Optimal frequency combs from cnoidal waves in Kerr microresonators

We present a thorough computational study of the existence, stability, and comb properties of cnoidal waves—dissipative periodic patterns—in Kerr microresonators. We show that cnoidal waves comprise a large set with multiple periods. Optimal comb power efficiency and bandwidth are obtained for highly red-detuned, intermediate-strength pump, and short-period waves, that are similar to a train of cavity solitons. We demonstrate a deterministic access path for optimal waves that yields combs of soliton-class bandwidth with a much higher power efficiency.