Phase dynamics in vertical-cavity surface-emitting lasers with delayed optical feedback and cross-polarized reinjection

Abstract

We study theoretically the nonlinear polarization dynamics of vertical-cavity surface-emitting lasers in the presence of an external cavity providing delayed optical feedback and cross-polarized reinjection. We show that, far from the laser threshold, the dynamics remains confined close to the equatorial plane of a Poincar\'e sphere with a fixed radius. It entails that the evolution of the system is described by two phase variables: the orientation phase of the quasilinear polarization and the optical phase of the field. We explore the complex modal structure given by the double reinjection configuration and how it evolves between the cases of single cross-polarized reinjection and single optical feedback, hence disclosing the relationship with the Lang-Kobayashi model. We also reinterpret the square-wave switching observed by J. Mulet et al. [Phys. Rev. A 76, 043801 (2007)] in terms of phase kinks.