Semiconductor lasers as dynamical systems

Semiconductor lasers are being used every day in their millions, for example, in CD and DVD players and in optical communications networks. Mathematically, a semiconductor laser is a damped nonlinear oscillator. However, due to its nonlinear nature and a low reflectivity of its facet mirrors, such a laser may show an amazing range of complicated dynamics in the presence of external influences. In this paper we discuss two `classical' examples of laser systems to show how tools from dynamical systems theory can be used to understand their behaviour. First, we consider a semiconductor laser with optical injection and demonstrate that the bifurcation diagram of a three-dimensional vector field model is in excellent agreement with an experimental stability diagram. Second, we discuss a semiconductor laser receiving optical feedback of its own light after reflection on a mirror. This system is modelled by a system of delay differential equations, and we show how transitions to chaos can be understood with the help of numerical bifurcation techniques.