STABILITY CONDITIONS FOR COUPLED LASERS - SERIES COUPLING VERSUS PARALLEL COUPLING

The equations for N coupled semiconductor lasers in a ring geometry ar e considered. The lasers are coupled either in series or parallel. Par allel coupling is known as a strong synchronization mechanism but has never been studied analytically. In this paper, we analyze the stabili ty of the in-phase solutions for a system of N lasers coupled in paral lel. We obtain a condition for its stability in terms of the laser par ameters, the coupling strength eta and the number of lasers N. This co ndition is compared to the stability condition for N lasers coupled in series. Of particular interest is the effect of N. As N is increased, the stability condition is eta>eta(s)(N)=O(N2) for series coupling an d is eta>eta(p)(N)=O(N-1)<<eta(s)(N) for parallel coupling.