Semiconductor laser with filtered optical feedback: bridge between conventional feedback and optical injection.

We study a model for a semiconductor laser subject to filtered optical feedback, i.e. a system of delay differential equations (DDEs). In this model, the filter is characterized by a mean frequency Omega(m) and a filter width A. In the limit of a narrow filter (lambda -> 0), the laser equations reduce to the equations for a laser with optical injection, whereas they become the Lang-Kobayasbi equations in the limit of an unbounded filter width (lambda ->infinity). We perform a bifurcation analysis of steady-state solutions with the parameter A as main bifurcation parameter. In this way, we get an insight in the relation between the filter width and the number of possible steady states. In particular, we obtain the result that there exist parameter regions in which the number of possible steady states decreases when), is increased. From a mathematical point of view, our approach to combine information about limiting systems with precise bifurcation results may be of interest for a wider class of systems of DDEs.