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Linear time-invariant Systems01:23

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Updated: Oct 2, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Modeling and optimization of an unbalanced delay interferometer based OPLL system.

Ling Zhang, Weilin Xie, Yuxiang Feng

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    |February 25, 2022
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    Summary
    This summary is machine-generated.

    We developed an analytical model to optimize phase noise in optical phase-locked loops (OPLLs). This model accounts for laser frequency noise and practical sources, improving closed-loop performance.

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    Area of Science:

    • Photonics and Optical Engineering
    • Control Systems

    Background:

    • Optical phase-locked loops (OPLLs) are critical for stable laser frequency control.
    • Phase noise performance is a key metric limiting OPLL applications.
    • Existing models often oversimplify laser noise characteristics.

    Purpose of the Study:

    • To present a versatile analytical model for phase noise analysis and optimization of delay interferometer-based OPLLs.
    • To enable comprehensive investigation of noise interactions and their impact on performance.
    • To provide a design tool for optimizing OPLLs.

    Main Methods:

    • Developed a versatile analytical model for OPLL phase noise.
    • Incorporated arbitrary laser frequency noise properties.
    • Accounted for various practical noise sources.
    • Performed quantitative analysis of noise evolution with interferometer delay.

    Main Results:

    • The model quantifies the impact of noise sources on phase noise dynamics.
    • Analysis reveals how interferometer delay affects fundamental noise limits.
    • Optimization leads to balanced loop bandwidth and sensitivity for improved closed-loop noise performance.
    • Numerical verification with different lasers confirmed model precision.

    Conclusions:

    • The proposed analytical model accurately predicts phase noise performance in OPLLs.
    • The model serves as a valuable design tool for insightful analysis and optimization.
    • It offers guiding significance for practical applications in optical systems.