The ECM-backbone of the Lang-Kobayashi equations:: A geometric picture

We perform an analytical study of the external cavity modes of a semiconductor laser subject to conventional optical feedback as modeled by the well-known Lang-Kobayashi equations. Specifically, the bifurcation set is derived in the three-dimensional parameter space of feedback phase, feedback strength and pump current of the laser. Different open regions in this space correspond to different numbers of physically relevant external cavity modes of the laser. Some of their stability properties are determined from the characteristic equation.