volume | PIER Journals

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 2D or cylindrical body into a line. Some components of the electrical parameters of the cloaking material (ε, μ) are required to have infinite or zero value at the boundary of the hidden object. In order to eliminate the zero or infinite values of the electrical parameters, approximate cloaking can be used by transforming the cylindrical body virtually into a small cylinder rather than a line, but this produces some scattering. The solution is obtained by rigorously solving Maxwell equations using angular harmonics expansion. In this work, the scattering pattern, and the backscattering cross section against the frequency for cloaked conducting and dielectric cylinders are studied for both transverse magnetic (TM_z) and transverse electric (TE_z) polarizations of the incident plane wave for different transformed body radii.

1. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, 1780-1782, 2006.
doi:10.1126/science.1125907

2. Kwon, D. and D. Werner, "Transformation electromagnetics: An overview of the theory and applications," IEEE Ant. and Prop. Mag., Vol. 52, No. 1, 24-46, 2010.
doi:10.1109/MAP.2010.5466396

3. Yan, M., Z. Ruan, and M. Qiu, "Scattering characteristics of simplified cylindrical invisibility cloaks," Opt. Exp., Vol. 15, No. 26, 17772-17782, 2007.
doi:10.1364/OE.15.017772

4. Alitalo, P. and S. Tretyakov, "Numerical modeling and characterization of selected electromagnetic cloaking structures," Inter. J. of RF and Micro. Computer --- Aided Eng., Vol. 22, No. 4, 483-495, 2012.
doi:10.1002/mmce.20638

5. Cummer, S., B. Popa, D. Schurig, D. Smith, and . Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E, Vol. 74, 36621-1-36621-5, 2006.

6. Li, J., Y. Huang, and W. Yang, "Developing a time-domain finite-element method for modeling of electromagnetic cylindrical cloaks," J. of Comp. Phys., Vol. 231, No. 7, 2880-2891, 2012.
doi:10.1016/j.jcp.2011.12.026

7. Schurig, D., 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, 977-980, Oct. 2006.

8. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewar, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Transactions on Microwave Theory and Techniques, Vol. 47, No. 11, 2075-2084, Nov. 1999.
doi:10.1109/22.798002

9. Eleftheriades, G. V. and K. G. Balmain, Negative Refraction Metamaterials --- Fundamental Principles and Applications, John Wiley, 2005.
doi:10.1002/0471744751

10. Engheta, N. and R. W. Ziolkowski, "Metamaterials: Physics and Engineering Explorations," Wiley-IEEE Press, 2006.

11. Wang, J., S. Qu, J. Zhang, H. Ma, Y. Yang, C. Gu, X. Wu, and Z. Xu, "A tunable left-handed metamaterial based on modiˉed broadside-coupled split-ring resonators," Progress In Electromagnetics Research Letters, Vol. 6, 35-45, 2009.

12. Ruan, Z., M. Yan, C. W. Neff, and M. Qiu, "Ideal cylindrical cloak: Perfect but sensitive to tiny perturbations," Phys. Rev. Lett., Vol. 99, 113903-1-113903-4, 2007.
doi:10.1103/PhysRevLett.99.113903

13. Shahzad, A., F. Qasim, S. Ahmed, and Q. A. Naqvi, "Cylindrical invisibility cloak incorporating PEMC at perturbed void region," Progress In Electromagnetics Research M, Vol. 21, 61-76, 2011.
doi:10.2528/PIERM11061302

14. Liu, H., "Virtual reshaping and invisibility in obstacle scattering," Inverse Problems, Vol. 25, No. 4, 1-10, 2009.
doi:10.1088/0266-5611/25/4/045006

15. Zhou, T., "Electromagnetic inverse problems and cloaking,", Ph. D. Thesis, Washington University, 2010.

16. Isic, G., R. Gajic, B. Novakovic, Z. V. Popovic, and K. Hingerl, "Radiation and scattering from imperfect cylindrical electromagnetic cloaks," Opt. Exp., Vol. 16, 1413-1422, 2008.
doi:10.1364/OE.16.001413

17. Song, W., X. Yang, and X. Sheng, "Scattering characteristics of 2-D imperfect cloaks with layered isotropic materials," IEEE Ant. and Propag. Let.., Vol. 11, 53-56, 2012.
doi:10.1109/LAWP.2011.2182590

18. Kohn, R., D. Onofrei, M. Vogelius, and M. Weinstein, "Cloaking via change of variables for the Helmholtz equation," Comm. on Pure and App. Math., Vol. 63, No. 8, 973-1016, 2010.

19. Tinghua, T., M. Huang, W. Li, J. Yang, and Q. Zhang, "A novel proposal for simplified design of metamaterial shrinking device," Int. Jour. for Light and Electron. Optics, Vol. 124, No. 21, 5232-5236, 2013.
doi:10.1016/j.ijleo.2013.03.059

20. Jiang, W., T. Cui, X. Yang, H. Ma, and Q. Cheng, "Shrinking an arbitrary object as one desires using metamaterials," App. Phys. Let., Vol. 98, 204101-1-204101-3, 2011.

21. Li, J. Z. and H. Y. Liu, "A class of polarization-invariant directional cloaks by concatenation via transformation optics," Progress In Electromagnetics Research, Vol. 123, 175-187, 2012.
doi:10.2528/PIER11111706

22. Liu, H. Y. and T. Zhou, "On approximate electromagnetic cloaking by transformation media," SIAM J. Appl. Math., Vol. 71, 218-241, 2011.
doi:10.1137/10081112X

23. Bao, G., H. Y. Liu, and J. Zou, "Nearly cloaking the full Maxwell equations: Cloaking active contents with general conducting layers," J. Math. Pures et Appl., 1-18, 2013.

24. Liu, H. Y., "On near-cloak in acoustic scattering," J. Differential Equations, Vol. 254, 1230-1246, 2013.
doi:10.1016/j.jde.2012.10.015

25. Liu, H. Y. and H. Sun, "Enhanced near-cloak by FSH lining," J. Math. Pures et Appl., Vol. 99, No. 1, 17-42, 2013.
doi:10.1016/j.matpur.2012.06.001

26. Li, J., H. Y. Liu, and H. Sun, "Enhanced approximate cloaking by SH and FSH lining," Inverse Problems, Vol. 28, No. 7, 075011-1-075011-21, 2012.
doi:10.1088/0266-5611/28/7/075011

27. McGuirk, J., "Electromagnetic field control and optimization using metamaterial,", Ph.D. Thesis, Air University, Ohio, USA, 2009.

28. Hu, J, X. Zhou, and G. Hu, "Design method for electromagnetic cloak with arbitrary shapes based on Laplace's equation," Opt. Exp., Vol. 17, No. 15, 13070, 2009.
doi:10.1364/OE.17.013070

29. Yan, M., W. Yan, and M. Qiu, "Invisibility cloaking by coordinate transformation," Progress in Optics, Vol. 52, 261-304, 2009.
doi:10.1016/S0079-6638(08)00006-1

30. Zamel, H., E. El-Diwany, and H. El-Hennawy, "Approximate electromagnetic cloaking of spherical bodies," National Radio Science Conference (NRSC), 19-28, Egypt, 2012.

31. McGuirk, J. and P. Collins, "Controlling the transmitted field into a cylindrical cloak's hidden region," Optics Express, Vol. 16, No. 22, 17560-17573, 2008.
doi:10.1364/OE.16.017560

32. Zhang, B., "Study of transformation-based invisibility cloaks,", Ph.D. Thesis, Massachusetts, 2009.

33. Harrington, R. F., Time Harmonic Electromagnetic Fields, McGraw-Hill, 1961.

34. Jin, J., "Theory and Computation of Electromagnetic Fields," John Wiley, 2010.

35. Ruck, G. T., D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook, Kluwer Academic, 1970.
doi:10.1007/978-1-4899-5324-7

36. Li, C. and Z. Shen, "Electromagnetic scattering by a conducting cylinder coated with metamaterials," Progress In Electromagnetics Research, Vol. 42, 91-105, 2003.
doi:10.2528/PIER03012901

37. Abramowitz, M. and I. Stegun, Handbook of Mathematical Functions, Dover, 1965.

Dr. Hany Mahmoud Zamel

Dr. Essam Eldiwany

Dr. Hadia El-Hennawy