  We study theoretically the non linear polarization dynamics of
Vertical-Cavity Surface-Emitting Lasers in the presence of an external cavity
providing delayed optical feedback and cross polarization re-injection. We show
that far from the laser threshold, the dynamics remains confined close to the
equatorial plane of a Stokes sphere of a given radius and we reduce the
dynamics to a dynamical system composed of two phases: the orientation phase of
the quasi-linear polarization and the optical phase of the field. We explore
the complex modal structure given by the double feedback configuration and
recovers as particular cases the Lang-Kobayashi modes and the modes founds by
Giudici et al. [1]. We also re-interpret the square waves switching dynamics as
phase kinks.
