Rate equations for vertical-cavity surface-emitting lasers

By applying a multiple time scale perturbation method, we simplify the spin-flip model equations [San Miguel et al., Phys. Rev. A $52,$ 1728 (1995)] describing the polarization behavior of vertical-cavity surface-emitting lasers. The reduced problem consists of three rate equations for a two-mode semiconductor laser. The asymptotic theory is based on the natural values of the laser parameters and considers the case of large values of the spin-flip rate and birefringence with respect to the relaxation oscillation frequency. Our analysis corrects and complements previous derivations of rate equations from the spin-flip model equations. We find that the cross-gain saturation coefficients due to spin-flip processes are not symmetric and may become negative. As a result, a new physical interpretation of polarization switching from the high-frequency mode to the low-frequency mode and for high values of the birefringence is possible.