  We analyze the dynamics of a solid-state laser driven by an injected
sinusoidal field. For this type of laser, the cavity round-trip time is much
shorter than its fluorescence time, yielding a dimensionless ratio of time
scales $\sigma \ll 1$. Analytical criteria are derived for the existence,
stability, and bifurcations of phase-locked states. We find three distinct
unlocking mechanisms. First, if the dimensionless detuning $\Delta$ and
injection strength $k$ are small in the sense that $k = O(\Delta) \ll
\sigma^{1/2}$, unlocking occurs by a saddle-node infinite-period bifurcation.
This is the classic unlocking mechanism governed by the Adler equation: after
unlocking occurs, the phases of the drive and the laser drift apart
monotonically. The second mechanism occurs if the detuning and the drive
strength are large: $k =O(\Delta) \gg \sigma^{1/2}$. In this regime, unlocking
is caused instead by a supercritical Hopf bifurcation, leading first to phase
trapping and only then to phase drift as the drive is decreased. The third and
most interesting mechanism occurs in the distinguished intermediate regime $k,
\Delta = O(\sigma^{1/2})$. Here the system exhibits complicated, but
nonchaotic, behavior. Furthermore, as the drive decreases below the unlocking
threshold, numerical simulations predict a novel self-similar sequence of
bifurcations whose details are not yet understood.
