A four-level model which takes account of the polarization of the laser field by including the spin sublevels of the conduction and valence bands of a semiconductor allows us to introduce vector rate equations which account for the polarization degree of freedom of the laser emission. Analysis of these rate equations and their extension to include transverse degrees of freedom provides important physical insight into the nature of polarization instabilities in surface-emitting semiconductor lasers. In the absence of transverse effects the model predicts a marginally stable linearly polarized state. The type of dynamical response of the polarization degrees of freedom is linked to the relative time scale of spontaneous-emission and spin-relaxation processes. With transverse effects included, we predict the existence of stable transverse spatially homogeneous intensity outputs with arbitrary direction of linear polarization in the transverse plane. The stability of the off-axis emission solutions to long-wavelength perturbations is investigated and, in addition to an Eckhaus instability associated with a global phase, we predict a polarization instability associated with a relative phase of the complex field vector. The role of phase anisotropy in the laser cavity is explored close to threshold and we predict that it stabilizes two preferred orthogonal directions of polarization, which, however, are discriminated in their stability properties by transverse effects.

• Received 12 January 1995

DOI:https://doi.org/10.1103/PhysRevA.52.1728