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Mathematical Simulation of Cloaking Metamaterial Structures

Published online by Cambridge University Press:  03 June 2015

Jichun Li  and
Yunqing Huang
Jichun Li*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, Nevada 89154-4020, USA
Yunqing Huang*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China
*
Corresponding author. URL: http://faculty.unlv.edu/jichun/, Email: [email protected]
Email: [email protected]
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Abstract

In this paper we present a rigorous derivation of the material parameters for both the cylinder and rectangle cloaking structures. Numerical results using these material parameters are presented to demonstrate the cloaking effect.

Keywords

78M1065N3035L15Maxwell’s equationsmetamaterialfinite element methodcloaking structures
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 1 , February 2012 , pp. 93 - 101
Copyright
Copyright © Global-Science Press 2012

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References

[1] Aluú, A. and Engheta, N., Achieving transparency with plasmonic and metamaterial coatings, Phys. Rev. E., 72 (2005), 016623.Google Scholar
[2] Chen, H., Chan, C. T. and Sheng, P., Transformation optics and metamaterials, Nature. Mater., 9 (2010), pp. 387–396.CrossRefGoogle ScholarPubMed
[3] Cummer, S. A., Popa, B.-I., Schurig, D., Smith, D. R. and Pendry, J., Full-wave simulations of electromagnetic cloaking structures, Phys. Rev. E., 74 (2006), 036621.Google Scholar
[4] Demkowicz, L., Kurtz, J., Pardo, D., Paszynski, M., Rachowicz, W. and Zdunek, A., Computing with hp Finite Elements II-Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications, Chapman & Hall/CRC, 2007.Google Scholar
[5] Engheta, N. and Ziolkowski, R. W., Electromagnetic Metamaterials: Physics and Engineering Explorations, Wiley-IEEE Press, Hoboken, NJ, 2006.CrossRefGoogle Scholar
[6] Greenleaf, A., Kurylev, Y., Lassas, M. and Uhlmann, G., Cloaking devices, electromagnetics wormholes and transformation optics, SIAM Rev., 51 (2009), pp. 3–33.CrossRefGoogle Scholar
[7] Huang, Y. and Li, J., Recent advances in time-domain Maxwell’s equations in metamaterials, in “Lecture Notes in Computer Sciences” (eds. By Zhang, W. et al.), 5938 (2010), pp. 48–57.Google Scholar
[8] Huang, Y., Li, J. and Yang, W., Interior penalty DG methods for Maxwell’s equations in dispersive media, J. Comput. Phys., 230 (2011), pp. 4559–4570.CrossRefGoogle Scholar
[9] Kohn, R. V., Onofrei, D., Vogelius, M. S. and Weinstein, M. I., Cloaking via change of variables for the Helmholtz equation, Commun. Pure. Appl. Math., 63 (2010), pp. 0973–1016.Google Scholar
[10] Leonhardt, U., Optical conformal mapping, Science., 312 (2006), pp. 1777–1780.Google Scholar
[11] Li, J., Chen, Y. and Elander, V., Mathematical and numerical study of wave propagation in negative-index materials, Comput. Methods. Appl. Mech. Eng., 197 (2008), pp. 3976–3987.CrossRefGoogle Scholar
[12] Li, J. and Wood, A., Finite element analysis for wave propagation in double negative metamaterials, J. Sci. Comput., 32 (2007), pp. 263–286.CrossRefGoogle Scholar
[13] Lin, Q. and Li, J., Superconvergence analysis for Maxwell’s equations in dispersive media, Math. Comput., 77 (2008), pp. 757–771.CrossRefGoogle Scholar
[14] Milton, G. W., Briane, M. and Willis, J. R., On cloaking for elasticity and physical equations with a transformation invariant form, New. J. Phys., 8 (2006), 248.Google Scholar
[15] Pendry, J. B., Schurig, D. and Smith, D. R., Controlling electromagnetic fields, Science., 312 (2006), pp. 1780–1782.Google Scholar
[16] Post, E. J., Formal Structure of Electromagnetics: General Covariance and Electromagnetics, Dover, 1997.Google Scholar
[17] Qiao, Z., Yao, C. and Jia, S., Superconvergence and extrapolation analysis of a nonconforming mixed finite element approximation for time-harmonic Maxwell’s equations, J. Sci. Comput., 46 (2011), pp. 1–19.Google Scholar
[18] Rahm, M., Schurig, D., Roberts, D. A., Cummer, S. A., Smith, D. R. and Pendry, J. B., Design of electromagnetic cloaks and concentrations using form-invariant coordinate transformations of Maxwell’s equations, Photonic. Nanostruct., 6 (2008), pp. 87–95.Google Scholar
[19] Zhang, J., Huangfu, J., Luo, Y., Chen, H., Kong, J. A. and Wu, B.-I., Cloak for multi-layered and gradually changing media, Phys. Rev. B., 77 (2008), 035116.Google Scholar
[20] Zhao, Y. and Hao, Y., Full-wave parallel dispersive finite-difference time-domain modeling of three-dimensional electromagnetic cloaking structures, J. Comput. Phys., 228 (2009), pp. 7300–7312.Google Scholar