We consider a new class of periodic solutions to the Lugiato–Lefever equations (LLE) that govern the electromagnetic field in a microresonator cavity. Specifically, we rigorously characterize the stability and dynamics of the Jacobi elliptic function solutions of the LLE and show that the dn solution is stabilized by the pumping of the microresonator. In analogy with soliton perturbation theory, we also derive a microcomb perturbation theory that allows one 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 cavity dynamics. The perturbation theory gives a simple analytic platform for potentially engineering new resonator designs.
|Original language||English (US)|
|Number of pages||13|
|Journal||Journal of the Optical Society of America B: Optical Physics|
|State||Published - Jun 1 2018|
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Atomic and Molecular Physics, and Optics