  An analytical study of dynamical properties of a semiconductor laser with
optical injection of arbitrary polarization is presented. It is shown that if
the injected field is sufficiently weak, then the laser has nine equilibrium
points, however, only one of them is stable. Even if the injected field is
linearly polarized, six of the equilibrium points have a state of polarization
that is elliptical. Dependence of the equilibrium points on the injected field
is described, and it is shown that as the intensity of the injected field
increases, the number of equilibrium points decreases, with only a single
equilibrium point remaining for strong enough injected fields. As an
application, a complex-valued optical neural network with working principle
based on injection locking is proposed.
