volume | PIER Journals

Abstract

A volume-surface integral equation (VSIE) formulation is developed for determining the electromagnetic TM scattering by a two-dimensional conducting cylinder coated with an inhomogeneous dielectric/magnetic material. The electric field integral equations (EFIEs) are utilized to derive the VSIE. The surface EFIE is applied to the conducting surface, while the volume EFIE is applied to the coating region. By employing the surface and equivalence principles, the problem is reduced into a set of coupled integral equations in terms of equivalent electric and magnetic currents radiating into unbounded space. The moment method is used to solve the integral equations. Numerical results for the bistatic radar cross section for different structures are presented. The well-known exact series-solution for a conducting circular cylinder coated with multilayers of homogeneous materials is used along with the available published data to validate the results. The influence of using coatings with double-positive (DPS) and/or double-negative (DNG) materials on the radar cross section is investigated.

1. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley, New York, 1989.

2. Tang, C. C. H., "Backscattering from dielectric-coated infinite cylindrical obstacles," J. Appl. Phys., Vol. 28, 628-633, 1957.
doi:10.1063/1.1722815 Google Scholar

3. Richmond, J. H., "Scattering by a conducting elliptic cylinder with dielectric coating," Radio Sci., Vol. 23, 1061-1066, 1988.
doi:10.1029/RS023i006p01061 Google Scholar

4. Kakogiannos, N. B. and J. A. Roumeliotis, "Electromagnetic scattering from an infinite elliptic metallic cylinder coated by a circular dielectric one," IEEE Trans. Microwave Theory Tech., Vol. 38, 1660-1666, 1990.
doi:10.1109/22.60013 Google Scholar

5. Roumeliotis, J. A., H. K. Manthopoulos, and V. K. Manthopoulos, "Electromagnetic scattering from an infinite circular metallic cylinder coated by an elliptic dielectric one," IEEE Trans. Microwave Theory Tech., Vol. 41, 862-869, 1993.
doi:10.1109/22.234523 Google Scholar

6. 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

7. Zouros, G. P., D. P. Kanoussis, and J. A. Roumeliotis, "Scattering by an infinite circular metallic cylinder coated by a lossless or lossy elliptical cylinder: Closed-form solutions," 7th European Conference on Antennas and Propagation (EuCAP), 2343-2347, Gothenburg, Sweden, 2013. Google Scholar

8. Bussy, H. E. and J. H. Richmond, "Scattering by a lossy dielectric circular cylindrical multilayer numerical values," IEEE Trans. Antennas Propagat., Vol. 23, 723-725, 1975.
doi:10.1109/TAP.1975.1141146 Google Scholar

9. Sebak, A., L. Shafai, and H. A. Ragheb, "Electromagnetic wave scattering by a two-layered piecewise homogeneous confocal elliptic cylinder," Radio Sci., Vol. 26, 111-119, 1991.
doi:10.1029/90RS01843 Google Scholar

10. Caorsi, S., M. Pastorino, and M. Raffetto, "Scattering by a conducting elliptic cylinder with a multilayer dielectric coating," Radio Sci., Vol. 32, 2155-2166, 1997.
doi:10.1029/97RS02205 Google Scholar

11. Lin, J. M., Theory and Computation of Electromagnetic Fields, J. Wiley IEEE Press, Hobkon, New Jersey, 2010.

12. Poggio, A. J. and E. K. Miller, "Integral equation solutions of three-dimensional scattering problems," Computer Techniques for Electromagnetics, R. Mittra (ed.), Ch. 4, 129-163, Pergamon Press, New York, 1973. Google Scholar

13. Sheng, X. Q., J. M. Jin, J. Song, W. C. Chew, and C. C. Lu, "Solution of combined field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies," IEEE Trans. Antennas Propagat., Vol. 46, 1718-1726, 1998.
doi:10.1109/8.736628 Google Scholar

14. Wu, T. K. and L. L. Tsai, "Scattering from arbitrarily-shaped lossy dielectric bodies of revolution," Radio Sci., Vol. 12, 709-718, 1977.
doi:10.1029/RS012i005p00709 Google Scholar

15. Umashankar, K., A. Taflove, and S. M. Rao, "Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects," IEEE Trans. Antennas Propagat., Vol. 34, 758-766, 1986.
doi:10.1109/TAP.1986.1143894 Google Scholar

16. Harrington, R. F., "Boundary integral formulations for homogeneous material bodies," Journal of Electromagnetic Waves and Applications, Vol. 3, No. 1, 1-15, 1989.
doi:10.1163/156939389X00016 Google Scholar

17. Muller, C., Foundation of the Mathematical Theory of Electromagnetic Waves, Springer-Verlag, Berlin, 1969.
doi:10.1007/978-3-662-11773-6_1

18. Glisson, A. W., "An integral equation for electromagnetic scattering from homogeneous dielectric bodies," IEEE Trans. Antennas Propagat., Vol. 32, 173-175, 1984.
doi:10.1109/TAP.1984.1143279 Google Scholar

19. Swatek, D. R. and I. R. Ciric, "Single source integral equation for wave scattering by multiply-connected dielectric cylinders," IEEE Trans. Magnetics, Vol. 32, 878-881, 1996.
doi:10.1109/20.497381 Google Scholar

20. Swatek, D. R. and I. R. Ciric, "A recursive single-source surface integral equation analysis for wave scattering by heterogeneous dielectric bodies," IEEE Trans. Antennas Propagat., Vol. 48, 1175-1185, 2000. Google Scholar

21. Menshov, A. and V. Okhmatovski, "New single-source surface integral equations for scattering on penetrable cylinders and current °ow modeling in 2-D conductors," IEEE Trans. Microwave Theory Tech., Vol. 61, 341-350, 2013.
doi:10.1109/TMTT.2012.2227784 Google Scholar

22. Huddleston, P. L., L. N. Medgyesi-Mitschang, and J. M. Putnam, "Combined field integral equation formulation for scattering by dielectrically coated conducting bodies," IEEE Trans. Antennas Propagat., Vol. 34, 510-520, 1986.
doi:10.1109/TAP.1986.1143846 Google Scholar

23. Arvas, E., M. Ross, and Y. Qian, "TM scattering from a conducting cylinder of arbitrary cross-section covered by multiple layers of lossy dielectrics," IEE Proc., Pt. H, Vol. 135, 226-230, 1988. Google Scholar

24. Arvas, E. and T. K. Sarkar, "RCS of two-dimensional structures consisting of both dielectrics and conductors of arbitrary crosssection," IEEE Trans. Antennas Propagat., Vol. 37, 546-554, 1989.
doi:10.1109/8.24182 Google Scholar

25. Rao, S. M., C. C. Cha, R. L. Cravey, and D. L. Wilkes, "Electromagnetic scattering from arbitrary shaped conducting bodies coated with lossy materials of arbitrary thickness," IEEE Trans. Antennas Propagat., Vol. 39, 627-631, 1991.
doi:10.1109/8.81490 Google Scholar

26. Swatek, D. R. and I. R. Ciric, "Single integral equation for wave scattering by a layered dielectric cylinder," IEEE Trans. Magnetics, Vol. 34, 2724-2727, 1998.
doi:10.1109/20.717632 Google Scholar

27. Harrington, R. F., Field Computation by Moment Methods, Macmillan, New York, 1968, Reprinted by Krieger Publishing Co., Melbourne, FL, 1982.

28. Min, X., W. Sun, W. J. Gesang, and K. M. Chen, "An efficient formulation to determine the scattering characteristics of a conducting body with thin magnetic coatings," IEEE Trans. Antennas Propagat., Vol. 39, 448-454, 1991.
doi:10.1109/8.81456 Google Scholar

29. Lin, C. S. and M. T. Yaqoob, "Scattering from a conducting surface coated with multilayers of lossy dielectric material (transverse electric polarization)," J. Appl. Phys., Vol. 72, 3005-3008, 1992.
doi:10.1063/1.351508 Google Scholar

30. Lin, C. S. and M. T. Yaqoob, "An efficient formulation to find the scattering field of a conducting cylinder coated with lossy magnetic material," J. Appl. Phys., Vol. 73, 4038-4041, 1993.
doi:10.1063/1.352871 Google Scholar

31. Jin, J. M., V. V. Liepa, and C. T. Tai, "A volume-surface integral equation for electromagnetic scattering by inhomogeneous cylinders," Journal of Electromagnetic Waves and Applications, Vol. 2, No. 5-6, 573-588, 1988.
doi:10.1163/156939388X00170 Google Scholar

32. Jin, J. M. and V. V. Liepa, "Simple moment method program for computing scattering from complex cylindrical obstacles," IEE Proc., Pt. H, Vol. 136, 321-329, 1989. Google Scholar

33. Volakis, J. L., "Alternative field representations and integral equations for modeling inhomogeneous dielectrics," IEEE Trans. Microwave Theory Tech., Vol. 40, 604-608, 1992.
doi:10.1109/22.121745 Google Scholar

34. Volakis, J. L. and K. Sertel, Integral Equation Methods for Electromagnetics, Scitech Publishing Raleigh, NC, 2012.

35. Jin, J. M. and V. V. Liepa, "Application of hybrid finite element method to electromagnetic scattering from coated cylinders," IEEE Trans. Antennas Propagat., Vol. 36, 50-54, 1988.
doi:10.1109/8.1074 Google Scholar

36. Wu, K. L., G. Y. Delisle, and D. G. Fang, "EM scattering of an arbitrary multiple dielectric coated conducting cylinder by coupled finite boundary element method," IEE Proc., Pt. H, Vol. 137, 1-4, 1990. Google Scholar

37. Leviatan, Y., A. Boag, and A. Boag, "Analysis of electromagnetic scattering from dielectrically coated conducting cylinders using a multifilament current model," IEEE Trans. Antennas Propagat., Vol. 36, 1602-1607, 1988.
doi:10.1109/8.9711 Google Scholar

38. Chen, Z. N. and W. X. Zhang, "Electromagnetic scattering from a dielectric coated cylinder using OSRC-GMT," Electron. Lett., Vol. 29, 853-854, 1993.
doi:10.1049/el:19930570 Google Scholar

39. Rao, T. C. K. and M. A. K. Hamid, "G.T.D. analysis of scattering from a dielectric-coated conducting cylinder," IEE Proc., Pt. H, Vol. 127, 143-153, 1980. Google Scholar

40. Wang, N., "Electromagnetic scattering from a dielectric coated cylinder," IEEE Trans. Antennas Propagat., Vol. 33, 960-963, 1985.
doi:10.1109/TAP.1985.1143696 Google Scholar

41. Kim, H. T. and N. Wang, "UTD solution for electromagnetic scattering by a circular cylinder with thin lossy coatings," IEEE Trans. Antennas Propagat., Vol. 37, 1463-1472, 1989.
doi:10.1109/8.43566 Google Scholar

42. Tanyer, S. G. and R. G. Olsen, "High-frequency scattering by a conducting circular cylinder coated with a lossy dielectric of nonuniform thickness," IEEE Trans. Antennas Propagat., Vol. 45, 689-697, 1997.
doi:10.1109/8.564095 Google Scholar

43. Hussar, P., "A uniform GTD treatment of surface diffraction by impedance and coated cylinders," IEEE Trans. Antennas Propagat., Vol. 46, 998-1008, 1998.
doi:10.1109/8.704801 Google Scholar

44. Goto, K., L. H. Loc, T. Kawana, and T. Ishihara, "Extended UTD solution for scattered fields by a coated conducting cylinder," Antennas and Propagation Society International Symposium (APSURSI), 1-2, Chicago, IL, 2012. Google Scholar

45. Sun, J., W. Sun, T. Jiang, and Y. Feng, "Directive electromagnetic radiation of a line source scattered by a conducting cylinder coated with left-handed metamaterial," Microwave & Opt. Technol. Lett., Vol. 47, 274-279, 2005.
doi:10.1002/mop.21145 Google Scholar

46. Zainud-Deen, S. H., A. Z. Botros, and M. S. Ibrahim, "Scattering from bodies coated with metamaterial using FDFD method," Progress In Electromagnetics Research B, Vol. 2, 279-290, 2008.
doi:10.2528/PIERB07112803 Google Scholar

47. Richmond, J. H., "Scattering by a dielectric cylinder of arbitrary cross-section shape," IEEE Trans. Antennas Propagat., Vol. 13, 334-341, 1965.
doi:10.1109/TAP.1965.1138427 Google Scholar

48. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, IEEE Press, Piscataway, NJ, 1998.

49. Bin-Jie, H., E. Y. Kai-Ning, Z. Jun, and T. Serge, "Scattering characteristics of conducting cylinder coated with nonuniform magnetized ferrite," Chinese Physics, Vol. 14, 2305-2313, 2005.
doi:10.1088/1009-1963/14/11/027 Google Scholar

Dr. Ahmed A. Sakr

Professor Ezzeldin A. Soliman

Dr. Alaa Abdelmageed