Return-map for semiconductor lasers with optical feedback

It is well known that a semiconductor laser exposed to moderate optical feedback and biased near threshold exhibits the phenomenon of low-frequency intensity fluctuations (LFF). While this behavior can be numerically simulated using the so-called Lang-Kobayshi model, the interpretation of the phenomenon has remained a controversy. The LFF consist of a sudden drop in intensity followed by a build-up in steps of the external cavity roundtrip time, τ, before a new drop-out occurs. The phenomenon has been attributed to a kind of chaotic itinerancy and a bifurcation cascade has been identified very recently. These results give insight into the behavior observed on a short time-scale, but do not explain some of the pronounced features of the LFF seen for moderate feedback levels; namely the stepwise build-up and its characteristic time of about 15 steps close to the solitary laser threshold. We present new results related to the slow time-scale behaviour of LFF which give a simple explanation of these general characteristics, as well as providing a new tool for studying the statistics of the LFF