Mükemmel Elektrik İletkeni Yarım Düzlemle Düzlem Dalga Saçılımına Seri Çözüm

Yıl 2024, Cilt: 16 Sayı: 2, 603 - 610, 30.06.2024

Mustafa Mutlu

https://doi.org/10.29137/umagd.1386186

Öz

Toplam saçılan alanı ifade etmek için Bessel serisi aracılığıyla düzlem dalgaların mükemmel elektrik iletken yüzeyin yarım düzlemi tarafından saçılması dikkate alınır. İlk olarak, gelen ve yansıyan alanların seri toplamı ve Helmhotz denkleminin çözümü kullanılarak Fresnel fonksiyonu cinsinden toplam saçılmış alan elde edilir. Daha sonra, Fresnel fonksiyonu birim adım fonksiyonuna ve işaret fonksiyonu çarpı Fresnel fonksiyonuna ayrıştırılır. Elde edilen dağınık, kırınımlı ve geometrik optik (GO) alanları sayısal olarak çizilmiştir. Saçılan, geometrik optiklerin, kırılan alanların davranışları elektromanyetik saçılma teorisi dikkate alınarak gözlemlenir ve yorumlanır. Gelen kırınıma uğramış ve yansıtılmış kırınıma sahip alanlardan oluşan kırınımlı alan, saçılmış alanla birlikte çizilmiştir. Kırılan alan bileşenleri (kırılan ve yansıtılan kırılan alanlar) Signum fonksiyonu ile Fresnel fonksiyonunun çarpımından elde edilir. Ayrıca geometrik optik (GO) alanı birim adım fonksiyonu ile ifade edilir.

Anahtar Kelimeler

Kırınım, Helmholtz denklemi, Fresnel fonksiyonu, Saçılma

Kaynakça

• Borghi, F., Santarsiero, M., Frezza, F., Schettini, G. (1996). Plane-wave Scattering by A Perfectly Conducting Circular Cylinder Near A Plane Wave Surface: Cylindrical Wave Approach. Journal of Optical Society of America, 13(3), 483-493.
• Bucci, O.M., Franceschetti, G. (1976). Electromagnetic Scattering by a Half-plane with two Face Impedances. Radio Science, 11(1), 49-59.
• Büyükaksoy, A., Uzgören, G. (1988). Diffraction of High Frequency Waves by A Cylindrically Curved Surface with Different Face Impedance. IEEE Transactions on Antennas and Propagation, 36 (5), 592-600.
• James, G.L. (1986). Geometrical Theory of Diffraction for Electromagnetic Waves. The Institution of Engineering and Technology. London.
• Jones, D.S., Pidduck, F.B. (1950). Diffraction by a Metal wedge at Large Angles. The Quarterly Journal of Mathematics, 1(1), 229-237.
• Kara, M. (2016). Scattering of a Plane wave by a Cylindrical Parabolic Perfectly Electric Conducting Reflector, Optik, 127(10), 4531-4535, DOI:10.1016/j.ijleo.2016.01.146.
• Kara, M. (2019). Scattering of Inhomogeneous Plane Waves by a Slit Formed With Impedance and Perfectly Electric Conducting Half Planes, Journal of Modern Optics, 66(3), 281-286, 2019, DOI: 10.1080/09500340.2018.1518550.
• Kara, M. (2019). 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), 697-710, DOI: 10.17482/uumfd.428378
• Kara, M. (2020). Diffracted Fields by a Parabolic Reflector Offset-Fed by a Line Source, BSEU Journal of Science, 7(2), 1049-1060, DOI: 10.35193/bseufbd.735678
• Kara, M. (2021). Diffraction of a plane wave by an aperture composed of two different resistive half planes between isorefractive media, Optical and Quantum Electronics, 53(7), 392, 2021, DOI: 10.1007/s11082-021-03049-w
• Kara, M., Mutlu, M. (2023). Scattering and Diffraction Evaluated by Physical Optics Surface Current on a Truncated Cylindrical Conductive Cap, River Publishers, 38(5), 304-308.
• Kouyoumjian, R.G., Pathak, P. H. (1974). A Uniform Theory of Diffraction for Edge in A Perfectly Conducting Surface. Proceedings of IEEE, 62(11), 1448-1461.
• Maliuzhinets, G.D. (1958). Excitation, Reflection and Emission of Surface Waves from a Wedge with given Face Impedances. Soviet Physics Doklady, 3, 752-755.
• Malyughinetz, G.D. (1960). Das Sommerlefdsche Integral Und Die Lo sung Von Beugungsaufgaben in Winkelgebeiten. Annalen der Physik (Leipzig), 461(1-2), 107-112.
• Raman, C.V., Krishnan, K.S. (1927). The Diffraction of Light by Metallic Screens. Proceedings of the Royal Society of London Series A, 116(774), 254-267.
• Rojas, R.G. (1988). Electromagnetic Diffraction Of An Obliquely Incident Plane Wave Field By a Wedge With Impedance Faces. IEEE Transactions on Antennas and Propagation, 36(7), 956-970.
• Sanyal, S., Bhattacharyya, A.K. (1986). Diffraction by a Half-plane with Two Face Impedances Uniform Asymptotic Expansion for Plane Wave and Arbitrary Line Source Incidence. IEEE Transactions on Antennas and Propagation AP, 34(5), 718-723.
• Senior, T.B.A. (1952). Diffraction By a Semi-Infinite Metallic Sheet. Proceedings of the Royal Society of London Series A, 213(1115), 436-458.
• Sommerfeld, A. (1896). Mathematische Theorie der Diffraction. Mathematische Annalen, 47(2-3), 317-374.
• Tiberio, R., Pelosi, G., Manara, G. (1985). A Uniform GTD Formulation for the Diffraction by a Wedge with Impedance Faces. IEEE Transactions on Antennas Propagation AP, 33(8), 867-873.
• Umul, Y.Z. (2004). Modified theory of physical optics. Optics Express, 12(20), 4959-4972.
• Umul, Y.Z. (2008). Scattering of A Line Source by A Cylindrical Parabolic Impedance Surface. Journal of Optical Society of America, 25(7), 1652-1659.
• Umul, Y.Z. (2009a). Closed form Series Solution of the Diffraction Problem of Plane Waves by an Impedance Half-plane. Journal of Optics A: Pure and Applied Optics, 11(4), 045709.
• Umul, Y.Z. (2009b). Scattering by an Impedance Half-plane: Comparison of the Solutions of Raman/Krishnan and Maliuzhinets/Senior. Progress in Electromagnetics Research M, 8, 39-50.
• Umul, Y.Z. (2013). Scattering of Waves By a Half-Screen With Different Face Impedances: Closed Form Series Solution. International Journal of Electronics, 100(7), 928-941.
• Umul, Y.Z., Yalçın, U. (2010a). Diffraction Theory of Waves by Resistive Surfaces. Progress in Electromagnetics Research B, 23, 1-13.
• Umul, Y.Z., Yalçın, U. (2010b). Scattered Fields of Conducting Half-plane Between Two Dielectric Media. Applied Optics, 49(20), 4010-4017.