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2008-08-15
Analysis of High Frequency Plane Wave Scattering from a Double Negative Cylinder via the Modified Watson Transformation and Debye Expansion
By
Progress In Electromagnetics Research, Vol. 84, 55-92, 2008
Abstract
The modifiedWatson transform is applied to the Mie series expression of the electromagnetic field scattered by a high frequency plane wave incident on an infinitely long double negative cylinder. The Debye expansion is applied to the Mie series coefficients to obtain a physical insight into the scattering mechanisms and achieve an efficient approach for the computation of the scattered field. The first two terms of the Debye series are computed using the residue series in the geometrical shadow regions and using the steepest descent method in the geometrically lit regions. It is observed that the results obtained from the series and from the modified Watson transform are in good agreement. The angular boundaries for the geometrically lit and the geometrical shadow regions of the double negative cylinder corresponding to the first two terms of the Debye series are determined. These are compared with the corresponding angular boundaries for a double positive cylinder. It is observed that the spatial extent of the geometrical shadow of the double negative cylinder corresponding to the second term of the Debye series is very small compared to that of the double positive cylinder due to the negative refraction in the double negative cylinder when the magnitude of the refractive index n is greater than √2.
Citation
Saffet Sen, and Mustafa Kuzuoğlu, "Analysis of High Frequency Plane Wave Scattering from a Double Negative Cylinder via the Modified Watson Transformation and Debye Expansion," Progress In Electromagnetics Research, Vol. 84, 55-92, 2008.
doi:10.2528/PIER08061703
References

1. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of ε and μ," Soviet Physics Uspekhi, Vol. 10, No. 4, January-February 1968.
doi:10.1070/PU1968v010n04ABEH003699

2. Pendry, J. B., A. J. Hold, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Transactions on Microwave Theory and Techniques, Vol. 47, 2075-2084, November 1999.
doi:10.1109/22.798002

3. Pendry, J. B., A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Physical Review Letters, Vol. 76, 4773, June 17 1996.
doi:10.1103/PhysRevLett.76.4773

4. Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Physical Review Letters, Vol. 84, 4184, May 1 2000.
doi:10.1103/PhysRevLett.84.4184

5. Pendry, J. B., "Negative refraction makes a perfect lens," Physical Review Letters, Vol. 85, No. 18, October 2000.
doi:10.1103/PhysRevLett.85.3966

6. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, 77-79, April 6 2001.
doi:10.1126/science.1058847

7. Ziolkowski, R. W. and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Physical Review E, Vol. 64, No. 056625, 2001.

8. Ziolkowski, R. W. and A. D. Kipple, "Causality and double-negative metamaterials," Physical Review E, Vol. 68, 026615, Part 2, 2003.

9. Caloz, C., H. Okabe, T. Iwai, and T. Itoh, "Transmission line approach of left-handed (LH) materials," Proc. USNC/URSI National Radio Science Meeting, Vol. 1, 39 San Antonio, TX, June 2002.

10. Grbic, A. and G. V. Eleftheriades, "A backward-wave antenna based on negative refractive index," Proc. IEEE AP-S Int. Symp., Vol. 4, 340-343, San Antonio, TX, June 2002.

11. Iyer, A. K. and G. V. Eleftheriades, "Negative refractive index metamaterials supporting 2-D waves," Proc. IEEE MTT-S Int. Symp., Vol. 2, 1067-1070, San Antonio, TX, June 2002.
doi:10.1109/TMTT.2002.805197

12. Eleftheriades, G. V., A. K. Iyer, and P. C. Kramer, "Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Transactions on Microwave Theory and Techniques, Vol. 50, No. 12, December 2002.
doi:10.1063/1.1343489

13. Shelby, R. A., D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial," Applied Physics Letters, Vol. 78, 489-491, 2001.
doi:10.1103/PhysRevLett.89.257401

14. Pacheco, Jr., J., T. M. Grzegorczyk, B.-I. Wu, Y. Zhang, and J. A. Kong, "Power propagation in homogeneous isotropic frequency-dispersive left-handed media," Physical Review Letters, Vol. 89, 257401, 2002.
doi:10.1063/1.1408261

15. Caloz, C., C.-C. Chang, and T. Itoh, "Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations," Journal of Applied Physics, Vol. 90, 5483-5486, 2001.

16. Ziolkowski, R. W. and A. D. Kipple, "Application of double negative materials to increase the power radiated by electrically small antennas," IEEE Transactions on Antennas and Propagation, Vol. 51, No. 10, October 2003.
doi:10.1109/LPT.2003.818950

17. Xiao, S. H., L. F. Shen, and S. L. He, "A novel directional coupler utilizing a left-handed material," IEEE Photonics Technology Letters, Vol. 16, No. 1, January 2004.
doi:10.1163/156939306777442908

18. Yang, R., Y.-J. Xie, P. Wang, and L. Li, "Microstrip antennas with left-handed materials substrates," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 9, 1221-1233, 2006.
doi:10.1163/156939307780749165

19. Zhang, J., B. Cui, J.-Z. Gu, and X.-W. Sun, "A harmonic suppressed Wilkinson power divider using complementary split ring resonators (CSRRs)," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 6, 811-819, 2007.

20. Li, Z. and T. J. Cui, "Novel waveguide directional couplers using left-handed materials," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 8, 1053-1062, 2007.

21. Guo, Y. and R. Xu, "Ultra-wideband power splitting/combining technique using zero-degree left-handed transmission lines," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 8, 1109-1118, 2007.
doi:10.1163/156939307783134425

22. Yang, R., Y. Xie, D. Li, J. Zhang, and J. Jiang, "Bandwidth enhancement of microstrip antennas with metamaterial bilayered substrates," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 15, 2321-2330, 2007.

23. Zhang, J. and X.-W. Sun, "Harmonic suppression of branch-line and rat-race coupler using complementary split ring resonators (CSRR) cell," Progress In Electromagnetics Research Letters, Vol. 2, 73-79, 2008.
doi:10.2528/PIERL07111808

24. Abdalla, M. A. and Z. Hu, "On the study of left-handed coplanar waveguide coupler on ferrite substrate," Progress In Electromagnetics Research Letters, Vol. 1, 69-75, 2008.
doi:10.1103/PhysRevB.66.045116

25. Kuzmiak, V. and A. A. Maradudin, "Scattering properties of a cylinder fabricated from a left-handed material," Physical Review B, Vol. 66, 045116, 2002.
doi:10.1002/mop.10705

26. Ruppin, R., "Intensity distribution inside scatterers with negative-real permittivity and permeability," Microwave and Optical Technology Letters, Vol. 36, No. 3, February 5 2003.
doi:10.1163/156939307783152777

27. Wang, M. Y., J. Xu, J. Wu, Y. B. Yan, and H. L. Li, "FDTD study on scattering of metallic column covered by double-negative metamaterial," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1905-1914, 2007.
doi:10.2528/PIERB07112906

28. Valagiannopoulos, C. A., "Electromagnetic scattering from two eccentric metamaterial cylinders with frequency-dependent permittivities differing slightly each other," Progress In Electromagnetics Research B, Vol. 3, 23-34, 2008.
doi:10.2528/PIERB07121107

29. Hady, L. K. and A. A. Kishk, "Electromagnetic scattering from conducting circular cylinder coated by metamaterials and loaded with helical strips under oblique incidence," Progress In Electromagnetics Research B, Vol. 3, 189-206, 2008.
doi:10.2528/PIERB07120803

30. Oraizi, H. and A. Abdolali, "Combination of MLS, GA & CG for the reduction of RCS of multilayered cylindrical structures composed of dispersive metamaterials," Progress In Electromagnetics Research B, Vol. 3, 227-253, 2008.
doi:10.2528/PIERB07112803

31. Zainud-Deen, S. H., A. Z. Botrosand, and M. S. Ibrahim, "Scattering from bodies coated with metamaterial using FDFD method," Progress In Electromagnetics Research B, Vol. 2, 279-290, 2008.
doi:10.1163/156939306779322620

32. Grzegorczyk, T. M. and J. A. Kong, "Review of left-handed metamaterials: Evolution from theoretical and numerical studies to potential applications," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 14, 2053-2064, 2006.
doi:10.1163/156939306779322585

33. Chen, H., B.-I. Wu, and J. A. Kong, "Review of electromagnetic theory in left-handed materials," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 15, 2137-2151, 2006.

34. Physik. Z., Vol. 9, 775, 1908.
doi:10.1098/rspa.1918.0050

35. Watson, G. N., "The diffraction of electric waves by the earth," Proceedings of the Royal Society of London, Vol. 95, No. 666, 83-99, 1918.
doi:10.1119/1.1975793

36. Pumplin, J., "Application of Sommerfeld-Watson transformation to an electrostatics problem," American Journal of Physics, Vol. 37, No. 7, 737-739, 1969.

37. Uberall, H., "Acoustic scattering from elastic cylinders and spheres: Surface waves (Watson transform) and transmitted waves," Diffusion et Diffraction, Vol. 2, No. 5, 353-387, 1985.

38. Wang, H.-L., Q. Wu, X.-J. He, and L.-W. Li, "Computation of wave scattering problems from a spheric body: Derivation of the new Sommerfeld-Watson transformation," Progress In Electromagnetics Research Symposium 2005, 707-710, Hangzhou, China, August 22-26 2005.
doi:10.2528/PIER07052502

39. Valagiannopoulos, C. A., "An overview of the Watson transformation presented through a simple example," Progress In Electromagnetics Research, Vol. 75, 137-152, 2007.
doi:10.1029/RS010i002p00205

40. Inada, H., "Diffracted field computations by a series expansion," Radio Science, Vol. 10, 205-220, February 1975.
doi:10.1002/ecjb.4420780405

41. Sasamori, T., T. Uno, and S. Adachi, "High-frequency analysis of electromagnetic scattering due to a dielectric cylinder," Electronics and Communications in Japan, Part II - Electronics, Vol. 78, No. 4, 41-55, 1995.
doi:10.1063/1.1664764

42. Nussenzweig, H. M., "High-frequency scattering by a transparent sphere. 1. Direct reflection and transmission," Journal of Mathematical Physics, Vol. 10, No. 1, 82-124, January 1969.
doi:10.1016/0003-4916(65)90041-2

43. Nussenzweig, H. M., "High-frequency scattering by an impenetrable sphere," Annals of Physics, Vol. 34, 23-95, 1965.

44. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications Inc., New York, 1972.