We study the nonlinear dynamics of a vertical-cavity surface-emitting laser (VCSEL) subject to a repetitive
optical pulse injection numerically using the SFM model. In our study, a linearly polarized slave laser is optically
injected by a train of optical pulses from a master laser, where the polarization of the master laser is orthogonal
to the polarization of the solitary slave laser (x-polarized). By varying the strength and the repetition frequency
of the injected pulses, different dynamical states, including regular pulsations, period-doubled pulsations, chaotic
pulsations, periodic oscillations, quasi-periodic oscillations, and chaotic oscillations, are found. Instead of having
only one polarization mode at the slave laser output, both the y- and x-polarized modes are observed for
the pulsation and oscillation states. While the pulsation states with y-polarization follow a period-doubling
route to chaotic pulsations, the oscillation states with the
x-polarization undergo a quasi-periodic route to
chaos oscillations. Then, with adequate strength of the injection, the x-polarized mode will be suppressed (i.e.
polarization switching) and eventually the slave laser will lock to the master laser with higher injection strength.
Also, the switching points, the boundary of the injection-locked, and the regions of the chaotic states are found
to be strongly influenced by the repetition frequency of the injection pulses and the detuning frequency between the two lasers.