave; (b) the wideband mode-locked microcomb spectrum assisted by the dispersion wave

Fig. 4. Mode-locked microcombs dominated by high-order dispersion in near-zero dispersion microcavities. (a) Mode-locked microcomb dominated by the third-order dispersion^[48]; (b) mode-locked microcomb dominated by the forth-order dispersion^[49]; (c) mode-locked microcomb dominated by the fifth-order dispersion^[50]

Fig. 5. The influence of local dispersion changing. (a) The dispersion wave^[62]; (b) the high-conversion-efficiency soliton microcomb^[64]; (c) the microcomb stimulation in normal dispersion microcavities^[27] ; (d) the dark pulse microcomb in a normal dispersion cavity^[58]

Fig. 6. Dispersion engineering based on the design of waveguide structures. (a) The Influence of width and height of silicon nitride rectangular waveguides on integrated dispersion^[67]; (b) the tapered waveguide width scheme^[49]; (c) the concentric microresonator scheme^[24]; (d) local dispersion changing induced by inter-mode coupling in a multi-mode waveguide^[58]; (e) the tuning of resonance splitting based on the tuning of inter-mode coupling strength^[68]

Fig. 7. Dispersion engineering based on the photonic crystal microrings. (a) Dispersion tuning of single frequency^[76]; (b) dispersion tuning of multiple frequencies^[77]; (c) inverse-designed dispersion engineering^[78]

Fig. 8. Dispersion engineering based on the coupled microrings. (a) Local dispersion tuning using two similar microrings^[65]; (b) local dispersion tuning using a large ring and a small ring^[64]; (c) wideband dispersion tuning based on two similar microrings with strong coupling^[26]