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    Researchers developed generalized Fibonacci photon sieves (GFiPS) offering multiple on-axis foci. This innovation allows adjustable focal distances and focal spot compression ratios for advanced optical applications.

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    Area of Science:

    • Optics and Photonics
    • Diffractive Optics
    • Nanophotonics

    Background:

    • Standard Fibonacci zone plates offer limited dual-foci capabilities.
    • Photon sieves provide enhanced focusing properties but often lack multifocal control.
    • Controlling focal properties is crucial for advanced optical systems.

    Purpose of the Study:

    • To extend Fibonacci zone plates to create generalized Fibonacci photon sieves (GFiPS).
    • To achieve multiple on-axis foci with GFiPS.
    • To enable adjustable focal distances and focal spot compression ratios.

    Main Methods:

    • Developed direct and inverse design methods based on generalized Fibonacci sequences.
    • Utilized characteristic roots of the recursion relation for design.
    • Switched transparent and opaque zones according to generalized Fibonacci sequences.

    Main Results:

    • Successfully created GFiPS with multiple on-axis foci.
    • Demonstrated adjustable multifocal distances.
    • Achieved adjustable compression ratios for focal spots in different directions.

    Conclusions:

    • GFiPS represent a significant advancement over standard Fibonacci zone plates.
    • The proposed design methods offer precise control over multifocal properties.
    • GFiPS hold potential for applications requiring flexible and controllable focusing.