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Abstract

This paper is concerned with the diffraction of an electromagnetic wave by a perfectly conducting half-plane in a homogeneous bi-isotropic medium (asymptotically). Similar analysis in a source-free field is done in S. Asghar and A. Lakhtakia (1994), Planewave diffraction by a perfectly conducting half-plane in a homogeneous bi-isotropic medium. Int. J. Appl. Electromagnetics in materials, 5, (1994), 181-188. In this paper attention is focused on the wave coming from a line source. The objective is to study the scattering of an electromagnetic wave from the boundary of a half-plane and thereby to provide a theoretical framework for the line source diffraction asymptotical ly. In far field approximation it is shown that an incident wave coming from a line source behaves like a plane wave. The scattered field is calculated by using the Fourier transform and the Wiener-Hopf techniques. The scattered field in the far zone is determined by using contour integration.

1. Asghar, S. and A. Lakhtakia, "Plane-wave diffraction by a perfectly conducting half-plane in a homogeneous bi-isotropic medium," Int. J. Appl. Electromagnetics in Materials, Vol. 5, 181-188, 1994. Google Scholar

2. Athanasiadis, C., G. Costakis, and I. G. Stratis, "Electromagnetic scattering by a perfectly conducting obstacle in a homogeneous chiral environment: solvability and low frequency theory," Math, Vol. 25, 927-944, 2002. Google Scholar

3. Athanasiadis, C. and S. Giotopoulos, "The Atkinson-Wilcox expansion theorem for electromagnetic chiral waves," Applied Mathematics Letters, Vol. 16, 675-681, 2003.
doi:10.1016/S0893-9659(03)00066-1 Google Scholar

4. Beltrami, E., Rend. Inst. Lombardo Acad. Sci. Lett., and Vol. 22, 121, Vol. 167, 1889. Trkal, 1986.

5. Faulkner, T. R., "Diffraction of an electromagnetic plane-wave by a metallic strip," J. Inst. Maths Applics, Vol. 1, 149-163, 1965. Google Scholar

6. Galaktionov, V. A., "On asymptotic self-similar behaviour for a quasilinear heat equation: single point blow-up," SIAM J. Math. Anal., Vol. 26, No. 3, 675-693, 1995.
doi:10.1137/S0036141093223419 Google Scholar

7. Ishimaru, A., Electromagnetic Wave Propagation, Radiation and Scattering, 1991.

8. Kalhor, H. A. and M. R. Zunoubi, "Electromagnetic scattering and absorption by arrays of lossless/lossy metallic or dielectric strips," Journal of Electromagnetic Waves and Applications, Vol. 19, 497-512, 2005.
doi:10.1163/1569393053303956 Google Scholar

9. Lakhtakia, A., Beltrami Fields in Chiral Media, World Scientific Publishing Co., 1994.

10. Lakhtakia, A. and B. Shanker, "Beltrami fields within continuous source regions, volume integral equations, scattering algorithms, and the extended Maxwell-Garnett model," International Journal of Applied Electromagnetics in Materials, Vol. 4, 65-82, 1993. Google Scholar

11. Lakhtakia, A., "Linear constitutive relations for Beltrami- Maxwell postulates," Microwave and Optical Technology Letters, Vol. 7, 580-581, 1994. Google Scholar

12. Lakhtakia, A. and T. G. Mackay, "Infinite phase velocity as the boundary between positive and negative phase velocities," Microwave Opt. Technol. Lett., Vol. 20, 165-166, 2004.
doi:10.1002/mop.20081 Google Scholar

13. Lakhtakia, A., M. W. McCall, and W. S. Weiglhofer, Negative Phase Velocity Mediums, Weiglhofer, 2003.

14. Mackay, T. G., "Plane waves with negative phase velocity in isotropic chiral mediums," Microwave and Optical Technology Letters, Vol. 45, No. 2, 120-121, 2005.
doi:10.1002/mop.20742 Google Scholar

15. Mackay, T. G. and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev., Vol. E69, 2004. Google Scholar

16. Morro, A., "Modelling of optically active electromagnetic media," Applied Mathematics Letters, Vol. 15, 285-291, 2002.
doi:10.1016/S0893-9659(01)00132-X Google Scholar

17. Nazarchuk, Z. and K. Kobayashi, "Mathematical modelling of electromagnetic scattering from a thin penetrable target," Progress In Electromagnetics Research Vol. 55, Vol. '' Progress In Electromagnetics Research 55, 95-116, 2005.
doi:10.2528/PIER05022003 Google Scholar

18. Noble, B., Methods Based on the Weiner-Hopf Techniques for the Solution of Partial Differential Equations, Pergamon, 1958.

19. Przezdziecki, S., Acta Physica Polonica, Vol. A83, Vol. A83, 1993.

20. Rawlins, A. D., "Acoustic diffraction by an absorbing semi-infinite half plane in a moving fluid," Proc. Roy. Soc. Edinburgh, Vol. A72, 337-357, 1974. Google Scholar

21. Senior, T. B. A and E. Topsakal, "Diffraction by an anisotropic impedance half plane â€” Revised solution," Progress In Electromagnetics Research Vol. 53, Vol. '' Progress In Electromagnetics Research 53, 1-19, 2005.
doi:10.2528/PIER04061702 Google Scholar

22. Sheen, J., "Time harmonic electromagnetic fields in an biaxial anisotropic medium," Journal of Electromagnetic Waves and Applications, Vol. 19, 753-768, 2005.
doi:10.1163/1569393054069082 Google Scholar

23. Weiglhofer, W. S. and A. Lakhtakia, "Time-dependent scalar Beltrami-Hertz potentials in free space," International Journal of Infrared and Mil limeter Waves, Vol. 15, No. 6, 1994. Google Scholar

24. Weiglhofer, W. S., "Isotropic chiral media and scalar Hertz potentials," J. Phys. A: Math. Gen., Vol. 21, 2249-2251, 1988.
doi:10.1088/0305-4470/21/9/036 Google Scholar

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