We consider a class-A laser operating on the three Gauss-Hermite modes
of the frequency-degenerate family m + n = 2, and deliberately break
the cylindrical symmetry of the system assuming that the pumped region
has a square section. Having identified in the parameter space region
s of spatial mono-, bi-, tetra- and esa-stability, we analyze the poss
ibility of inducing optical switching between coexisting states, by th
e injection both of a signal with the same spatial distribution of the
final desired stationary state and of a gaussian signal strategically
positioned in the transverse plane. In either cases we demonstrate lo
w energy switching, respectively without and with the necessity of con
trol on the phase of the injected field.