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Time and frequency -Domain Interpretation of Phase-lag Control01:21

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Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
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Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
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Related Experiment Video

Updated: Mar 12, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Temporal coherence effects on target-based phasing of laser arrays.

Milo W Hyde, Glenn A Tyler

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |November 10, 2016
    PubMed
    Summary

    This study examines how laser linewidth broadening impacts fiber laser array phasing on targets. Results show coherence length is crucial for accurate remote target phasing, even with scattering surfaces.

    Area of Science:

    • Optics and Photonics
    • Laser Physics
    • Array Beamforming

    Background:

    • Fiber laser arrays are essential for high-power beam generation.
    • Stimulated Brillouin scattering (SBS) can degrade laser performance.
    • Temporal coherence, specifically linewidth, is a critical parameter in laser systems.

    Purpose of the Study:

    • To investigate the effect of temporal coherence, particularly linewidth broadening for SBS suppression, on target-based phasing of fiber laser arrays.
    • To theoretically analyze radio-frequency modulated fiber laser arrays fed by broadband sources and phased on a remote target.
    • To derive and discuss the expression for detector plane irradiance used in array phasing.

    Main Methods:

    • Theoretical analysis of a radio-frequency modulated fiber laser array.

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  • Derivation of the detector plane irradiance expression.
  • Numerical simulations of a seven-element hexagonal array phasing on a step target with scattering surfaces.

    • Main Results:

    • The study provides a detailed theoretical expression for detector plane irradiance.
    • Simulation results validate the theoretical findings for a seven-element hexagonal array.
    • The impact of coherence length on phasing accuracy over scattering surfaces is demonstrated.

    Conclusions:

    • Temporal coherence significantly influences the accuracy of target-based phasing in fiber laser arrays.
    • Linewidth broadening, used for SBS suppression, must be considered in array phasing strategies.
    • The derived irradiance expression and simulation results offer valuable insights for designing and controlling phased fiber laser arrays.