Locking range in a sideband-injection-controlled frequency comb

A microresonator-based optical frequency comb pumped by a continuous-wave laser and regulated by an independent, injected tone is studied with focus on the locking range wherein the repetition rate can be controlled by the auxiliary laser. A generic phase synchronization model applicable to co- and counter-propagating injected tones and predicated on experimentally motivated assumptions is derived and investigated. The predictions of the model are compared with numerical integration of coupled mode equations describing frequency combs and with experimental data, demonstrating rich dynamics and excellent agreement despite simplicity. Applications of sideband injection in Kerr microcombs including to low phase noise radio frequency generation and the realization of dissipative discrete time crystals are discussed.