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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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A function's graph can be modified by changing its position or size without altering its overall shape. These transformations allow the graph to be moved across the coordinate plane while preserving its pattern and structure. One of the most common transformations is shifting, which repositions the graph without distorting it.When the output of a function is adjusted by adding or subtracting a constant, the graph shifts vertically. A positive value moves the graph upward, while a negative value...
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Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces
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Metasurface transformation for surface wave control.

E Martini1, M Mencagli1, S Maci2

  • 1Department of Information Engineering and Mathematics, University of Siena, Siena 53100, Italy.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|July 29, 2015
PubMed
Summary
This summary is machine-generated.

Metasurfaces (MTSs) are thin metamaterials that control surface waves (SWs) at microwave frequencies. By spatially modulating their impedance, MTSs can deform SW wavefronts along complex paths, as reviewed in this article.

Keywords:
high-impedance surfacemetamaterialsmetasurfacessurface-wavestransformation optics

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Area of Science:

  • Metamaterials and Nanophotonics
  • Electromagnetics and Wave Propagation

Background:

  • Metasurfaces (MTSs) are engineered thin-film metamaterials.
  • They are used to control plane waves and surface waves (SWs).
  • At microwave frequencies, MTSs consist of sub-wavelength metallic textures on dielectric substrates.

Purpose of the Study:

  • To review the theory and implementation of Metasurface (MTS) transformation.
  • To demonstrate the control of surface waves (SWs) using MTSs.
  • To analyze the deformation of SW wavefronts via MTS modulation.

Main Methods:

  • Characterizing MTSs using homogenized boundary conditions derived from averaged tangential fields.
  • Describing MTSs via a homogeneous equivalent impedance.
  • Spatially modulating the equivalent impedance by altering texture element size/orientation.

Main Results:

  • MTSs support surface wave (SW) propagation.
  • Spatially modulated impedance allows for deformation of the SW wavefront.
  • The local wavevector can be steered along non-rectilinear paths.
  • Transformation optics framework is applicable for analyzing MTS effects.

Conclusions:

  • Metasurfaces offer a powerful method for manipulating surface waves (SWs) at microwave frequencies.
  • The impedance modulation technique enables precise control over wave propagation.
  • This review highlights the theoretical underpinnings and practical implementations of MTS transformations.