Mapping of delayed dynamics in short external cavity

Abstract

We study the influence of delayed optical feedback from a short external cavity on the emission dynamics of semiconductor lasers using the Lang and Kobayashi rate equation model. We present the bifurcation scenario leading to regular pulse packages (RPP) and give examples of bistability between RPP and time-periodic or steady state solutions. We investigate the change of the shape of the envelope of RPP in the transition to LFF. We analyze regions of feedback parameters for which RPP occurs. Detailed mapping shows that with increasing the delay time the windows of RPP broaden, merge and finally shrink when approaching the relaxation oscillation (RO) period. In such a way the largest region of RPP occurs for delays around half of the RO period of the solitary laser. Moreover, the period of RPP also possesses a minimum as a function of the delay time corresponding to approximately the half of the RO period. For smaller delays the RPP period shows an oscillatory behavior with the delay which we identify as being due to the destabilization of the RPP in the vicinity of newly born external cavity modes. Furthermore, we reveal continuous increase of the period of the RPP with the feedback rate. Finally, we study the scaling of the frequency of the pulse package envelope with the injection current. Our results contribute to better understanding of the origin and the peculiarities of the RPP dynamics.