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We consider a new class of periodic solutions to the Lugiato-Lefeverequations (LLE) that govern the electromagnetic field in a microresonatorcavity. Specifically, we rigorously characterize the stability and dynamics ofthe Jacobi elliptic function solutions of LLE and show that the dn solution isstabilized by the pumping of the microresonator. In analogy with solitonperturbation theory, we also derive a microcomb perturbation theory that allowsone to consider the effects of physically realizable perturbations on the combline stability, including effects of Raman scattering and stimulated emission.Our results are verified through full numerical simulations of the LLE cavitydynamics. The perturbation theory gives a simple analytic platform forpotentially engineering new resonator designs.

Stability and Dynamics of Microring Combs: Elliptic function solutions of the Lugiato-Lefever equation