Universal Kerr-Thermal Dynamics of Self-Injection-Locked Microresonator Dark Pulses

Microcombs, formed in optical microresonators driven by continuous-wave lasers, are miniaturized optical frequency combs. Leveraging integrated photonics and laser self-injection locking, compact microcombs can be constructed via hybrid integration of a semiconductor laser with a chip-based microresonator. While the current linear self-injection locking theory has successfully addressed the linear coupling between the laser cavity and the external microresonator, it fails to describe the complicated nonlinear processes, especially for dark-pulse microcomb formation. Here, we investigate-theoretically, numerically, and experimentally-the Kerr-thermal dynamics of a semiconductor laser self-injection locked to an integrated silicon nitride microresonator. We unveil intriguing yet universal dark-pulse formation and switching behavior with discrete steps, and establish a theoretical model scrutinizing the synergy of laser-microresonator mutual coupling, Kerr nonlinearity, and photothermal effect. Numerical simulation confirms the experimental result and identifies the origins. Exploiting this unique phenomenon, we showcase an application on low-noise photonic microwave generation with phase noise purified by 23.5 dB. Our study not only adds critical insight of pulse formation in laser-microresonator hybrid systems, but also enables all-passive, photonic-chip-based microwave oscillators with high spectral purity.