Nonlinear dynamics of a solid-state laser with injection

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 much less than 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)much less than 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)much greater than 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 self-similar sequence of bifurcations, the details of which are not yet understood. [S1063-651X(98)05510-X].