In this paper, a new analytically regularizing method, based on Helmholtz decomposition and Galerkin method, for the analysis of the electromagnetic scattering by a hollow finite-length perfectly electrically conducting (PEC) circular cylinder is presented. After expanding the involved functions in cylindrical harmonics, the problem is formulated as an electric field integral equation (EFIE) in a suitable vector transform (VT) domain such that the VT of the surface curl-free and divergence-free contributions of the surface current density, adopted as new unknowns, are scalar functions. A fast convergent second-kind Fredholm infinite matrix-operator equation is obtained by means of Galerkin method with suitable expansion functions reconstructing the expected physical behaviour of the unknowns. Moreover, the elements of the scattering matrix are efficiently evaluated by means of analytical asymptotic acceleration technique.
2. Michalski, K. A. and D. Zheng, "Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media, part I: Theory," IEEE Trans. Antennas Propagat., Vol. 38, 335-344, Mar. 1990.
3. Michalski, K. A. and D. Zheng, "Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media, part II: Implementation and results for contiguous half-spaces," IEEE Trans. Antennas Propagat., Vol. 38, 345-352, Mar. 1990.
4. Eswaran, K., "On the solutions of a class of dual integral equations occurring in diffraction problems," Proc. Roy. Soc. London, Ser. A, 399-427, 1990.
5. Veliev, E. I. and V. V. Veremey, "Numerical-analytical approach for the solution to thewave scattering by polygonal cylinders and flat strip structures," Analytical and Numerical Methods in Electromagnetic Wave Theory, M. Hashimoto, M. Idemen, and O. A. Tretyakov, Eds., Science House, Tokyo, 1993.
6. Davis, A. M. J. and R. W. Scharstein, "Electromagnetic plane wave excitation of an open-ended finite-length conducting cylinder," Journal of Electromagnetic Waves and Applicatioons, Vol. 7, No. 2, 301-319, 1993.
7. Vitebskiy, S., K. Sturgess, and L. Carin, "Short-pulse plane-wave scattering from buried perfectly conducting bodies of revolution," IEEE Trans. Antennas Propagat., Vol. 44, 143-151, Feb. 1996.
8. Sheng, X. Q., J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, "Solution of combined-field integral equation using multievel fast multipole algorithm for scattering by homogeneous bodies," IEEE Trans. Antennas Propagat., Vol. 46, No. 11, 1718-1726, Nov. 1998.
9. Hongo, K. and H. Serizawa, "Diffraction of electromagnetic plane wave by rectangular plate and rectangular hole in the conducting plate," IEEE Trans. Antennas Propag., Vol. 47, No. 6, 1029-1041, Jun. 1999.
10. He, J. Q., T. J. Yu, N. Geng, and L. Carin, "Method of moments analysis of electromagnetic scattering from a general three-dimensional dielectric target embedded in a multilayered medium," Radio Sci., Vol. 35, 305-313, Mar./Apr. 2000.
11. Geng, N., A. Sullivan, and L. Carin, "Fast multipole method for scattering from an arbitrary PEC target above or buried in a lossy half space," IEEE Trans. Antennas Propagat., Vol. 49, 740-748, May 2001.
12. Tsalamengas, J. L., "Rapidly converging direct singular integral-equation techniques in the analysis of open microstrip lines on layered substrates," IEEE Trans. Microw. Theory Tech., Vol. 49, No. 3, 555-559, Mar. 2001.
13. Araneo, R., S. Celozzi, G. Panariello, F. Schettino, and L. Verolino, "Analysis of microstrip antennas by means of regularization via Neumann series," Review of Radio Science 1999-2002, 111-124, W. R. Stone, Ed., IEEE Press, Wiley Interscience, Piscataway, NJ/newyork, 2002.
14. Ozkan, E., F. Dikmen, and Y. A. Tuchkin, "Scalar wave diffraction by perfectly soft thin circular cylinder of finite length; Analytical regularization method," Turkish Journal of Electrical Engineering, Vol. 10, No. 3, 459-472, 2002.
15. Losada, V., R. R. Boix, and F. Medina, "Fast and accurate algorithm for the short-pulse electromagnetic scattering from conducting circular plates buried inside a lossy dispersive half-space," IEEE Trans. Geosci. Remote Sensing, Vol. 41, 988-997, May 2003.
16. Lucido, M., G. Panariello, and F. Schettino, "Accurate and efficient analysis of stripline structures," Microwave and Optical Technology Letters, Vol. 43, No. 1, 14-21, Oct. 2004.
17. Tsalamengas, J. L., "Exponentially converging Nystrom's methods for systems of singular integral equations with applications to open/closed strip- or slot-loaded 2-D structures," IEEE Antennas Propag. Mag., Vol. 54, No. 5, 1549-1558, 2006.
18. Hongo, K. and Q. A. Naqvi, "Diffraction of electromagnetic wave by disk and circular hole in a perfectly conducting plane," Progress In Electromagnetics Research, Vol. 68, 113-150, 2007.
19. Mei, C., M. Hasanovic, J. K. Lee, and E. Arvas, "Electromagnetic scattering from an arbitrarily shaped three-dimensional inhomogeneous bianisotropic body," PIERS Online, Vol. 3, No. 5, 680-684, 2007.
20. Lucido, M., G. Panariello, and F. Schettino, "Electromagnetic scattering by multiple perfectly conducting arbitrary polygonal cylinders," IEEE Trans. Antennas Propag., Vol. 56, 425-436, Feb. 200.
21. Lucido, M., G. Panariello, and F. Schettino, "TE scattering by arbitrarily connected conducting strips," IEEE Trans. Antennas Propag., Vol. 57, 2212-2216, Jul. 2009.
22. Sauleau, R., T. M. Benson, and A. I. Nosich, "Dual integral equations technique in electromagnetic scattering by a thin disk," Progress In Electromagnetic Research B, Vol. 16, 107-126, 2009.
23. Panin, S. B., P. D. Smith, E. D. Vinogradova, Y. A. Tuchkin, and S. S. Vinogradov, "Diffraction from arbitrary shaped bodies of revolution: Analytical regularization," Journal of Engineering Mathematics, Vol. 65, No. 2, 125-141, Oct. 2009.
24. Balaban, M. V., R. Sauleau, T. M. Benson, and A. I. Nosich, "Accurate qualification of the purcell effect in the presence of a dielectric microdisk of nanoscale thickness," IET Micro and Nano Letters, Vol. 6, No. 6, 393-396, 2011.
25. Bulygin, V. S., A. I. Nosich, and Y. V. Gandel, "Nystrom-type method in three-dimensional electromagnetic diffraction by a finite PEC rotationally symmetric surface," IEEE Trans. Antennas Propag., Vol. 60, No. 10, 4710-4718, 2012.
26. Coluccini, G., M. Lucido, and G. Panariello, "TM scattering by perfectly conducting polygonal cross-section cylinders: A new surface current density expansion retaining up to the second-order edge behavior," IEEE Trans. Antennas Propag., Vol. 60, No. 1, 407-412, Jan. 2012.
27. Lucido, M., "An analytical technique to fast evaluate mutual coupling integrals in spectral domain analysis of multilayered coplanar coupled striplines," Microwave and Optical Technology Letters, Vol. 54, No. 4, 1035-1039, Apr. 2012.
28. Lucido, M., "A new high-efficient spectral-domain analysis of single and multiple coupled microstrip lines in planarly layered media," IEEE Trans. Microw. Theory Tech., Vol. 60, No. 7, 2025-2034, Jul. 2012.
29. Balaban, M. V., O. V. Shapoval, and A. I. Nosich, "THz wave scattering by a graphene strip and a disk in the free space: Integral equation analysis and surface plasmon resonances," IOP Journal of Optics, Vol. 15, No. 11, 114007/9, 2013.
30. Bulygin, V. S., T. M. Benson, Y. V. Gandel, and A. I. Nosich, "Full-wave analysis and optimization of a TARA-like shield-assisted paraboloidal reflector antenna using nystrom-type method," IEEE Trans. Antennas Propag., Vol. 61, No. 10, 4981-4989, 2013.
31. Coluccini, G., M. Lucido, and G. Panariello, "Spectral domain analysis of open single and coupled microstrip lines with polygonal cross-section in bound and leaky regimes," IEEE Trans. Microw. Theory Tech., Vol. 61, No. 2, 736-745, Feb. 2013.
32. Lucido, M., "An efficient evaluation of the self-contribution integrals in the spectral-domain analysis of multilayered striplines," IEEE Antennas and Wireless Propagation Letters, Vol. 12, 360-363, Mar. 2013.
33. Coluccini, G. and M. Lucido, "A new high e±cient analysis of the scattering by a perfectly conducting rectangular plate," IEEE Trans. Antennas Propag., Vol. 61, No. 5, 2615-2622, May 2013.
34. Lucido, M., "Electromagnetic scattering by a perfectly conducting rectangular plate buried in a lossy half-space," IEEE Trans. Geosci. Remote Sensing, Vol. 52, No. 10, 6368-6378, Oct. 2014.
35. Lucido, M., G. Panariello, and F. Schettino, "An EFIE formulation for the analysis of leaky-wave antennas based on polygonal cross-section open waveguides," IEEE Antennas and Wireless Propagation Letters, Vol. 13, 983-986, May 2014.
36. Lucido, M., "Scattering by a tilted strip buried in a lossy half-space at oblique incidence," Progress In Electromagnetics Research M, Vol. 37, 51-62, 2014.
37. Corsetti, F., M. Lucido, and G. Panariello, "Effective analysis of the propagation in coupled rectangular-core waveguides," IEEE Photonics Technology Letters, Vol. 26, No. 18, 1855-1858, Sept. 2014.
38. Di Murro, F., M. Lucido, G. Panariello, and F. Schettino, "Guaranteed-convergence method of analysis of the scattering by an arbitrarily oriented zero-thickness PEC disk buried in a lossy half-space," IEEE Trans. Antennas Propag., Vol. 63, No. 8, 3610-3620, Aug. 2015.
39. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, New York, 1989.
40. Dudley, D. G., "Error minimization and convergence in numerical methods," Electromagnetics, Vol. 5, 89-97, 1985.
41. Hsiao, G. C. and R. E. Kleinman, "Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics," IEEE Trans. Antennas Propag., Vol. 45, 316-328, Mar. 1997.
42. Nosich, A. I., "The method of analytical regularization in wave-scattering and eigenvalue problems: Foundations and review of solutions," IEEE Antennas Propag. Mag., Vol. 42, No. 3, 34-49, Jun. 1999.
43. Kolmogorov, A. and S. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover, New York, 1999.
44. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Verlag Harri Deutsch, 1984.
45. Meixner, J., "The behavior of electromagnetic fields at edges," IEEE Trans. Antennas Propag., Vol. 20, 442-446, 1972.
46. Van Bladel, J., "A discussion of Helmholtz' theorem on a surface," AEU, Vol. 47, No. 3, 1993.
47. Geng, N. and L. Carin, "Wide-band electromagnetic scattering from a dielectric BOR buried in a layered lossy dispersive medium," IEEE Trans. Antennas Propag., Vol. 47, 610-619, Apr. 1999.
48. Gradstein, S. and I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York, 2000.