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Related Concept Videos

Quadric Surfaces01:28

Quadric Surfaces

Quadric surfaces are three-dimensional surfaces characterized by second-degree equations in the variables x, y, and z. These surfaces are smooth and continuous, and specific combinations of squared and linear terms define their shapes. The main types of quadric surfaces include ellipsoids, cones, paraboloids, and hyperboloids. Each type exhibits distinct geometric features depending on how the variables are arranged and related within the equation.Ellipsoids are closed surfaces formed when all...
Interpretations of Partial Derivatives01:14

Interpretations of Partial Derivatives

A surface defined by a function of two variables can be visualized as a vast, uneven terrain, where each point is identified using Cartesian coordinates. The elevation of the terrain at any point is determined by a function that assigns a height value to every pair of horizontal coordinates. This representation allows the surface to be studied in terms of how its height varies across different directions.At a specific point on this terrain, understanding how the height changes requires...
Tangent Planes to Surfaces01:19

Tangent Planes to Surfaces

In multivariable calculus, the concept of a tangent plane plays a central role in approximating curved surfaces. When dealing with a surface defined by a function of two variables, such as z = f(x, y), the tangent plane at a given point provides the best linear approximation to the surface near that point. This local linearization allows complex, nonlinear geometries to be treated using simpler, planar models.The construction of the tangent plane involves taking vertical slices of the surface...
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...
Parametric Surfaces01:30

Parametric Surfaces

A parametric surface in three-dimensional space is defined through a vector-valued function\begin{equation*}\mathbf{r}(u, v) = x(u, v)\mathbf{i} + y(u, v)\mathbf{j} + z(u, v)\mathbf{k}\end{equation*}where u and v are parameters within a specified domain D in the uv-plane. The functions x(u, v), y(u, v), and z(u, v) define the coordinates of points on the surface. As u and v vary over D, the position vector r(u, v) traces a continuous surface in space. This parametric representation is essential...
Tangent Planes to a Parametric Surface01:22

Tangent Planes to a Parametric Surface

A tangent plane provides a linear approximation to a curved surface at a specific point, capturing the local behavior of the surface. It can be understood as the plane that just touches the surface at that point and is defined by the tangent directions of curves lying on the surface. These tangent directions arise naturally when the surface is described parametrically, allowing systematic construction of the plane.For a surface expressed in parametric form, the position of any point is...

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Updated: Jun 18, 2026

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material
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Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

Published on: May 20, 2013

Metasurfaces enable sculpting light in three dimensions.

Joohoon Kim1,2, Junsuk Rho3,4,5,6

  • 1Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea. kimjuhoon@postech.ac.kr.

Light, Science & Applications
|March 2, 2026
PubMed
Summary
This summary is machine-generated.

Researchers developed a novel metasurface platform for 3D vectorial holography. This breakthrough allows independent control over light intensity and polarization for advanced optical encryption.

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Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces
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11:57

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

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Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces
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Area of Science:

  • Optics and Photonics
  • Materials Science

Background:

  • Metasurfaces offer unique light manipulation capabilities.
  • Holography traditionally lacks independent control over light properties along the propagation axis.

Purpose of the Study:

  • To demonstrate a metasurface platform for 3D vectorial holography.
  • To achieve independent control of light intensity and polarization along the propagation axis.
  • To enable multi-dimensional optical encryption.

Main Methods:

  • Utilizing longitudinally engineered meta-atoms.
  • Designing a novel metasurface architecture.
  • Implementing holographic principles with advanced light control.

Main Results:

  • Demonstrated independent control of light intensity and polarization.
  • Achieved 3D vectorial holographic capabilities.
  • Established a multi-dimensional optical encryption platform.

Conclusions:

  • The developed metasurface platform is effective for 3D vectorial holography.
  • This technology opens new avenues for optical encryption and information security.