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    Area of Science:

    • Optics and Photonics
    • Wave Physics
    • Computational Electromagnetics

    Background:

    • Laguerre-Gaussian (LG) modes are crucial in optics, but numerical expansion of arbitrary fields is challenging.
    • Variable LG mode parameters (beam waist, radial/azimuthal indices) complicate optimal expansion determination.
    • Existing methods struggle with accurate numerical LG mode decomposition for complex optical fields.

    Purpose of the Study:

    • To develop a general and accurate method for Laguerre-Gaussian (LG) mode expansion of arbitrary optical fields.
    • To establish clear criteria for selecting the optimal beam waist parameter and truncation order in LG series expansions.
    • To overcome the limitations of existing numerical LG mode decomposition techniques.

    Main Methods:

    • Developed a general method for LG mode expansion applicable to arbitrary fields.
    • Analyzed the local frequency distribution of LG functions, identifying quasi-periodic and chirped components.
    • Defined an effective space-bandwidth product for LG functions based on the quasi-periodic part.
    • Established criteria for determining the beam waist parameter and truncation order using the space-bandwidth product.

    Main Results:

    • The local frequency distribution of LG functions was found to have quasi-periodic and chirped parts.
    • An effective space-bandwidth product was defined for LG functions.
    • Criteria for optimal beam waist and truncation order selection were derived.
    • The method demonstrated high accuracy when applied to off-axis Hermite-Gaussian mode representation.

    Conclusions:

    • The proposed method provides accurate Laguerre-Gaussian (LG) mode expansion for arbitrary optical fields.
    • The defined space-bandwidth product offers a robust criterion for parameter selection in LG series.
    • This approach enhances the numerical decomposition of optical fields into LG modes.