Vector order parameter for an unpolarized laser and its vectorial topological defects

We consider the full set of equations ruling the interaction of an electromagnetic field with matter in a laser, without assuming that the direction of the transverse electric field is fixed. Near the lasing threshold, we reduce the dynamics to its normal form equation, and show that the electromagnetic field can be described by a Ginzburg-Landau equation in a vector form. Then by using topological arguments we show the possibility of vectorial topological defects which are not predictable by the scalar theory.