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

Date

2010-06-01

Author

Ozgun, Ozlem
Kuzuoğlu, Mustafa

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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.

Subject Keywords

Transforms, Coordinate transformation, Anisotropic media, Metamaterials, Cloaking, Reshaping, Waveguides, Waveguide miniaturization, Finite element methods

URI

https://hdl.handle.net/11511/47704

Collections

Department of Electrical and Electronics Engineering, Article