Tunable all-optical comb generation via harmonic locking of cascaded period-one dynamics

This work examines frequency comb generation in a cascaded arrangement of optically injected semiconductor lasers operating within the P1 dynamic regime. The system comprises two injection stages, where the first-stage laser is driven by a continuous-wave master laser, and its output is used to inject a second slave laser. By varying the injection strength and frequency detuning at each stage, frequency-locked comb states emerge, characterized by rational winding numbers that follow a Farey tree structure. These combs result from nonlinear interactions between the P1 oscillation frequencies of the two stages and exhibit tunable comb spacing without reliance on external modulators or high-frequency RF sources. The locked bands form Arnold tongues in the injection parameter space, within which period-doubling bifurcations lead to fractional comb spacing, indicating transitions to denser frequency comb states. The results reveal that the intrinsic P1 dynamics are responsible for the optical and microwave comb formation, enabling broadly tunable spacing beyond fractional harmonics of the free-running slave laser's relaxation resonance frequency. This highlights the potential of cascaded optical injection as a compact and versatile platform for all-optical frequency comb generation in semiconductor laser systems.