  The Kuramoto model is a mathematical model for describing the collective
synchronization phenomena of coupled oscillators. We theoretically demonstrate
that an array of coupled photonic crystal lasers emulates the Kuramoto model
with non-delayed nearest-neighbor coupling (the local Kuramoto model). Our
novel strategy employs indirect coupling between lasers via additional cold
cavities. By installing cold cavities between laser cavities, we avoid the
strong coupling of lasers and realize ideal mutual injection-locking with
effective non-delayed dissipative coupling. First, after discussing the limit
cycle interpretation of laser oscillation, we demonstrate the synchronization
of two indirectly coupled lasers by numerically simulating coupled-mode
equations. Second, by performing a phase reduction analysis, we show that laser
dynamics in the proposed device can be mapped to the local Kuramoto model.
Finally, we briefly demonstrate that a chain of indirectly coupled photonic
crystal lasers actually emulates the one-dimensional local Kuramoto chain. We
also argue that our proposed structure, which consists of periodically aligned
cold cavities and laser cavities, will best be realized by using
state-of-the-art buried multiple quantum well photonic crystals.
