Dual-mode self-injection locking in a laser diode-coupled-cavity system

Stabilized narrow-linewidth laser sources and soliton microcombs based on self-injection locking have driven revolutionary advancements from metrological to astronomical applications. Recently, coupled cavities have shown critical significance in optical frequency comb generation, particularly in achieving high conversion efficiency and enabling the formation of ultra-broadband soliton microcombs. In this work, we have developed a methodology for investigating self-injection locking in a laser diode-coupled-cavity system with Rayleigh backscattering. We have derived a set of rate equations to describe the system, obtained the analytical expression for effective detuning, and analyzed the critical coupling conditions and locking range for the coupled cavities. The analytical and numerical simulation results demonstrate that when the coupled-cavity structures induce mode splitting, the self-injection locking system exhibits dual-mode locking behavior. Furthermore, the auxiliary cavity introduces additional phase and losses to the coupled cavity, and the physical explanation for resonance splitting arises from the phase-balancing effect of pump detuning on the additional phase. On the other hand, the losses introduced by the auxiliary cavity can be effectively compensated by tuning the coupling strength between the waveguide and the main cavity. Therefore, we have also derived an analytical expression for the critical coupling coefficient in such laser diode-coupled-cavity systems. The proposed method can be extended to investigate self-injection locking in multi-coupled-cavity systems and provides a theoretical foundation for the realization of stabilized multi-frequency narrow-linewidth laser sources and high-efficiency, broadband soliton microcombs.