Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium
American Journal of Electromagnetics and Applications
Volume 1, Issue 1, July 2013, Pages: 1-7
Received: May 23, 2013;
Published: Jul. 10, 2013
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Vladimir M. Serdyuk, Institute of Applied Physical Problems, Belarusian State University, Minsk, Belarus
Joseph A. Titovitsky, Institute of Applied Physical Problems, Belarusian State University, Minsk, Belarus
The Sommerfeld’s problem of plane wave diffraction by a perfectly conducting half-plane is considered for the general case of an absorbing medium and an inhomogeneous incident wave, whose the constant phase planes are not parallel to the constant amplitude ones. The exact solution is represented in terms of parameters of incident wave propagation in the coordinate axes, but not in terms of angular variables, as usually. We adduce the original derivation of this solution, which use generalized functions and admits complex values for propagation parameters. Our approach is based on calculation of diffraction integrals by the method of transformations on the real axis without using a complex argument of integration. The results of diffraction field computation for the cases of an absorbing medium and of a decaying incident wave in a transparent medium are presented.
Vladimir M. Serdyuk,
Joseph A. Titovitsky,
Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium, American Journal of Electromagnetics and Applications.
Vol. 1, No. 1,
2013, pp. 1-7.
A. Sommerfeld, "Mathematische Theorie der Diffraktion," Mathematische Annalen, vol. 47, pp. 317–374, 1896 (in German).
M. Born, and E. Wolf, Principles of Optics, 7th ed., Cambridge, Cambridge University Press, 1999.
L. A. Weinstein, The Theory of Diffraction and the Factorization Method, Boulder, Golem, 1969.
R. Mittra, and S. W. Lee, Analytical Techniques in the Theory of Guided Waves, New York, Macmillan, 1971.
B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations, London, Pergamon, 1958.
Y. Z. Umul, "Scattering of a Gaussian beam by an impedance half-plane," JOSA A, vol. 24, issue 10, pp. 3159–3167, 2007.
S. P. Anokhov, "Plane wave diffraction by a perfectly transparent half-plane," JOSA A, vol. 24, issue 9, pp. 2493–2498, 2007.
A. Ciarkowski, "Electromagnetic pulse diffraction by a moving half-plane," Progress In Electromagnetics Research, vol. PIER 64, pp. 53–67, 2006.
W. Hussain, "Asymptotic analysis of a line source diffraction by a perfectly conducting half-plane in a bi-isotropic medium," Progress In Electromagnetics Research, vol. PIER 58, pp. 271–283, 2006.
Y. Z. Umul, and U. Yalçın, "Scattered fields of conducting half-plane between two dielectric media," Applied Optics, vol. 49, issue 20, pp. 4010–4017, 2010.
K. L. McDonald, "Diffraction of spherical vector waves by an infinite half-plane," JOSA, vol. 43, issue 8, pp. 641–646, 1953.
Y. Luo, and B. Lü, "Polarization singularities of Gaussian vortex beams diffracted at a half-plane screen beyond the paraxial approximation," JOSA A, vol. 26, issue 9, pp. 1961–1966, 2009.
Y. Z. Umul, "Uniform theory for the diffraction of evanescent plane waves," JOSA A, vol. 24, issue 8, pp. 2426–2430, 2007.
Y. Z. Umul, "Diffraction of evanescent plane waves by a resistive half-plane," JOSA A, vol. 24, issue 10, pp. 3226–3232, 2007.
Y. Z. Umul, "Diffraction by a black half plane: Modified theory of physical optics approach," Optics Express, vol. 13, No. 19, pp. 7276–7287, 2005.
J. B. Schneider, and R. J. Kruhlak, "Dispersion of homogeneous and inhomogeneous waves in the Yee finite-difference time-domain grid," IEEE Trans. Microwave Theory & Techn., vol. 49, No. 2, pp. 280–287, 2001.
J. A. Stratton, Electromagnetic Theory, New York, McGraw-Hill, 1941.
N. N. Bogolyubov, and D. V. Shirkov, Introduction to the Theory of Quantized Fields, New York, Wiley, 1980.
E. C. Titchmarsh, Theory of Functions, Oxford, Oxford University Press, 1976.
A. G. Sveshnicov, and A. N. Tikhonov, The Theory of Functions of a Complex Variable, Moscow, Mir Publ., 1978.