  Lasers can exhibit nonlinear and chaotic dynamics driven by the interaction
of multiple lasing modes, and investigating the different scenarios of mode
competition and bifurcations of their dynamics is of great interest on a
fundamental level as well as in view of applications. We study the dynamics of
a broad-area vertical-cavity surface-emitting laser (VCSEL) in solitary
continuous-wave operation with a comprehensive investigation of its
polarization state, lasing spectra, near-field distributions, and temporal
dynamics. Fluctuations at the frequency of birefringence splitting and other
frequency components develop in a series of bifurcations. The bifurcations
coincide with changes of the transverse lasing modes and/or the polarization
state, demonstrating the importance of both the spatial and polarization
degrees of freedom for mode competition. As a consequence, the inherent
nonlinear dynamics of broad-area VCSELs is significantly more complex than the
dynamics of VCSELs with a single spatial mode.
