The split density model: a unified description of polarization and array dynamics for vertical cavity surface emitting lasers

A rate equation model describing the laser dynamics of general one or two dimensional vertical cavity surface emitting laser (vcsel) arrays is introduced. It is shown that the theory includes both the previous theory for edge emitting semiconductor laser arrays and the theory of polarization dynamics in single quantum well vcsels in a single unified description. The model is based on the physical assumption of separate carrier density pools individually coupled to different light field modes. These modes interact through the coherent light field dynamics derived from Maxwell's equations. The special case of two densities and two light field modes is solved and the implications for larger arrays are discussed. Our analytic results show that typical solutions of the split density model range from phase locking to chaos, depending on the magnitude of the coherent interaction. For weak coupling the stable supermode is always the mode of highest frequency. This indicates that anti-phase locking is the only stable phase locking possible in semiconductor laser arrays.