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Abstract

The aim of the present paper is to obtain explicit asymptotic expressions for the "transfer (diffraction) coefficients" related to the diffraction of high frequency cylindrical waves from the discontinuity occurred in the material properties as well as in the thicknesses of a coated cylindrically curved metallic sheet characterized by the second order GIBCs. Relying on the locality of the high frequency diffraction phenomenon, the angular interval φ∈(-π;π) is extended to the abstract innite space φ∈(-∞;∞) wherein the diffracting structure is replaced by a two-part cylindrically curved second order impedance sheet ρ = a extending from φ = -∞ to φ = ∞. The resulting boundary value problem is formulated as a Hilbert equation which is solved asymptotically in the high frequency limit. Some graphical results showing the eects of various parameters on the transfer coecients are presented.

1. Kay, A. F., "Scattering of a surface wave by a discontinuity in reactance," IEEE Trans. Antennas and Propagat., Vol. 7, No. 1, 22-31, 1959.
doi:10.1109/TAP.1959.1144635 Google Scholar

2. Tiberio, R. and G. Pelosi, "High frequency scattering from the edges of impedance discontinuities on a at plane," IEEE Trans. Antennas and Propagat., Vol. 31, No. 4, 590-596, 1983.
doi:10.1109/TAP.1983.1143094 Google Scholar

3. Uzgören, G., A. Büyükaksoy, and A. H. Serbest, "Diffraction coefficients related to the discontinuity formed by impedance and resistive half planes," IEE Proceedings, Vol. 36, No. 1, 19-23, Pt. H, 1989.

4. Büyükaksoy, A., G. Uzgören, and A. H. Serbest, "Diffraction of an obliquely incident plane wave by the discontinuity of a two-part thin dielectric plane," Int. J. Engng. Sci., Vol. 27, No. 6, 701-710, 1989.
doi:10.1016/0020-7225(89)90022-0 Google Scholar

5. Büyükaksoy, A. and G. Uzgören, "High frequency scattering from the impedance discontinuity on a cylindrically curved surface," IEEE Trans. Antennas and Propagat., Vol. 35, No. 2, 234-236, 1987.
doi:10.1109/TAP.1987.1144079 Google Scholar

6. Weinstein, L. A., The Theory of Diffraction and the Factorization Method, The Golem Press, 1969.

7. Leppington, F. G., "Travelling waves in a dielectric slab with an abrupt change in thickness," Proc. R. Soc. London Ser. A, Vol. 386, 443-460, 1983. Google Scholar

8. Rojas, R. G., "Generalized impedance boundary conditions," Electronics Letters, Vol. 24, No. 17, 1093-1094, 1988.
doi:10.1049/el:19880741 Google Scholar

9. Rojas, R. G. and Z. Al-hekail, "Generalized impedance/resistive boundary conditions for electromagnetic scattering problems," Radio Sci., Vol. 24, No. 1, 1-12, 1989.
doi:10.1029/RS024i001p00001 Google Scholar

10. Senior, T. B. A. and J. L. Volakis, "Derivation and application of a class of generalized boundary conditions," IEEE Trans. Antennas Propagat., Vol. 37, No. 12, 1566-1572, 1989.
doi:10.1109/8.45099 Google Scholar

11. Rojas, R. G., H. C. Ly, and P. H. Pathak, "Electromagnetic plane wave diffraction by a planar junction of two thin dielectric/ferrite half planes," Radio Sci., Vol. 24, No. 4, 641-660, 1991.
doi:10.1029/91RS00247 Google Scholar

12. Senior, T. B. A., "Generalised boundary and transition conditions and the question of uniqueness," Radio Sci., Vol. 27, No. 6, 929-934, 1992.
doi:10.1029/92RS01426 Google Scholar

13. Buldyrev, V. S. and M. A. Lyalinov, Mathematical Methods in Modern Electromagnetic Diffraction Theory, Science House, 2001.

14. Ly, H. C., R. G. Rojas, and P. H. Pathak, "EM plane wave diffraction by a planar junction of two thin material half-planes --- Oblique incidence," IEEE Trans. Antennas Propagat., Vol. 41, No. 10, 429-441, 1993.
doi:10.1109/8.220975 Google Scholar

15. Ly, H. C. and R. G. Rojas, "Analysis of diffraction by material discontinuities in thin material-coated planar surfaces based on Maliuzhinets method," Radio Sci., Vol. 28, No. 3, 281-297, 1993.
doi:10.1029/92RS02880 Google Scholar

16. Büyükaksoy, A. and G. Çınar, "Line source scattering by a cylindrically curved surface with second-order generalized impedance boundary condition," Wave Motion, Vol. 47, No. 1, 45-58, 2010.
doi:10.1016/j.wavemoti.2009.07.004 Google Scholar

17. Idemen, M. and L. B. Felsen, "Diffraction of a whispering gallery mode by the edge of a thin concave cylindrically curved surface," IEEE Trans. Antennas Propagat., Vol. 29, No. 4, 571-579, 1981.
doi:10.1109/TAP.1981.1142643 Google Scholar

18. Noble, B., Methods Based on the Wiener-hopf Technique for the Solution of Partial Differential Equations, 2nd Ed., American Mathematical Society, 1988.

19. Felsen, L. B. and N. Marcuvitz, Radiation and Scattering of Waves, Prentice Hall, 1973.

20. Senior, T. B. A., "Half-plane edge diffraction," Radio Sci., Vol. 10, No. 6, 645-650, 1975.
doi:10.1029/RS010i006p00645 Google Scholar

21. Büyükaksoy, A. and O. Bıçakçı, "High-frequency scattering of a whispering gallery mode by a cylindrically curved surface with second-order generalized impedance boundary conditions," IEEE Trans. Antennas Propagat., Vol. 43, No. 12, 1512-1519, 1995.
doi:10.1109/8.475949 Google Scholar

Prof. Gokhan Cinar

Dr. Alinur Buyukaksoy