Stability analysis of spin-polarized VCSELs

The ability to control the output polarization of spin-polarized VCSELs, by electrical injection and/or optical pumping of spin-polarized carriers, holds much potential for ultrafast all-optical elements. Research interest has been boosted by recent experimental demonstrations of electrically-pumped and optically-pumped spin VCSELs, Such devices can exhibit rich dynamics due to the competition of spin-flip processes and birefringence. Stability maps for spin-VCSELs dynamics are reported here, for the first time to our knowledge, using the spin flip model (SFM) and the largest Lyapunov exponent (LLE) method. Our approach accounts for dichroism and birefringence with rates ya and χρ, respectively, using the parameter set used. We choose fixed values of cavity decay rate tc = 125 ns" , carrier recombination rate γ = 1 ns" and ya = 0. The stability maps are presented in terms of polarization ellipticity P and normalized amplitude η of the pumping (electrical or optical); only negative values of P are shown since the results are symmetric about P = 0.