Diffraction by a Thick Half Plane Composed of PEMC Metamaterial
Keywords:
Diffraction, Duality Transformation, PEMC Medium, Wiener-Hopf Technique, Thick Half PlaneAbstract
Diffraction of a plane wave by a thick half plane composed of metamaterial was examined by employing duality transformation proposed by Lindell and Sihvola [18, 20, 21, 24]. As perfect electric conductor (PEC) and perfect magnetic conductor (PMC) media can both be derived as limiting cases of perfect electromagnetic conductor medium, so it was thought worthwhile to attempt and generalize the problem of diffraction by a thick PEC half plane to thick PEMC half plane. The boundary value problem was solved by using an integral transform, the Wiener-Hopf (WH) technique and the method of steepest descent. Infinite algebraic equations, containing infinite constants, arose in the problem under consideration which were solved numerically. The effects of arising parameters of thickness and admittance on amplitude of the diffracted field were plotted and are discussed.
References
Noble, B. Methods Based on the Wiener-Hopf Technique. Pergamon, London (1958).
Rawlins, A.D. Acoustic diffraction by an absorbing semi-infinite half plane in a moving fluid. Proceedings of the Royal Society of Edinburgh Section A 72: 337-357 (1975).
Ahmad, B. An improved model for noise barriers in a moving fluid. Journal of Mathematical Analysis and Applications 321 (2): 609-620 (2006).
Clemmow, P.C. A method for the exact solution of a class of two diemensional diffraction problems. Proceedings of the Royal Society of Edinburgh Section A, 205: 286-308 (1951).
Senior, T.B.A. Diffraction by a semi-infinite metallic sheet. Proceedings of the Royal Society of Edinburgh Section A 213: 436-458 (1952).
Daniele, V.G. & R.D. Graglia. Diffraction by an imperfect half plane in a bianisotropic medium, Radio Science 42: RS6S05 (2007).
Jones, D.S. Diffraction by a thick semi-infinite plate. Proceedings of the Royal Society of Edinburgh Section A. 217: 153-175 (1953).
Lee, S.W. & R. Mittra. Diffraction by a thick conducting half-plane and a dielectric loaded waveguide. IEEE Trans. Antennas and Propagation AP-16: 454-461 (1968).
Crighton, D.G. & F.G. Leppington. Singular perturbation methods in acoustic diffraction by a plate of finite thickness. Proceedings of the Royal Society of Edinburgh Section A 335: 313-339 (1973).
Volakis, J.L. & M.A. Ricoy. Diffraction by a thick perfectly conducting half-plane. IEEE Trans. Antennas and Propagation 35: 62-72 (1987).
Volakis, J. L. Scattering by a thick impedance half plane. Radio Science, 22: 13-25 (1987).
Rawlins, A.D. & P. McIver, Diffraction by a thick half-plane with an absorbent end face. Proceedings of the Royal Society of London. A 454: 3167-3182 (1998).
Büyükaksoy, A., A.M. Cevik, & G. Uzgören, Scattering of plane waves by a thick half-plane with resistive vertical walls. Archivfür Elektronik und Ubertragungstechnik (AEU) 51: 97-102 (1997).
Cinar, G. & A. Büyükaksoy. Diffraction by a thick impedance half-plane with a different end face impedance. Electromagnetics 22: 565-580 (2002).
Tayyar, I.H. & A. Buyukaksoy, Plane wave diffraction by the junction of a thick impedance half-plane and a thick dielectric slab. IEE Proceedings – Science, Measurement and Technology 150(4): 169-176 (2003).
Turetken, B. & A. Alkumru, Plane wave diffraction by a dielectric loaded open parallel thick plate waveguide. Turkish Journal of Electical Engineering and Computer Sciences 10(3): 439-448 (2002).
Hames, Y. & I.H. Tayyar. Plane wave diffraction by dielectric loaded thick-walled parallel plate impedance waveguide. Progress in Electromagnetics Research 44: 143-167 (2004).
Lindell, I. V. & A. H. Sihvola. Transformation method for problems involving perfect electromagnetic conductor (PEMC) structures. IEEE Transactions on Antennas and Propagation 53: 3005-3011 (2005).
Büyükaksoy, A. & F. Birbir. Plane wave diffraction by an impedance step. IEEE Transactions on Antennas and Propagation 41(8): 1160-1164 (1993).
Lindell, I.V. & A.H. Sihvola. Perfect electromagnetic conductor, Journal of Electromagnetic Waves and Applications. 19(7): 861-869 (2005).
Lindell, I.V. & A.H. Sihvola. Realization of the PEMC boundary. IEEE Transactions on Antennas and Propagation 53: 3012-3018 (2005).
Lindell, I.V. Electromagnetic fields in self-dual media in differential-form representation. Progress in Electromagnetics Research 58: 319-333 (2006).
Ruppin, R. Scattering of electromagnetic radiation by a perfect electromagnetic conductor cylinder. Journal of Electromagnetic Waves and Applications 20(13): 53-60 (2006).
Lindell, I.V. & A.H. Sihvola, Reflection and transmission of waves at the interface of perfect electromagnetic conductor (PEMC). Progress in Electromagnetic Research B 5: 169-183 (2008).
Ahmed, S.M. Akbar & M. Shafiq. Diffraction by a perfectly electromagnetic conducting (PEMC) step. Journal of Modern Optics 60: 637-640 (2013).
Ahmed, S. & I. Mehmood. Diffraction of a plane wave by a perfectly electromagnetic conducting (PEMC) slot. Journal of Modern Optics 61: 335-338 (2014).
Ahmed, S. Magnetic line source diffraction by a perfect electromagnetic conductor (PEMC) step. Journal of Modern Optics., http://dx. doi.org/10.1080 / 09500340(2014).
Tiwana, M.H., S. Ahmed, A.B. Mann, & Q.A. Naqvi. Point source diffraction from a semi-infinite perfect electromagnetic conductor half plane. Optik 135: 1-7 (2017).
