Static and dynamic characteristics of VCSELs with polarisation-selective optical feedback

Static and dynamic characteristics of birefringent vertical-cavity surface-emitting lasers (VCSELs) subject to both isotropic and polarisation-selective optical feedback are investigated theoretically. The model considers two orthogonally polarised transverse modes; moreover, the spatial dependences of photon density, carrier density and injection current are taken into account. For a short external cavity, the two-mode VCSELs can be forced to operate with one mode by introducing the polarisation-selective optical feedback. It is further shown that the phase of feedback light determined by the external cavity length affects the laser operation characteristics greatly, that is, when the external cavity length is chosen, the reflected light strengthens (weakens) the optical field in the laser cavity, the mode that has the same polarisation direction can be enhanced (suppressed), while the other mode is suppressed (enhanced) correspondingly. For a relatively long external cavity, the continuous wave operation of VCSELs is destabilised and rich non-linear dynamics are excited. By increasing the external cavity length, the VCSELs follow a period-halving route to chaos. It is also found that the evolution of dynamics shows periodic repetition with respect to the external cavity length, and the period is half of the lasing wavelength. Further investigation shows that, for isotropic feedback, both modes exhibit the same dynamics and similar mode intensity; for polarisation-selective feedback, though similar non-linear behaviours are observed, the modal strengths are quite different, that is, the feedback light enhances one mode while greatly suppressing the orthogonally polarised mode.