Polarization dynamics of vertical-cavity surface- emitting lasers with optical feedback

The standard two-mode rate equations are extended to discuss polarization behavior of vertical-cavity surface-emitting lasers (VCSELs) with optical feedback. In the rate equations, a logarithmic gain formula and unit step function are used to simulate the experimental conditions more truly. Our simulation results show that weak polarization-preserving feedback will cause multiple polarization switches (PSs) with increasing bias current; strong feedback can suppress PSs and make the VCSEL work in a single polarized mode. The case is similar when y-polarized feedback is considered. The PS point does not disappear even under strong x-polarized feedback. Bifurcation diagrams show that the interplay of PSs and delayed feedback makes the nonlinear dynamics of the two polarized modes more complex. If the feedback is large enough, both chaotic pulses due to feedback and low-frequency fluctuations due to gain competition emerge in the time traces of the two modes. Polarization modulation is also demonstrated when a quarterwave plate is added to the external cavity, which agrees with the experimental observations.