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    Parity-time (PT) symmetry enables laser mode-locking (ML) through asymmetric coupling. Crossing the PT symmetry breaking point transitions lasers from single- to double-pulse emission, exhibiting turbulent behavior.

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    Area of Science:

    • Optics and Photonics
    • Nonlinear Dynamics
    • Laser Physics

    Background:

    • Parity-time (PT) symmetry has emerged as a significant concept in optics.
    • Active phase-locking of laser cavity modes is crucial for many applications.
    • Complex time crystals offer a novel platform for exploring PT symmetry.

    Purpose of the Study:

    • To introduce and investigate Parity-time (PT) mode-locking (ML) in a laser system.
    • To demonstrate the transition from single- to double-pulse emission by breaking PT symmetry.
    • To explore the turbulent dynamics associated with this transition.

    Main Methods:

    • Implementation of asymmetric mode coupling within a complex time crystal.
    • Experimental or theoretical analysis of laser emission characteristics.
    • Investigation of the role of a dimensionless modulation parameter.

    Main Results:

    • Successful realization of PT mode-locking (ML) via asymmetric coupling.
    • Observation of a clear transition from single-pulse to double-pulse emission upon PT symmetry breaking.
    • Identification of turbulent behavior in the transition, influenced by a modulation parameter analogous to the Reynolds number.

    Conclusions:

    • PT mode-locking (ML) is a viable technique for controlling laser emission.
    • The transition dynamics exhibit complex behavior, including turbulence, offering insights into nonlinear systems.
    • This work extends the application of PT symmetry to active laser dynamics.