We investigate experimentally and theoretically the polarization switching found in a single-transverse
mode VCSEL when subject to parallel optical injection. Our analysis focuses on a recently observed
state in which injection locking of the parallel polarization and excitation of the free-running orthogonal
polarization of the VCSEL are obtained. A simple nonlinear dependence between the power of both
linear polarizations and the frequency detuning is found. Also the total power emitted by the VCSEL
is constant and independent on the injected optical power and on the frequency detuning. We check
these results experimentally for a variety of frequency detunings and bias currents applied to the device.
We report experimental and theoretical stability maps in the injected power-frequency detuning plane
for different bias currents identifying the regions in which the state is observed. A simple analytical
expression that describes the map boundary for large and negative frequency detunings is obtained. This
provides a simple method to extract the linear dichroism of the device