  Stable and phase-locked emission in an extended topological supermode of
coupled laser arrays, based on concepts of non-Hermitian and topological
photonics, is theoretically suggested. We consider a non-Hermitian
Su-Schrieffer-Heeger chain of coupled microring resonators and show that
application of a synthetic imaginary gauge field via auxiliary passive
microrings leads to all supermodes of the chain, except one, to become edge
states. The only extended supermode, that retains some topological protection,
can stably oscillate suppressing all other non-topological edge supermodes.
Numerical simulations based on a rate equation model of semiconductor laser
arrays confirm stable anti-phase laser emission in the extended topological
supermode and the role of the synthetic gauge field to enhance laser stability.
