Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium

Vladimir M. Serdyuk; Joseph A. Titovitsky

doi:doi:10.11648/j.ajea.20130101.11

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Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium

Vladimir M. Serdyuk, Joseph A. Titovitsky

Published in American Journal of Electromagnetics and Applications (Volume 1, Issue 1)

Received: 23 May 2013 Published: 10 July 2013

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Abstract

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.

Published in	American Journal of Electromagnetics and Applications (Volume 1, Issue 1)
DOI	10.11648/j.ajea.20130101.11
Page(s)	1-7
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Exact Solution, Inhomogeneous Wave, Perfectly Conducting Half-Plane

References

[1]	A. Sommerfeld, "Mathematische Theorie der Diffraktion," Mathematische Annalen, vol. 47, pp. 317–374, 1896 (in German).
[2]	M. Born, and E. Wolf, Principles of Optics, 7th ed., Cambridge, Cambridge University Press, 1999.
[3]	L. A. Weinstein, The Theory of Diffraction and the Factorization Method, Boulder, Golem, 1969.
[4]	R. Mittra, and S. W. Lee, Analytical Techniques in the Theory of Guided Waves, New York, Macmillan, 1971.
[5]	B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations, London, Pergamon, 1958.
[6]	Y. Z. Umul, "Scattering of a Gaussian beam by an impedance half-plane," JOSA A, vol. 24, issue 10, pp. 3159–3167, 2007.
[7]	S. P. Anokhov, "Plane wave diffraction by a perfectly transparent half-plane," JOSA A, vol. 24, issue 9, pp. 2493–2498, 2007.
[8]	A. Ciarkowski, "Electromagnetic pulse diffraction by a moving half-plane," Progress In Electromagnetics Research, vol. PIER 64, pp. 53–67, 2006.
[9]	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.
[10]	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.
[11]	K. L. McDonald, "Diffraction of spherical vector waves by an infinite half-plane," JOSA, vol. 43, issue 8, pp. 641–646, 1953.
[12]	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.
[13]	Y. Z. Umul, "Uniform theory for the diffraction of evanescent plane waves," JOSA A, vol. 24, issue 8, pp. 2426–2430, 2007.
[14]	Y. Z. Umul, "Diffraction of evanescent plane waves by a resistive half-plane," JOSA A, vol. 24, issue 10, pp. 3226–3232, 2007.
[15]	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.
[16]	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.
[17]	J. A. Stratton, Electromagnetic Theory, New York, McGraw-Hill, 1941.
[18]	N. N. Bogolyubov, and D. V. Shirkov, Introduction to the Theory of Quantized Fields, New York, Wiley, 1980.
[19]	E. C. Titchmarsh, Theory of Functions, Oxford, Oxford University Press, 1976.
[20]	A. G. Sveshnicov, and A. N. Tikhonov, The Theory of Functions of a Complex Variable, Moscow, Mir Publ., 1978.

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Vladimir M. Serdyuk, Joseph A. Titovitsky. (2013). Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium. American Journal of Electromagnetics and Applications, 1(1), 1-7. https://doi.org/10.11648/j.ajea.20130101.11

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Vladimir M. Serdyuk; Joseph A. Titovitsky. Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium. Am. J. Electromagn. Appl. 2013, 1(1), 1-7. doi: 10.11648/j.ajea.20130101.11

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AMA Style

Vladimir M. Serdyuk, Joseph A. Titovitsky. Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium. Am J Electromagn Appl. 2013;1(1):1-7. doi: 10.11648/j.ajea.20130101.11

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@article{10.11648/j.ajea.20130101.11,
  author = {Vladimir M. Serdyuk and Joseph A. Titovitsky},
  title = {Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium},
  journal = {American Journal of Electromagnetics and Applications},
  volume = {1},
  number = {1},
  pages = {1-7},
  doi = {10.11648/j.ajea.20130101.11},
  url = {https://doi.org/10.11648/j.ajea.20130101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajea.20130101.11},
  abstract = {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.},
 year = {2013}
}

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TY  - JOUR
T1  - Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium
AU  - Vladimir M. Serdyuk
AU  - Joseph A. Titovitsky
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DO  - 10.11648/j.ajea.20130101.11
T2  - American Journal of Electromagnetics and Applications
JF  - American Journal of Electromagnetics and Applications
JO  - American Journal of Electromagnetics and Applications
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PB  - Science Publishing Group
SN  - 2376-5984
UR  - https://doi.org/10.11648/j.ajea.20130101.11
AB  - 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.
VL  - 1
IS  - 1
ER  -

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Author Information

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

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APA Style

Vladimir M. Serdyuk, Joseph A. Titovitsky. (2013). Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium. American Journal of Electromagnetics and Applications, 1(1), 1-7. https://doi.org/10.11648/j.ajea.20130101.11

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ACS Style

Vladimir M. Serdyuk; Joseph A. Titovitsky. Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium. Am. J. Electromagn. Appl. 2013, 1(1), 1-7. doi: 10.11648/j.ajea.20130101.11

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AMA Style

Vladimir M. Serdyuk, Joseph A. Titovitsky. Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium. Am J Electromagn Appl. 2013;1(1):1-7. doi: 10.11648/j.ajea.20130101.11

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@article{10.11648/j.ajea.20130101.11,
  author = {Vladimir M. Serdyuk and Joseph A. Titovitsky},
  title = {Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium},
  journal = {American Journal of Electromagnetics and Applications},
  volume = {1},
  number = {1},
  pages = {1-7},
  doi = {10.11648/j.ajea.20130101.11},
  url = {https://doi.org/10.11648/j.ajea.20130101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajea.20130101.11},
  abstract = {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.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Diffraction of a Plane Inhomogeneous Electromagnetic Wave by a Perfectly Conducting Half-Plane in an Absorbing Medium
AU  - Vladimir M. Serdyuk
AU  - Joseph A. Titovitsky
Y1  - 2013/07/10
PY  - 2013
N1  - https://doi.org/10.11648/j.ajea.20130101.11
DO  - 10.11648/j.ajea.20130101.11
T2  - American Journal of Electromagnetics and Applications
JF  - American Journal of Electromagnetics and Applications
JO  - American Journal of Electromagnetics and Applications
SP  - 1
EP  - 7
PB  - Science Publishing Group
SN  - 2376-5984
UR  - https://doi.org/10.11648/j.ajea.20130101.11
AB  - 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.
VL  - 1
IS  - 1
ER  -

Copy | Download