Effects of dissipation rates on dispersive waves and mode families in microresonators with avoided mode-crossing

In microresonators with avoided mode-crossing, the dispersive waves and mode families can be affected by dissipation rates, which also cause different hysteresis of the dispersive waves. Based on the Lugiato-Lefever equations and the single-mode dispersive wave model, the effects of dissipation rates on dispersive waves and mode families in microresonators are investigated. Results showed that the dispersive wave power curve exhibits hysteresis because of the avoided mode-crossing and the frequency shift curves can be convex, contrary to the absence of hysteresis. Moreover, the distribution of the two mode families in the microresonator is different at various detuning frequencies due to the dispersive wave, and it is relatively flat in the hysteresis state. The dispersive wave power and frequency shift are varied due to the different dissipation rates. The power of the two mode families decreases with the increase in mode dissipations. The results are significant for investigating dissipative Kerr solitons associated with dispersive waves in microresonators with avoided mode-crossing in practice.