2014-03-19
Electromagnetic Scattering by Approximately Cloaked Dielectric Cylinder
By
Progress In Electromagnetics Research B, Vol. 59, 59-70, 2014
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 (TMz) and transverse electric (TEz) polarizations of the incident plane wave for different transformed body radii.
Citation
Hany Mahmoud Zamel, Essam Eldiwany, and Hadia El-Hennawy, "Electromagnetic Scattering by Approximately Cloaked Dielectric Cylinder," Progress In Electromagnetics Research B, Vol. 59, 59-70, 2014.
doi:10.2528/PIERB14011806
References

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

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        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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.        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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.        Google Scholar

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

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

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        Google Scholar

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