Dynamics of microresonator frequency comb generation: models and stability

Microresonator frequency combs hold promise
for enabling a new class of light sources that are simultaneously
both broadband and coherent, and that could
allow for a profusion of potential applications. In this article,
we review various theoretical models for describing
the temporal dynamics and formation of optical frequency
combs. These models form the basis for performing numerical
simulations that can be used in order to better understand
the comb generation process, for example helping to
identify the universal combcharacteristics and their different
associated physical phenomena. Moreover, models allow
for the study, design and optimization of comb properties
prior to the fabrication of actual devices. We consider
and derive theoretical formalisms based on the Ikeda map,
the modal expansion approach, and the Lugiato-Lefever
equation. We further discuss the generation of frequency
combs in silicon resonators featuring multiphoton absorption
and free-carrier effects. Additionally, we review comb
stability properties and consider the role of modulational
instability as well as of parametric instabilities due to the
boundary conditions of the cavity. These instability mechanisms
are the basis for comprehending the process of frequency
comb formation, for identifying the different dynamical
regimes and the associated dependence on the
comb parameters. Finally, we also discuss the phenomena
of continuous wave bi- and multistability and its relation
to the observation of mode-locked cavity solitons.