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James Clerk Maxwell formulated a single theory combining all the electric and magnetic effects scientists knew during that time, calling the phenomena his theory predicted “Electromagnetic waves”. He brought together all the work that had been done by brilliant physicists such as Oersted, Coulomb, Gauss, and Faraday and added his own insights to develop the overarching theory of electromagnetism. Maxwell’s equations, combined with the Lorentz force law, encompass all the laws...
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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
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Spatially variant periodic structures in electromagnetics.

Raymond C Rumpf1, Javier J Pazos2, Jennefir L Digaum3

  • 1EM Lab, W. M. Keck Center for 3D Innovation, University of Texas at El Paso, 500 West University Avenue, El Paso, TX 79968, USA rcrumpf@utep.edu.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|July 29, 2015
PubMed
Summary

This study introduces a numerical technique for creating spatially varied periodic structures, enabling novel electromagnetic applications. The method efficiently generates complex lattices for advanced metamaterials and photonic crystals.

Keywords:
functionally gradedmetamaterialsmetasurfacesphotonic crystalsspatially varianttransformation optics

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Area of Science:

  • Electromagnetism
  • Materials Science
  • Nanotechnology

Background:

  • Periodic structures are crucial for designing inhomogeneous materials with specific electromagnetic properties.
  • Metamaterials and photonic crystals offer anisotropic and magnetic responses, but generating spatially varied designs remains challenging.
  • Existing spatial transform techniques can deform unit cells, compromising electromagnetic performance.

Purpose of the Study:

  • To present a simple numerical technique for spatially varying periodic structures.
  • To minimize unit cell deformations and preserve electromagnetic properties in functionally graded lattices.
  • To enable new design paradigms for metamaterials and photonic crystals.

Main Methods:

  • A novel numerical algorithm for spatial variation of periodic structures.
  • Minimization of unit cell deformations during lattice grading.
  • Development of efficient algorithms for lattice generation and quality improvement.

Main Results:

  • Demonstration of spatially variant self-collimating photonic crystals for tight wave bending.
  • Design of multi-mode waveguides in spatially variant band gap materials that prevent mode mixing.
  • Application of spatially variant anisotropic materials to sculpt near-fields for improved electromagnetic compatibility.

Conclusions:

  • The developed technique allows for the creation of complex, spatially varied periodic structures with preserved electromagnetic properties.
  • This method unlocks new design possibilities for photonic crystals, metamaterials, and electromagnetic compatibility.
  • The algorithm's efficiency and quality improvements facilitate the design of aplanatic metasurfaces and other advanced electromagnetic devices.