  We consider a line of three mutually coupled lasers with time delays and
study chaotic synchronization of the outer lasers. Two different systems are
presented: optoelectronically coupled semiconductor lasers and optically
coupled fiber lasers. While the dynamics of the two systems are very different,
robust synchronization of end lasers is obtained in both cases over a range of
parameters. Here, we present analysis and numerical simulation to explain some
of the observed synchronization phenomena. First, we introduce the system of
three coupled semiconductor lasers and discuss the onset of oscillations that
occurs via a bifurcation as the coupling strength increases. Next, we analyze
the synchronization of the end lasers by examining the dynamics transverse to
synchronized state. We prove that chaotic synchronization of the outer
semiconductor lasers will occur for sufficiently long delays, and we make a
comparison to generalized synchronization in driven dissipative systems. It is
shown that the stability of synchronous state (as indicated by negative
Lyupunov exponents transverse to the synchronization manifold) depends on the
internal dissipation of the outer lasers. We next present numerical simulations
for three coupled fiber lasers, highlighting some of the differences between
the semiconductor and fiber laser systems. Due to the large number of coupled
modes in fiber lasers, this is a good system for investigating spatio-temporal
chaos. Stochastic noise is included in the fiber laser model, and synchrony of
the outer lasers is observed even at very small coupling strengths.
