Eigenmodes and symmetry selection mechanisms in circular large-aperture vertical-cavity surface-emitting lasers

The characteristics of the spatial eigenmodes of vertical-cavity surface-emitting lasers with a large circular aperture are considered close to the lasing threshold. Experiments yield patterns based on rotational symmetry (“flowerlike” patterns) or on Cartesian symmetry (stripelike patterns) for very close operating conditions. The former are compatible with the boundary conditions whereas the latter are expected in infinite devices. Theoretically, the problem is considered in the framework of an eigenmode analysis of a linear partial differential equation for the optical field valid at threshold. This formulation allows for a simple implementation of asymmetries due to the reflection properties of Bragg mirrors as well as of transverse variations of gain and refractive index due to the device structure or due to imperfections in the growth process. A sharp transition between flowerlike modes and stripelike modes is shown to occur, if the device aperture is increased.