External cavity mode structure of a two-mode VCSEL subject to optical feedback

We consider a multi-transverse-mode vertical-cavity surface-emitting laser (VCSEL) subject to optical feedback. The system is modeled by a partial differential equation for the spatial carrier population, which is coupled to delay differential equations for the electric fields of the participating transverse modes that are subject to external optical feedback. We consider here the case that the VCSEL supports the two basic, rotationally symmetric, linearly polarized optical modes LP01 and LP02. In our model each LP mode receives feedback not only from itself but also from the other LP mode; the amount of cross-feedback can be controlled by a parameter. Specifically, we use numerical continuation techniques to present a detailed analysis of the steady state, external cavity mode (ECM) structure in dependence on the feedback strength, the feedback phase and the amount of cross-feedback. This shows that the case of zero cross-feedback is degenerate and changes quite dramatically even in the presence of small feedback from the other transverse mode. On the other hand, in an intermediate range of cross-feedback the ECM structure does not change qualitatively in a physically relevant range of feedback strength. We consider the entire transition from zero cross-feedback to zero self-feedback, in which we identify the key changes in the ECM structure.