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Tangent Planes to Level Surfaces01:31

Tangent Planes to Level Surfaces

A level surface consists of all points in space where a function of three variables takes the same fixed value. If a point lies on this surface, understanding the surface’s geometry there requires more than just knowing the point’s coordinates; it requires describing how the surface is oriented, or how it tilts, near that point.To probe this local geometry, imagine tracing a path that stays entirely on the level surface and passes through the point of interest. This path can be described as a...

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Updated: Jun 19, 2026

Demonstration of Spin-Multiplexed and Direction-Multiplexed All-Dielectric Visible Metaholograms
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Bragg holograms with binary synthetic surface-relief profile.

J Turunen, P Blair, J M Miller

    Optics Letters
    |October 14, 2009
    PubMed
    Summary

    Researchers designed synthetic binary surface-relief elements for efficient light manipulation. These elements achieve near 100% diffraction efficiency, enabling advanced optical applications.

    Area of Science:

    • Optics and Photonics
    • Nanotechnology
    • Materials Science

    Background:

    • Binary surface-relief elements are crucial for manipulating light.
    • Subwavelength features enable advanced optical functionalities.
    • Diffraction efficiency is a key performance metric for optical elements.

    Purpose of the Study:

    • To design synthetic pulse-position-modulated binary surface-relief elements.
    • To achieve high diffraction efficiency using a combination of scalar and rigorous electromagnetic diffraction theories.
    • To demonstrate a reflective binary Bragg-type multiple beam splitter.

    Main Methods:

    • Utilizing scalar and rigorous electromagnetic diffraction theories for element design.
    • Employing direct-write electron-beam lithography for fabrication.

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  • Using reactive ion etching for precise material removal.

    • Main Results:

    • Theoretical achievement of nearly 100% diffraction efficiency for both reflection- and transmission-type elements at Bragg incidence.
    • Demonstration of a reflective binary Bragg-type multiple beam splitter.
    • Successful operation at a wavelength of lambda = 1.064 microm.

    Conclusions:

    • Synthetic binary surface-relief elements with subwavelength features can achieve near-perfect diffraction efficiency.
    • The demonstrated beam splitter is a viable component for optical systems operating at 1.064 microm.
    • This work advances the design and fabrication of diffractive optical elements.