Intensity equations for birefringent spin lasers

Semiconductor spin lasers are distinguished from their conventional counterparts by the presence of spin-polarized carriers. The transfer of angular momentum of the spin-polarized carriers to photons provides important opportunities for the operation of lasers. With the injection of spin-polarized carriers, which lead to the circularly polarized light, the polarization of the emitted light can be changed an order of magnitude faster than its intensity. This ultrafast operation of spin lasers relies on a large birefringence, usually viewed as detrimental in spin and conventional lasers. We introduce a transparent description of spin lasers using intensity equations which elucidate the influence of birefringence on the intensity and polarization modulation of lasers. Unlike commonly describing the role of birefringence on laser dynamics by employing complex quantities, our approach is simpler, because it is relying on real quantities and allowing analytical solutions. While intensity modulation is independent of birefringence, for polarization modulation an increase in birefringence directly increases the resonant frequency. Our results for dynamical operation of lasers provide a guide for their spin-dependent response and spintronic applications beyond magnetoresistance.