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An analytical study of dynamical properties of a semiconductor laser withoptical injection of arbitrary polarization is presented. It is shown that ifthe injected field is sufficiently weak, then the laser has nine equilibriumpoints, however, only one of them is stable. Even if the injected field islinearly polarized, six of the equilibrium points have a state of polarizationthat is elliptical. Dependence of the equilibrium points on the injected fieldis described, and it is shown that as the intensity of the injected fieldincreases, the number of equilibrium points decreases, with only a singleequilibrium point remaining for strong enough injected fields. As anapplication, a complex-valued optical neural network with working principlebased on injection locking is proposed.

Analysis of a dynamical system modeling lasers and applications for optical neural networks