Whispering gallery mode resonators (WGMRs) are a promising platform for the generation of entangled photons and by extension their use in quantum communication and more
specifically quantum key distribution protocols. Furthermore, some quantum communication protocols require the use of a pulsed source in order to work. In this document, we show the
design of an optical pulse generator relying on time-lens assisted soliton compression and generating picosecond pulses at GHz repetition rate. We study the dynamics of Kerr combs arising inside a magnesium fluoride whispering gallery mode resonator when it is driven by a pulsed source with a repetition rate closely matched to the free spectral range of the resonator.

The dynamic of the light inside the resonator was simulated with a model based on the classic Lugiato-Lefever equation that take into account the pulsed nature of the source and implement
it numerically as to compare it to experimental result. An emphasis is set specifically on the effect of the frequency mismatch between the repetition rate of the pulsed laser and the free spectral range of the cavity. The results presented in this document were also used in the writing of the scientific paper : Thomas Daugey, Cyril Billet, John Dudley, Jean-Marc
Merolla, and Yanne K Chembo. Kerr optical frequency comb generation using whisperinggallery- mode resonators in the pulsed-pump regime. Physical Review A, 103(2):023521,
2021.