Soliton number as a critical degree of freedom for high-efficiency Kerr soliton crystals in microresonators

Soliton crystals have multiple self-organized temporal pulses filling the microresonator cavity and achieve high pump-to-comb conversion efficiency, making them of great interest in many potential applications such as communication and meteorology. Optimization of operational parameters such as pump power and coupling rates is a simple method for improving efficiency besides dispersion design. However, soliton number as a freedom has not been extensively investigated before. Here, we systematically investigate the dependence of efficiency on soliton number of soliton crystals, revealing a distinct nonmonotonic relationship. Through soliton number optimization, the system theoretically achieves 100% pump-to-comb conversion efficiency. Based on the model, we successfully achieved 40% efficiency of a $33\ifmmode\times\else\texttimes\fi{}\mathrm{FSR}$ (free spectral range) soliton crystal on a ${\mathrm{MgF}}_{2}$ platform. This work provides useful insights of efficiency into Kerr soliton microcombs, establishing guiding significance for high-efficiency microcomb generation.