Stability and Dynamics of Microring Combs: Elliptic function solutions of the Lugiato-Lefever equation
arXiv:1712.00417 · doi:10.1364/JOSAB.35.001341
Abstract
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 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 comb line 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.
orig: 13 pages, 14 figures. post-peer-review update 1: 13 pages 11 figures, corrected derivation of modulation equations, corrected proof of prop 1, numerical results and conclusions unchanged, fixed typos, added refs to background section, clarifications, aesthetic changes to figs, removed unnecessary background
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