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Wigner function for highly convergent three-dimensional wave fields.

C J Sheppard, K G Larkin

    Optics Letters
    |November 28, 2007
    PubMed
    Summary
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    A new angle-impact Wigner function simplifies analyzing 3D scalar wave fields. This real, four-dimensional function directly calculates spatial intensity, enhancing optical transfer function applications.

    Area of Science:

    • Optics
    • Mathematical Physics

    Background:

    • The Wigner function is a phase-space representation used in quantum mechanics and optics.
    • Analyzing three-dimensional (3D) scalar wave fields can be complex.
    • Existing methods may involve high-dimensional functions.

    Purpose of the Study:

    • To derive a novel angle-impact Wigner function for 3D scalar wave fields.
    • To simplify the analysis of intensity distribution in optical systems.

    Main Methods:

    • Direct derivation using the three-dimensional generalized optical transfer function.
    • Avoidance of a six-dimensional Wigner function.

    Main Results:

    • The angle-impact Wigner function is a real, four-dimensional function.

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  • It allows for straightforward determination of spatial intensity.

    • Conclusions:

    • The derived angle-impact Wigner function offers a more accessible method for analyzing 3D scalar wave fields.
    • This approach simplifies intensity calculations in optical systems.