Bifurcation analysis of frequency locking in a semiconductor laser with phase-conjugate feedback

We present a detailed study of the external-cavity modes (ECMs) of a semiconductor laser with phase-conjugate feedback. Mathematically, lasers with feedback are modeled by delay differential equations (DDEs) with an infinite-dimensional phase space. We employ new numerical bifurcation tools for DDEs to continue steady states and periodic orbits, irrespective of their stability. In this way, we show that the periodic orbits corresponding to the ECMs are connected to the steady state solution associated with the locking range of the laser. We also identify symmetric and nonsymmetric homoclinic orbits and hysteresis in the system

Accumulating regions of winding periodic orbits in optically driven lasers

We investigate the route to locking in class B lasers subject to optically injected light for injection strengths and detunings near a codimension-two saddle-node Hopf point. This is the parameter region where the Adler approximation is not valid and where Yeung and Strogatz recently reported a self-similar cascade of periodic orbits in the case of a solid-state laser. We explain this cascade as an accumulation of large regions bounded by saddle-node bifurcations of periodic orbits, but also containing further bifurcations, such as period-doubling, torus bifurcations and small pockets of chaos. In the vicinity of the simultaneous saddle-node and Hopf bifurcations, successive periodic orbits wind more and more near the point in phase space where the saddle-node bifurcation is about to occur. This leads to a self-similar period-adding cascade. By varying the linewidth enhancement parameter α from zero, the case of a solid-state or C

Stability implications of delay distribution for first-order and second-order systems

Kiss, G., & Krauskopf, B. (2009). Stability implications of delay distribution for first-order and second-order systems. Early version, also known as pre-print Link to publication record in Explore Bristol Research PDF-documen