Abstract

We propose a bifurcation analysis of Martin-Regalado et al [1] model equations for polarization switching in vertical-cavity-surface-emitting lasers. The model considers the active quantum well medium of the laser as a four-level system, includes both phase and amplitude anisotropy, and is described by five equations which are difficult to analyze. A first attempt to simplify these equations have been proposed recently by Travagnin et al [2] who eliminate adiabatically the two carrier variables. A similar objective is proposed in our analysis where the equations of Martin-Regalado et al [1] are examined using asymptotic methods. Taking advantage of the different orders of magnitude of typical values of the photon, spin and carrier lifetimes, we are able to reduce the problem from five to two equations only, thereby showing that the mode intensities obey a simple conservation law. The reduced problem reveals a strong amplitude/phase coupling and allow a complete analysis of the steady states and their bifurcations. We determine several Hopf bifurcations to time-periodic states which are leading to distinct branches of periodic states. Distinct orbits may coexist and merge together. These time-periodic orbits explain the oscillatory transitions between linearly polarized states noted ir. earlier numerical investigations.

© 1998 IEEE