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Complexity in pulsed nonlinear laser systems interrogated by permutation entropy.

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    Permutation entropy (PE) and weighted permutation entropy (WPE) reveal complexity changes in pulsed laser systems. Unexpected inversions in WPE identify transitions from irregular dynamics to pulsed signals with jitter.

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    Area of Science:

    • Nonlinear dynamics
    • Laser physics
    • Information theory

    Background:

    • Permutation entropy (PE) is a key measure for nonlinear system complexity.
    • PE has been successfully applied to nonlinear laser systems.
    • Weighted permutation entropy (WPE) offers an advanced complexity measure.

    Purpose of the Study:

    • Investigate the behavior of PE and WPE in pulsed nonlinear laser systems.
    • Explain the observed inversion of PE and WPE values.
    • Utilize WPE to quantify amplitude and timing jitter in pulsed laser outputs.

    Main Methods:

    • Calculated PE and WPE for nonlinear laser output power sequences.
    • Analyzed WPE as a function of delay time for experimental time series.
    • Correlated WPE features with simulated data exhibiting controlled jitter and amplitude variations.

    Main Results:

    • Observed an unexpected inversion in PE and WPE values at characteristic frequencies for pulsed outputs.
    • Demonstrated that WPE minimum and peak width indicate amplitude variation and timing jitter.
    • Linked WPE behavior to the transition from irregular dynamics to regular pulsed signals.

    Conclusions:

    • The WPE inversion serves as an indicator for the transition to pulsed laser dynamics.
    • WPE analysis provides a quantitative method to assess signal quality in terms of jitter and amplitude variations.
    • This approach enhances the characterization of complex dynamics in nonlinear laser systems.