Approximate Electromagnetic Cloaking of a Dielectric Sphere Using Homogeneous Isotropic Multi-Layered Materials


In cloaking, a body is hidden from detection by surrounding it by a coating consisting of an unusual anisotropic nonhomogeneous material. The permittivity and permeability of such a cloak are determined by the coordinate transformation of compressing a hidden body into a point or a line. The radially-dependent spherical cloaking shell can be approximately discretized into many homogeneous anisotropic layers; each anisotropic layer can be replaced by a pair of equivalent isotropic sub-layers, where the effective medium approximation is used to find the parameters of these two equivalent sub-layers. In this work, the scattering properties of cloaked dielectric sphere is investigated using a combination of approximate cloaking, where the dielectric sphere is transformed into a small sphere rather than to a point, together with discretizing the cloaking material using pairs of homogeneous isotropic sub-layers. The back-scattering normalized radar cross section, the scattering patterns are studied and the total scattering cross section against the frequency for different number of layers and transformed radius.

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H. Zamel, E. Diwany and H. Hennawy, "Approximate Electromagnetic Cloaking of a Dielectric Sphere Using Homogeneous Isotropic Multi-Layered Materials," Journal of Electromagnetic Analysis and Applications, Vol. 5 No. 10, 2013, pp. 379-387. doi: 10.4236/jemaa.2013.510060.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. B. Pendry, D. Schurig and D. R. Smith, “Controlling Electromagnetic Fields,” Science, Vol. 312, No. 5781, 2006, pp. 1780-1782.
[2] Q. Cheng, W. X. Jiang and T. J. Cui, “Investigations of the Electromagnetic Properties of Three-Dimensional Arbitrarily-Shaped Cloaks,” Progress in Electromagnetics Research, Vol. 94, 2009, pp. 105-117.
[3] J. J. Yang, M. Huang, Y. L. Li, T. H. Li and J. Sun, “Reciprocal Invisible Cloak with Homogeneous Metamaterials,” Progress in Electromagnetics Research M, Vol. 21, 2011, pp. 105-115.
[4] A. Shahzad, F. Qasim, S. Ahmed and Q. A. Naqvi, “Cylindrical Invisibility Cloak Incorporating PEMC at Perturbed Void Region,” Progress in Electromagnetics Research M, Vol. 21, 2011, pp. 61-76.
[5] X. X. Cheng, H. S. Chen and X. M. Zhang, “Cloaking a Perfectly Conducting Sphere with Rotationally Uniaxial Nihility Media in Monostatic Radar System,” Progress in Electromagnetics Research, Vol. 100, 2010, pp. 285-298.
[6] J. Zhang and N. A. Mortensen, “Ultrathin Cylindrical Cloak,” Progress in Electromagnetics Research, Vol. 121, 2011, pp. 381-389.
[7] Y. B. Zhai and T. J. Cui, “Three-Dimensional Axisymmetric Invisibility Cloaks with Arbitrary Shapes in Layered-Medium Background,” Progress in Electromagnetics Research B, Vol. 27, 2011, pp. 151-163.
[8] D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science, Vol. 314, No. 5801, 2006, pp. 977-980.
[9] J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Transactions on Microwave Theory and Techniques, Vol. 47, No. 11, 1999, pp. 2075-2084.
[10] G. V. Eleftheriades and K. G. Balmain, “Negative Refraction Metamaterials—Fundamental Principles and Applications,” John Wiley, Hoboken, 2005.
[11] N. Engheta and R. W. Ziolkowski, “Metamaterials: Physics and Engineering Explorations,” Wiley-IEEE Press, Hoboken, 2006.
[12] J. Wang, S. Qu, J. Zhang, H. Ma, Y. Yang, C. Gu, X. Wu and Z. Xu, “A Tunable Left-Handed Metamaterial Based on Modified Broadside-Coupled Split-Ring Resonators,” Progress in Electromagnetics Research Letters, Vol. 6, 2009, pp. 35-45.
[13] H. Liu, “Virtual Reshaping and Invisibility in Obstacle Scattering,” Inverse Problems, Vol. 25, No. 4, 2009, pp. 1-10.
[14] T. Zhou, “Electromagnetic Inverse Problems and Cloaking,” Ph. D. Thesis, Washington University, St Louis, 2010.
[15] Y. Huang, Y. Feng and T. Jiang, “Electromagnetic Cloaking by Layered Structure of Homogenous Isotropic Materials,” Optics Express, Vol. 15, No. 18, 2007, pp. 1-4.
[16] C. Qiu, L. Hu and S. Zouhdi, “Isotropic Non-Ideal Cloaks Providing Improved Invisibility by Adaptive Segmentation and Optimal Refractive Index Profile from Ordering Isotropic Materials,” Optics Express, Vol. 18, No. 14, 2010, pp. 14950-14959.
[17] C. Simovski and S. He, “Frequency Range and Explicit Expressions for Negative Permittivity and Permeability for an Isotropic Medium Formed by a Lattice of Perfectly Conducting Ω Particles,” Physics Letters A, Vol. 311, No. 2-3, 2003, pp. 254-263.
[18] C. Simovski and B. Sauviac, “Toward Creating Isotropic Microwave Composites with Negative Refraction,” Radio Science, Vol. 39, No. 2, 2004, pp. 1-18.
[19] C. W. Qiu, L. Hu, X. Xu and Y. Feng, “Spherical Cloaking with Homogenous Isotropic Multilayered Structures,” Physical Review E, Vol. 79, 2009, pp. 1-4.
[20] C. M. Ji, P. Y. Mao and F. D. Ning, “An Improved Method of Designing Multilayered Spherical Cloak for Electromagnetic Invisibility,” Chinese Physics Letters, Vol. 27, No. 3, 2010, pp. 1-4.
[21] H. Zamel, E. El-Diwany and H. El-Hennawy, “Approximate Electromagnetic Cloaking of a Conducting Sphere using Homogeneous Isotropic Multi-Layered Materials,” 2nd Middle East Conference on Antennas and Propagation, 29-31 December 2012, Cairo.
[22] W. Song, X. Yang and X. Sheng, “Scattering Characteristic of 2-d Imperfect Cloaks with Layered Isotropic Materials,” IEEE Antennas and Wireless Propagation Letters, Vol. 11, 2012, pp. 53-56.
[23] M. Yan, W. Yan and M. Qiu, “Invisibility Cloaking by Coordinate Transformation,” Progress in Optics, Vol. 52, 2009, pp. 261-304.
[24] H. Zamel, E. El-Diwany and H. El-Hennawy, “Approximate Electromagnetic Cloaking of Spherical Bodies,” 29th National Radio Science Conference (NRSC), Cairo, 10-12 April 2012, pp. 19-28.
[25] J. A. Stratton, “Electromagnetic Theory,” McGraw-Hill, Boston, 1941.
[26] R. F. Harrington, “Time Harmonic Electromagnetic Fields,” McGraw-Hill, Boston, 1961.
[27] J. Jin, “Theory and Computation of Electromagnetic Fields,” John Wiley, Hoboken, 2010.
[28] G. T. Ruck, D. E. Barrick, W. D. Stuart and C. K. Krichbaum, “Radar Cross Section Handbook,” Kluwer Academic, Boston, 1970.
[29] O. Pena and U. Pal, “Scattering of Electromagnetic Radiation by a Multilayered Sphere,” Computer Physics Communications, Vol. 180, No. 11, 2009, pp. 2348-2354.
[30] L. Kai and P. Massoli, “Scattering of Electromagnetic Plane Waves by Radially Inhomogeneous Spheres: A Finely Stratified Sphere Model,” Applied Optics, Vol. 33, No. 3, 1994, pp. 501-511.
[31] A. Aden and M. Kerker, “Scattering of Electromagnetic Waves from Two Concentric Spheres,” Journal of Applied Physics, Vol. 22, No. 10, 1951, pp. 1242-1246.
[32] N. Tsitsas and C. Athanasiadis, “On the Scattering of Spherical Electromagnetic Waves by a Layered Sphere,” Journal of Applied Mathematics and Mechanics, Vol. 59, No. 1, 2005, pp. 55-74.
[33] E. Jordan and K. Balmain, “Electromagnetic Waves and Radiating Systems,” Prentice-Hall, Upper Saddle River, 1968.

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