Stable microwave oscillations due to external-cavity-mode beating in laser diodes subject to optical feedback

Laser diodes subject to a delayed optical feedback may exhibit high-frequency oscillating intensities as a result of a beating between two external-cavity-modes (ECMs). We analyze the conditions for the stability of these microwave oscillations in the framework of the Lang-Kobayashi equations for a single-mode edge-emitting semiconductor laser [R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980)]. We show that two different scenarios are possible. If the linewidth enhancement factor is relatively large (α=2-5), the beating occurs between a stable ECM (mode) and an unstable ECM (antimode). The stability of the time-periodic solution is then limited in parameter space. But if the linewidth enhancement factor is sufficiently low (α≤αc≅1), a beating between two stable modes is possible allowing stable high-frequency oscillating outputs