Characterizing the dynamics of cavity solitons and frequency combs in the Lugiato-Lefever equation.

In this work we present a detailed analysis of bifurcation structures of cavity solitons (CSs) and determine the different dynamical regimes in the Lugiato-Lefever (LL) equation in the presence of anomalous and normal chromatic dispersion regimes. Such an analysis has been shown to also increase our understanding of frequency combs (FCs). A FC consists in a set of equidistant spectral lines that can be used to measure light frequencies and time intervals more easily and precisely than ever before. Due to the duality between CSs in microcavities and FCs, we can gain information about the behavior of FCs by analyzing the dynamics of CSs. In the anomalous dispersion case bright CSs are organized in what is known as a homoclinic snaking bifurcation structure. In contrast, in the normal dispersion regime dark CSs are organized differently, in a structure known as collapsing snaking. Despite the differences in bifurcation scenarios, both types of CSs present similar temporal instabilities.