We study the dynamics of two coupled solid state lasers subject to an
injected field. A singular perturbation technique is used to reduce th
e full set of rate equations; we present a comprehensive bifurcation a
nalysis of the resulting phase model. We find four distinct routes to
full entrainment as the injected field amplitude increases; bifurcatio
n diagram predicts that the entrainment (reflected in the total intens
ity) does not monotonically improve with the injected field strength.
Our numerical simulations suggest that the reduced phase model capture
s the relevant dynamics well beyond the asymptotic regime in which it
is derived.