Introduction

In this chapter we review our recent work on the dynamics of coherent semiconductor laser arrays. While most of the published literature on laser arrays has focused on the spatial properties of these sources, it is becoming increasingly apparent that their temporal behavior can be marvelously rich and complex. This complexity should not be surprising. A laser is, after all, a nonlinear oscillator. When one creates an array of coupled nonlinear oscillators the resulting dynamical behavior of the system will range from synchronization and phase locking to instabilities and chaos. An understanding of the complex dynamics is essential for the design of stable, compact, high-power sources for applications such as intersatellite optical communications. Because the characteristic time scale of semiconductor laser array dynamics is less than a nanosecond, it took the pioneering streak camera measurements of DeFreez et al., to provide the first indication of temporal instabilities in these lasers. Since then, complex dynamical behavior has been observed in most types of semiconductor laser arrays. Theoretical work has proceeded apace, from the early time-dependent coupled-mode theories to more recent partial differential equation models which treat the array as a single entity. The models predict both coupling induced instabilities and saturable-absorber induced instabilities, depending on array geometry and material parameters.