Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity-part I: theoretical analysis

A two modes rate equation model for vertical-cavity surface-emitting lasers (VCSELs) subject to optical feedback from an extremely short external cavity (ESEC) is presented. By making use of it we develop a map of bistability to investigate the parametric dependence of polarization properties of VCSELs in such configuration, finding out a periodic dependence of the polarization switching (PS) currents on the ESEC length. By increasing the external mirror reflectivity we can make this periodic dependence stronger and strongly asymmetric providing the possibility to prevent PS for any injection current achieving polarization stabilization in VCSELs. Further numerical simulations with isotropic and non isotropic feedback show how parameters as the compression coefficients, the frequency splitting between the linearly polarized (LP) modes, the differential gain and the top mirror reflection coefficient, affect the map of bistability.