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Mode analysis in optics through fractional transforms.

T Alieva, M J Bastiaans

    Optics Letters
    |December 13, 2007
    PubMed
    Summary
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    This study establishes the link between mode content and fractional transforms. The Laguerre-Gauss spectrum of rotationally symmetric wave fronts can be found using fractional Hankel transforms at the optical axis.

    Area of Science:

    • Optics and Photonics
    • Mathematical Physics

    Background:

    • Understanding wave front properties is crucial in optical systems.
    • Fractional transforms offer advanced mathematical tools for signal analysis.

    Purpose of the Study:

    • To establish the relationship between mode content and fractional Fourier and Hankel transforms.
    • To demonstrate a method for determining the Laguerre-Gauss spectrum of wave fronts.

    Main Methods:

    • Mathematical analysis establishing the connection between mode content and fractional transforms.
    • Application of fractional Hankel transforms to rotationally symmetric wave fronts.

    Main Results:

    • The relationship between mode content and fractional Fourier and fractional Hankel transforms is formally established.

    Related Experiment Videos

  • A method is presented to determine the Laguerre-Gauss spectrum from fractional Hankel transforms at the optical axis.

    • Conclusions:

    • The findings provide a new analytical approach for characterizing wave fronts.
    • This work offers a pathway for advanced optical metrology and system design.