Transition From Short-to-Long Cavity and From Self-Mixing to Chaos in a Delayed Optical Feedback Laser

We analyze the regime of strong perturbation in a laser diode subjected to delayed optical feedback (DOF) from an external reflector, and study the intermediate region between short and long cavities, using Lang and Kobayashi equations to follow the dynamic regimes of the DOF system. We find that well-known regimes of unperturbed oscillations, period one, multi-periodic, and chaos are dictated by interplay of coupling factor K, distance L, and phase $\Phi ({\rm mod}.2\pi)$ of the external reflector, and linewidth enhancement factor $\alpha$ . We plot the boundaries of different regimes in the ${\rm K}\hbox {-}\Phi$ plane for several values of L and $\alpha$ , and characterize them in the transition from very short cavity $({\rm L}< 0.01~{\rm L}_{{\rm fr}})$ with negligible high-level effects, to long cavity $({\rm L}=0.5~{\rm L}_{{\rm fr}})$ where the ${\rm K}\hbox {-}\Phi$ plane is almost completely filled with chaos. We show that chaos and periodicity regimes are only found at ${\rm C}>1$ , though for ${\rm C}< 1$ the DOF system is also subject to self-mixing perturbations. Self-mixing induced FM and AM of the optical signal are found in all regions of stable oscillations, and for ${\rm C}>1$ frequency switching occurs at a certain $\Phi$ for any K and L. Chaos develops at increased K and L in correspondence to loci of frequency switching.