Nonlinear frequency combs generated by cnoidal waves in microring resonators

Cnoidal waves are the periodic analog of solitons. Like solitons, they can be generated in microresonators and correspond to frequency combs. The generation of frequency combs in nonlinear microresonators is modeled by the Lugiato–Lefever equation. In this paper, we study the Lugiato–Lefever equation for a microresonator in the anomalous dispersion regime. In the lossless case, we show that the cnoidal waves can be expressed as a combination of Jacobi elliptic functions. These solutions reduce to known soliton-like solutions in particular cases. The properties of cnoidal waves in the realistic lossy case and their potential uses are also discussed.