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Total Reflection and Cloaking by Triangular Defects Embedded in Zero Index Metamaterials

Published online by Cambridge University Press:  23 March 2015

Yunqing Huang  and
Jichun Li
Yunqing Huang
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, China
Jichun Li*
Affiliation:
Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, Nevada 89154-4020, USA
*
*Corresponding author. Email: huangyq@xtu.edu.cn (Y. Q. Huang), jichun@unlv.nevada.edu (J. C. Li)
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Abstract

In this work, we investigate wave propagation through a zero index meta-material (ZIM) waveguide embedded with triangular dielectric defects. We provide a theoretical guidance on how to achieve total reflection and total transmission (i.e., cloaking) by adjusting the defect sizes and/or permittivities of the defects. Our work provides a systematical way in manipulating wave propagation through ZIM in addition to the widely studied dielectric defects with cylindrical and rectangular geometries.

Keywords

78M1065N3035L15Metamaterialsinvisibility cloaksMaxwell’s equatons
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 2 , April 2015 , pp. 135 - 144
Copyright
Copyright © Global-Science Press 2015 

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References

[1]Ziolkowski, R. W., Propagation in and scattering from a matched metamaterial having a zero index of refraction, Phys. Rev. E, 70 (2004), 046608.Google Scholar
[2]Edwards, B., Alú, A., Young, M. E., Silveirinha, M. and Engheta, N., Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide, Phys. Rev. Lett., 100 (2008), 033903.Google Scholar
[3]Liu, R., Cheng, Q., Hand, T., Mock, J. J., Cui, T. J., Cummer, S. A. and Smith, D. R., Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies, Phys. Rev. Lett., 100 (2008), 023903.Google Scholar
[4]Silveirinha, M. and Engheta, N., Tunneling of electromagnetic energy through subwavelength channels and bends using o-near-zero materials, Phys. Rev. Lett., 97 (2006), 157403.Google Scholar
[5]Ma, H. F., Shi, J. H., Jiang, W. X. and Cui, T. J., Experimental realization of bending waveguide using anisotropic zero-index materials, Appl. Phys. Lett., 101 (2012), 253513.Google Scholar
[6]Hao, J., Yan, W. and Qiu, M., Super-reflection and cloaking based on zero index metamaterial, Appl. Phys. Lett., 96 (2010), 101109.Google Scholar
[7]Huang, X., Lai, Y., Hang, Z. H., Zheng, H. and Chan, C. T., Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials, Nat. Mater., 10 (2011), 582.CrossRefGoogle ScholarPubMed
[8]Luo, J., Xu, P., Gao, L., Lai, Y. and Chen, H., Manipulate the transmissions using index-near-zero or epsilon-near-zero metamaterials with coated defects, Plasmonics, 7 (2012), 353.Google Scholar
[9]Nguyen, V. C., Chen, L. and Halterman, K., Total transmission and total reflection by zero index metamaterials with defects, Phys. Rev. Lett., 105 (2010), 233908.Google Scholar
[10]Xu, Y. and Chen, H., Total reflection and transmission by epsilon-near-zero metamaterials with defects, Appl. Phys. Lett., 98 (2011), 113501.Google Scholar
[11]Wu, Y. and Li, J., Total reflection and cloaking by zero index metamaterials loaded with rectangular dielectric defects, Appl. Phys. Lett., 102 (2013), 183105.Google Scholar
[12]Li, J. and Huang, Y., Time-Domain Finite Element Methods for Maxwell’s Equations in Metamaterials, Springer Series in Computational Mathematics, Vol. 43, Springer, January 2013.Google Scholar
[13]Mccartin, B. J., Eigenstructure of the equilateral triangle, Part I: The Dirichlet problem, SIAM Rev., 45(2) (2003), pp. 267–287.Google Scholar
[14]Damle, A. and Peterson, G. C., Understanding the eigenstructure of various triangles, SIAM Undergraduate Research Online, 3(1) (2010), pp. 187–208.Google Scholar
[15]Greenleaf, A., Lassas, M. and Uhlmann, G., On nonuniqueness for Calderón’s inverse problem, Math. Res. Lett., 10 (2003), pp. 685–693.Google Scholar
[16]Milton, G. W. and Nicorovici, N.-A. P., On the cloaking effects associated with anomalous localized resonance, Proc. R. Soc. Lond. Ser. A, 462 (2006), pp. 3027–3059.Google Scholar
[17]Pendry, J. B., Schurig, D. and Smith, D. R., Controlling electromagnetic fields, Science, 312 (2006), pp. 1780–1782.Google Scholar
[18]Leonhardt, U., Optical conformal mapping, Science, 312 (2006), pp. 1777–1780.Google Scholar
[19]Kohn, R., Shen, H., Vogelius, M. and Weinstein, M., Cloaking via change of variables in electrical impendance tomography, Inverse Problems, 24 (2008), 015016.Google Scholar
[20]Guevara Vasquez, F., Milton, G. W. and Onofrei, D., Broadband exterior cloaking, Opt. Express, 17(2009), pp. 14800–14805.Google Scholar
[21]Greenleaf, A., Kurylev, Y., Lassas, M. and Uhlmann, G., Cloaking devices, electromagnetics wormholes and transformation optics, SIAM Rev., 51 (2009), pp. 3–33.Google Scholar
[22]Ammari, H., Kang, H., Lee, H., Lim, M. and Yu, S., Enhancement of near cloaking for the full Maxwell equations, SIAM J. Appl. Math., 73 (2009), pp. 2055–2076.Google Scholar
[23]Li, J. and Huang, Y., Mathematical simulation of cloaking metamaterial structures, Adv. Appl. Math. Mech., 4(1) (2012), pp. 93–101.Google Scholar
[24]Li, J., Huang, Y. and Yang, W., Developing a time-domain finite-element method for modeling of electromagnetic cylindrical cloaks, J. Comput. Phys., 231 (2012), pp. 2880–2891.Google Scholar
[25]Bao, G. and Liu, H., Nearly cloaking the electromagnetic fields, SIAM J. Appl. Math., 74(3) (2014), pp. 724–742.Google Scholar
[26]Bao, G., Liu, H. and Zou, J., Nearly cloaking the full Maxwell equations: cloaking active contents with general conducting layers, J. Math. Pure Appl., 101 (2014), pp. 716–733.Google Scholar
[27]Li, J., Huang, Y., Yang, W. AND Wood, A., Mathematical analysis and time domain finite element simulation of carpet cloak, SIAM J. Appl. Math., 74(4) (2014), pp. 1136–1151.Google Scholar
[28]Huang, Y., Li, J. and Lin, Y., Finite element analysis of Maxwell’s equations in dispersive lossy bi-isotropic media, Adv. Appl. Math. Mech., 5(4) (2013), pp. 494–509.Google Scholar