Emulating the local Kuramoto model with an injection-locked photonic crystal laser array

TL;DR

This paper proposes a novel photonic crystal laser array design that emulates the local Kuramoto model of coupled oscillators, enabling controlled synchronization phenomena in photonic systems.

Contribution

It introduces a new indirect coupling strategy via cold cavities to realize the local Kuramoto model with photonic crystal lasers, avoiding strong direct laser coupling.

Findings

Demonstrated synchronization of two coupled lasers through numerical simulation.

Mapped laser dynamics to the local Kuramoto model via phase reduction analysis.

Showed that a chain of lasers emulates a one-dimensional local Kuramoto chain.

Abstract

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.