Dissipative Solitons in Microresonators

In this Chapter we will illustrate the state-of-art in the generation of dissipative solitons in Kerr microresonator-based systems. After a brief introduction on the origin of this field of research, we will discuss the modeling of these microcavities using the generalized Lugiato-Lefever equation. Further, we will discuss the different techniques used for dispersion engineering in these systems. We will then focus on the description of the frequency combs generated by microring resonators in the Kerr soliton regime and illustrate different schemes that have been developed in this context to grant better control of the microcavity dynamics. Finally, we will review the large number of applications that these objects have originated in several fields of optics.