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

Area of Science:

• Nonlinear Dynamics and Optics
• Condensed Matter Physics
• Photonics and Laser Technology

Background:

• The Kuramoto model is a fundamental framework for understanding collective synchronization in coupled oscillatory systems.
• Photonic crystal lasers offer a platform for integrated optical devices, but achieving controlled coupling for complex dynamics remains a challenge.

Purpose of the Study:

• To theoretically demonstrate that an array of coupled photonic crystal lasers can emulate the local Kuramoto model.
• To propose and analyze a novel indirect coupling mechanism using cold cavities for non-delayed nearest-neighbor interactions.

Main Methods:

• Numerical simulations of coupled-mode equations to demonstrate laser synchronization.
• Phase reduction analysis to map laser dynamics to the Kuramoto model.
• Theoretical framework for indirect coupling via cold cavities, enabling non-delayed dissipative coupling.

Main Results:

• Successful emulation of the local Kuramoto model by indirectly coupled photonic crystal lasers.
• Demonstration of synchronization in a two-laser system and a one-dimensional laser chain.
• Validation of the indirect coupling strategy for achieving ideal mutual injection-locking.

Conclusions:

• The proposed indirect coupling scheme effectively realizes non-delayed nearest-neighbor coupling, crucial for emulating the local Kuramoto model.
• Photonic crystal laser arrays coupled via cold cavities provide a viable platform for studying complex synchronization phenomena.
• The design is compatible with state-of-the-art fabrication techniques, particularly buried multiple quantum well photonic crystals.