Abstract

The problem of synchronization of coupled oscillators is fundamental to many areas of science. When synchronization is successful, the several oscillators act as one, with a unique frequency and a well-defined phase relationship between the oscillators. When synchronization fails, the behavior of the oscillators is marvelously complex. Here beat oscillations, quasiperiodic motions, and chaotic dynamics are the norm. Semiconductor laser arrays are an example of a set of coupled nonlinear oscillators. This paper presents a theoretical analysis of the stability of coupled laser arrays. The analysis shows that laser arrays with evanescent coupling are dynamically unstable over large regions of a parameter space spanned by the coupling constant and the pump current. The origin of the instability is a breakdown of phase locking due to an amplitude-phase coupling effect peculiar to semiconductor lasers. In the unstable regime the temporal evolution of the laser output is either quasiperiodic or chaotic. The theoretical results show that the undamped pulsations observed in streak camera measurements of laser arrays are intrinsic to the lasers themselves and are a manifestation of deterministic chaos.

© 1988 Optical Society of America