Dynamics of semiconductor lasers with filtered optical feedback

In the filtered optical feedback (FOF) scheme a part of the emission of the laser is spectrally filtered, for example by a Fabry-P´erot filter, and than fed back into the laser. If a semiconductor laser is subject to such delayed FOF qualitative different types of oscillations are possible: the well known relaxation oscillations and, more remarkably, frequency oscillations. We explain how the continuous wave operation of the FOF laser — the external filtered modes — lose their stability and the different types of oscillations arise due to the presence of the filter. This study is restricted to the case of a narrow filter. This means that there are only a few external filtered modes within the width of the filter, so that the influence of the feedback phase can be studied explicitly.