Form Invariance of Maxwell's Equations: The Pathway to Novel Metamaterial Specifications for Electromagnetic Reshaping

Ozgun O., KUZUOĞLU M.

IEEE ANTENNAS AND PROPAGATION MAGAZINE, vol.52, no.3, pp.51-65, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 3
  • Publication Date: 2010
  • Doi Number: 10.1109/map.2010.5586575
  • Journal Name: IEEE ANTENNAS AND PROPAGATION MAGAZINE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.51-65
  • Keywords: Transforms, coordinate transformation, anisotropic media, metamaterials, cloaking, reshaping, waveguides, waveguide miniaturization, finite element methods, ELEMENT MESH TRUNCATION, INVISIBILITY CLOAKS, OPTICAL CLOAKING, WAVE, TRANSFORMATIONS, CONCENTRATORS, ABSORBERS, DESIGNS, LAYERS
  • Middle East Technical University Affiliated: Yes

Abstract

We present spatial-coordinate transformation techniques to control the propagation of electromagnetic fields in several surprising and useful applications. The implementation of this approach is based on the fact that Maxwell's equations are form-invariant under coordinate transformations. Specifically, the effect of a general coordinate transformation can be realized by means of an equivalent anisotropic material, in which the original forms of Maxwell's equations are still preserved-in the transformed space. Constitutive parameters of the anisotropic material are determined to appropriately reflect the consequences of the coordinate transformation on the electromagnetic fields. In this paper, we introduce novel implementations and interpretations of the coordinate-transformation approach for the purpose of "reshaping" objects in electromagnetic scattering, and for reshaping and miniaturizing waveguides. We demonstrate the applications of the proposed techniques via several finite-element simulations.