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Tessellated and stellated invisibility.

André Diatta¹, André Nicolet, Sébastien Guenneau

¹Department of Mathematical Sciences, Peach Street, Liverpool L69 3BX, UK.

|August 6, 2009

Summary

This study presents designs for 2D cloaks using anisotropic heterogeneous materials. Numerical results show that increasing sides improves cloaking for polygonal shapes but worsens it for star shapes.

Area of Science:

Electromagnetism and Materials Science
Metamaterials and Nanophotonics

Background:

Metamaterials enable novel electromagnetic properties, including cloaking.
Anisotropic and heterogeneous materials offer advanced control over wave propagation.

Purpose of the Study:

To derive expressions for anisotropic heterogeneous permittivity and permeability matrices for 2D polygonal and star-shaped cloaks.
To investigate the impact of cloak geometry on scattering performance.

Main Methods:

Derivation of cloak designs using symmetry group theory.
Numerical analysis using the finite element method (FEM).
Rigorous asymptotic analysis to explain observed behaviors.

Main Results:

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Forward scattering improves with increasing sides for polygonal cloaks.

Forward scattering worsens with increasing sides for star-shaped cloaks.

Antagonistic scattering behaviors are explained through asymptotic analysis.

Conclusions:

The study provides a theoretical framework and numerical validation for designing 2D cloaks.
Geometric complexity influences cloaking effectiveness differently based on cloak shape.
Symmetry principles are crucial for optimizing cloak design.