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    Researchers developed a new analytical method to transform between Ince-Gaussian light modes with varying ellipticity. This breakthrough enables precise control and manipulation of structured light for advanced optical information processing.

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    Area of Science:

    • Optics and Photonics
    • Wave Physics

    Background:

    • Ince-Gaussian (IG) modes are solutions to the paraxial wave equation.
    • They offer a continuous transition between Laguerre- and Hermite-Gaussian modes via an ellipticity parameter (ε).
    • Existing IG bases for fixed ellipticities are orthogonal, but modes across different ellipticities are not mutually orthogonal.

    Purpose of the Study:

    • To derive an explicit analytical transformation between Ince-Gaussian bases of arbitrary ellipticity.
    • To enable direct and experimentally accessible mapping between non-orthogonal structured-light representations.
    • To introduce ellipticity as a controllable degree of freedom in structured light engineering.

    Main Methods:

    • Derivation of a finite analytical expression for transformation between IG bases.
    • Experimental implementation using spatial light modulators (SLMs).
    • Demonstration of ellipticity-resolved modal decomposition.

    Main Results:

    • The first explicit finite analytical expression for transforming between arbitrary ellipticity IG bases was derived.
    • An experimental method using SLMs was successfully demonstrated for modal decomposition.
    • Ellipticity was established as a controllable parameter for structured light.

    Conclusions:

    • The derived transformation provides a framework for mapping between non-orthogonal structured-light representations.
    • This work enables new strategies for mode conversion, optical encoding, and high-dimensional information processing.
    • The introduced framework enhances control over structured light for advanced optical applications.