Stable-unstable switching dynamics in semiconductor lasers with external cavities

Optical feedback in a semiconductor laser was recently used for photonic microwave square-wave generation by invoking quasiperiodicity for repeated switching between a stable stage of constant intensity and an unstable stage of intensity oscillations. Based on the Lang-Kobayashi model for a laser with external-cavity feedback, we investigate such stable-unstable switching dynamics. First, the model is verified to produce the stable-unstable switching dynamics as the feedback strength and delay are adjusted. The model agrees with former experiments in spite of previous doubts. Then, the analytical Hopf boundary for the minimum linewidth mode is derived to be matching the boundaries of the switching regions. Moreover, the trajectory in the plane of instantaneous frequency and gain is analyzed during the stable stage, where the laser is found to follow an ellipse in visiting different external cavity modes. Most importantly, an analytical derivation yields the switching period τ+τ_ɛ that is slightly expanded from the feedback delay time τ, where the expansion time τ_ɛ is found to be inversely proportional to the feedback strength. Such a switching period expansion explains the generation of a shifted frequency component below 1/τ in quasiperiodic laser dynamics. The results generally contribute to understanding the switching dynamics in photonic microwave generation.