Frequency comb generation threshold in $\chi^{(2)}$ optical microresonators

We investigate the threshold of $\chi^{(2)}$ frequency comb generation in lithium niobate whispering gallery microresonators theoretically and experimentally. When generating a frequency comb via second-harmonic generation, the threshold for the onset of cascaded second-order processes leading to a comb is found to be approximately 85 $\mu$W. The second-harmonic generation efficiency up to this value is in excellent agreement with a previously known theoretical framework. This framework is extended here, showing that the onset of cascaded $\chi^{(2)}$ processes and the maximum of the second-harmonic generation efficiency coincide. Furthermore, we observe that the frequency distance between the comb lines is a function of the pump power. It changes from 4 free spectral ranges at the oscillation threshold to 1 free spectral range at 590 ${\mu}$W.