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Derivation of Kirchhoff diffraction integrals for soft and hard surfaces of perfectly electric conductor half-planes

Mustafa Mutlu

Abstract


In this study, by applying the Kirchhoff diffraction integral to the problem of the soft and hard-surface half-planes, two different diffraction integrals are obtained. To obtain the diffracted fields by the soft and hard-surface half planes the edge point method is used. For the uniform field intensities, Signum function and Fresnel function are used. In the comparison of the obtained diffracted fields, the results are interpreted by means of the plots as well. Similarities and differences between the obtained diffracted fields are discussed for some parameters. It is concluded that in some regions diffracted wave by a soft surface has an intensity higher than the diffracted field intensity corresponding to the hard surface. In some regions, it is vice versa. At the critical points that are related to the incident angle, they have the same value.


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References


A. Sommerfeld, “Mathematische theorie der diffraction,” Math. Ann., 47(2-3), pp. 317-374, 1896.

C. A. Balanis, Advanced Engineering Electromagnetics, 2nd ed., Wiley, New Jersey, 2012.

H. Lamb, “On Sommerfeld’s diffraction problem; and on reflection by a parabolic mirror,” Proceedings of The London Mathematical Society, 2(1), pp. 190-203, 1907.

H. Lamb, “On the diffraction of a solitary wave,” Proceedings of The London Mathematical Society, vol. 8, pp. 422-437, 1910.

F. G. Friedlander, “The diffraction of sound pulses. I. Diffraction by a semi-infinite plane,”Proceedings of the Royal Society of London Series A,186(1006), pp. 322-344, 1946.

L. G. Chambers, “Diffraction by a half-plane,” Proc. Edin. Math. Soc., 10(2), pp. 92-99, 1954.

J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am., 52(2), pp. 116-130, 1962.

E. V. Jull, “Diffraction by a conducting half-plane in an anisotropic plasma,” Can. J. Phys., 42(8), pp. 1455-1468, 1964.

W. E. Williams, “Electromagnetic diffraction in an anisotropic medium,”J. Inst. Math. Appl. 2(2), pp.186-196, 1966.

S. Przezdziecki, “Diffraction by a half-plane perpendicular to the distinguished axis of a uniaxially anisotropic medium,” J. Appl. Phys., 37(7), pp. 2768-2775, 1966.

V. V. Fisanov, “Cylindrical wave diffraction at a half-plane in an anisotropic plasma,” Izvestiya VUZ, Fizika, 11(56-60), pp. 70-75, 1968.

G. Kirchhoff, “Zur Theorie der Lichtstrahlen,” Annalen der Physik, 254(4), pp. 663-695, 1883.

Y. Z. Umul, “Modified diffraction theory of Kirchhoff,” JOSAA, 25(8), pp. 1850-1860, 2008.

Y. Z. Umul, “A new representation of the Kirchhoff’s diffraction integral,” Optics Communications, 291(3), pp. 48-51, 2013.

M. Kara, “Scattering of inhomogeneous plane waves by a slit formed with impedance and perfectly electric conducting half planes,” Journal of Modern Optics, 66(3), pp. 281-286, 2019.

Y. Z. Umul, "Diffraction of evanescent plane waves by a resistive half-plane,” Journal of the Optical Society of America A, 24(10), pp. 3226-3232, 2007.

M. Kara, "Scattering of a plane wave by a cylindrical parabolic perfectly electric conducting reflector,” Optik, 127(10), pp. 4531-4535, 2016.

M. Kara, "Diffraction of a plane wave by an aperture composed of two different resistive half-planes between isorefractive media,” Optical and Quantum Electronics, 53(7), pp. 1-12, 2021.

J. J. Stamnes, "Hybrid integration technique for efficient andaccurate computation of diffraction integrals,” Journal of the Optical Society of America A, 6(9), pp.1330-1342, 1989.

M. Kara, “Diffracted fields by a parabolic reflector offset-fed by a line source,” BSEU Journal of Science, 7(2), pp. 1.49-1060, 2020.

V. Zernov, L. Fradkin, and M. Darmon, “A Refinement of the Kirchhoff approximation to the scattered elastic fields,” Ultrasonics, 52(17), pp. 830-835, 2012.

H. M. Macdonald, “The effect produced by an obstacle on a train of electric waves,” Phil. Trans. Royal Soc. London Series A Math. Phys. Sc., 212(484), pp. 299-337, 1912.

P. Ya Ufimtsev, “New insight into the classical Macdonald physical optics approximation,” IEEE Antennas and Propagation Magazine, 50(3), pp. 11-20, 2008.

A. I. Khizhnyak, S. P. Anokhov, R. A. Lymarenko, M. S. Soskin, and M. V. Vasnetsov, “Structure of an edge-dislocation wave originating in plane-wave diffraction by a half-plane,” Journal of the Optical Society of America A., 17(12), pp. 2199-2207, 2000.

M. Kara, “Asymptotic evaluation of scattering of inhomogeneous plane waves by a perfectly electric conducting half-plane,” Uludağ University Journal of The Faculty of Engineering, 24(2), pp. 697-709, 2019.

J. S. Kyoung, M. A. Seo, H. R. Park, K. J. Ahn, and D. S. Kim,"Far-field detection of terahertz near field enhancement of sub-wavelength slits using Kirchhoff integral formalism,” Optics Communications, 283(24), pp.4907-4910, 2010.




URN: https://sloi.org/urn:sl:tjoee82289



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