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Transformations of Functions III01:20

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Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...
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Measuring Spatially- and Directionally-varying Light Scattering from Biological Material
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Guiding light with conformal transformations.

Nathan I Landy1, Willie J Padilla

  • 1Department of Physics, Boston College, 140 Commonwealth Avenue, Chestnut Hill, MA 02467, USA.

Optics Express
|August 19, 2009
PubMed
Summary
This summary is machine-generated.

Researchers developed novel photonic devices using transformation optics and all-dielectric metamaterials. These devices enable broadband light manipulation with unprecedented control and reflectionless properties.

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Area of Science:

  • Electromagnetics
  • Materials Science
  • Optics

Background:

  • Metamaterials have revolutionized electromagnetics, enabling exotic effects like negative refraction.
  • Transformation optics (TO) combined with metamaterials has led to breakthroughs like invisibility cloaks.
  • Previous methods using quasi-conformal mapping achieved broadband cloaking but had limitations.

Purpose of the Study:

  • To extend transformation optics (TO) using strictly conformal mapping for advanced photonic devices.
  • To develop reflectionless, isotropic, and broadband photonic devices.
  • To combine the novel effects of TO with practical all-dielectric construction.

Main Methods:

  • Utilized strictly conformal mapping in conjunction with transformation optics (TO).
  • Employed all-dielectric construction for practical device fabrication.
  • Investigated the light-guiding capabilities of the designed structures.

Main Results:

  • Demonstrated reflectionless and inherently isotropic photonic devices.
  • Achieved broadband cloaking effects.
  • Showcased the ability to guide light in an almost arbitrary fashion over a wide range of frequencies.

Conclusions:

  • The developed method offers a practical approach to creating advanced photonic devices.
  • The all-dielectric, conformally mapped structures provide unprecedented control over light propagation.
  • This work paves the way for novel applications in electromagnetics and photonics.