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    Area of Science:

    • Nonlinear dynamics
    • Laser physics
    • Statistical mechanics

    Background:

    • Laser networks offer complex dynamics.
    • Ising models describe magnetic phenomena.
    • Injection locking synchronizes lasers.

    Purpose of the Study:

    • Implement a two-site Ising model using an injection-locked laser network.
    • Investigate ferromagnetic and antiferromagnetic orders in coupled slave lasers.
    • Analyze phase locking behavior under modulated coupling.

    Main Methods:

    • Constructed a laser network with one master and two mutually coupled slave lasers.
    • Applied injection locking to synchronize slave lasers to the master.
    • Modulated the coupling path between slave lasers to observe dynamic changes.

    Main Results:

    • Observed distinct ferromagnetic (in-phase) and antiferromagnetic (out-of-phase) coupling orders.
    • Demonstrated stable phase locking (0 or π) of slave lasers despite coupling modulation.
    • Showcased automatic frequency selection to meet coupling conditions when mutual coupling is dominant.

    Conclusions:

    • Laser networks can emulate Ising models, exhibiting emergent magnetic-like orders.
    • Phase locking in coupled lasers is robust against continuous modulation of coupling strength.
    • The system's self-selection of oscillation frequency is a key mechanism for maintaining stable phase relationships.