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

Affiliation(s)

Electronics Research Institute (ERI), Microwave Engineering Department, Cairo, Egypt.

Faculty of Engineering, Ain Shams University, Cairo, Egypt.

Electronics Research Institute (ERI), Microwave Engineering Department, Cairo, Egypt.

Faculty of Engineering, Ain Shams University, Cairo, Egypt.

ABSTRACT

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.

Cite this paper

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.

H. Zamel, E. Diwany and H. Hennawy, "Approximate Electromagnetic Cloaking of a Dielectric Sphere Using Homogeneous Isotropic Multi-Layered Materials,"

References

[1] J. B. Pendry, D. Schurig and D. R. Smith, “Controlling Electromagnetic Fields,” Science, Vol. 312, No. 5781, 2006, pp. 1780-1782.

http://dx.doi.org/10.1126/science.1125907

[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.

http://dx.doi.org/10.2528/PIER09060705

[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.

http://dx.doi.org/10.2528/PIERM11090904

[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.

http://dx.doi.org/10.2528/PIERM11061302

[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. http://dx.doi.org/10.2528/PIER09112002

[6] J. Zhang and N. A. Mortensen, “Ultrathin Cylindrical Cloak,” Progress in Electromagnetics Research, Vol. 121, 2011, pp. 381-389.

http://dx.doi.org/10.2528/PIER11091205

[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.

http://dx.doi.org/10.1126/science.1133628

[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. http://dx.doi.org/10.1109/22.798002

[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. http://dx.doi.org/10.1002/0471784192

[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.

http://dx.doi.org/10.2528/PIERL08120708

[13] H. Liu, “Virtual Reshaping and Invisibility in Obstacle Scattering,” Inverse Problems, Vol. 25, No. 4, 2009, pp. 1-10. http://dx.doi.org/10.1088/0266-5611/25/4/045006

[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.

http://dx.doi.org/10.1364/OE.18.014950

[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.

http://dx.doi.org/10.1016/S0375-9601(03)00494-8

[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.

http://dx.doi.org/10.1109/LAWP.2011.2182590

[23] M. Yan, W. Yan and M. Qiu, “Invisibility Cloaking by Coordinate Transformation,” Progress in Optics, Vol. 52, 2009, pp. 261-304.

http://dx.doi.org/10.1016/S0079-6638(08)00006-1

[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.

http://dx.doi.org/10.1109/NRSC.2012.6208502

[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.

http://dx.doi.org/10.1002/9780470874257

[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.

http://dx.doi.org/10.1016/j.cpc.2009.07.010

[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.

http://dx.doi.org/10.1364/AO.33.000501

[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.

http://dx.doi.org/10.1063/1.1699834

[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.

http://dx.doi.org/10.1093/qjmam/hbi031

[33] E. Jordan and K. Balmain, “Electromagnetic Waves and Radiating Systems,” Prentice-Hall, Upper Saddle River, 1968.

[1] J. B. Pendry, D. Schurig and D. R. Smith, “Controlling Electromagnetic Fields,” Science, Vol. 312, No. 5781, 2006, pp. 1780-1782.

http://dx.doi.org/10.1126/science.1125907

[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.

http://dx.doi.org/10.2528/PIER09060705

[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.

http://dx.doi.org/10.2528/PIERM11090904

[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.

http://dx.doi.org/10.2528/PIERM11061302

[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. http://dx.doi.org/10.2528/PIER09112002

[6] J. Zhang and N. A. Mortensen, “Ultrathin Cylindrical Cloak,” Progress in Electromagnetics Research, Vol. 121, 2011, pp. 381-389.

http://dx.doi.org/10.2528/PIER11091205

[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.

http://dx.doi.org/10.1126/science.1133628

[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. http://dx.doi.org/10.1109/22.798002

[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. http://dx.doi.org/10.1002/0471784192

[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.

http://dx.doi.org/10.2528/PIERL08120708

[13] H. Liu, “Virtual Reshaping and Invisibility in Obstacle Scattering,” Inverse Problems, Vol. 25, No. 4, 2009, pp. 1-10. http://dx.doi.org/10.1088/0266-5611/25/4/045006

[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.

http://dx.doi.org/10.1364/OE.18.014950

[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.

http://dx.doi.org/10.1016/S0375-9601(03)00494-8

[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.

http://dx.doi.org/10.1109/LAWP.2011.2182590

[23] M. Yan, W. Yan and M. Qiu, “Invisibility Cloaking by Coordinate Transformation,” Progress in Optics, Vol. 52, 2009, pp. 261-304.

http://dx.doi.org/10.1016/S0079-6638(08)00006-1

[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.

http://dx.doi.org/10.1109/NRSC.2012.6208502

[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.

http://dx.doi.org/10.1002/9780470874257

[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.

http://dx.doi.org/10.1016/j.cpc.2009.07.010

[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.

http://dx.doi.org/10.1364/AO.33.000501

[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.

http://dx.doi.org/10.1063/1.1699834

[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.

http://dx.doi.org/10.1093/qjmam/hbi031

[33] E. Jordan and K. Balmain, “Electromagnetic Waves and Radiating Systems,” Prentice-Hall, Upper Saddle River, 1968.