Vasil TABATADZE, Eldar Ismailovich VELIEV, Kamil KARAÇUHA

Plane wave diffraction by strip with an integral boundary condition

In this article, a new solution method is proposed for plane wave diffraction by a strip. On the surface of thestrip, an integral boundary condition is used. The impedance of the strip is investigated. The theoretical and numericalanalyses show that there is a relation between the complex-valued fractional order of the integral boundary conditionand properties of the material such as the impedance. As a further study, the total radar cross-section is investigatedusing the proposed method.

PDF

___

[1] Engheta N. Use of fractional integration to propose some “fractional” solutions for the scalar Helmholtz equation. Progress in Electromagnetics Research 1996; 12: 107-132.
[2] Engheta N. Fractional curl operator in electromagnetics. Microwave and Optical Technology Letters 1998; 17 (2): 86-91.
[3] Engheta N. Phase and amplitude of fractional‐order intermediate wave. Microwave and Optical Technology Letters 1999; 21(5): 338-343.
[4] Engheta N. Fractionalization methods and their applications to radiation and scattering problems. In: IEEE International Conference on Mathematical Methods in Electromagnetic Theory; Ukraine; 2000. pp. 34-40. doi: 10.1109/MMET.2000.888504
[5] Veliev EI, Engheta N. Generalization of Green’s theorem with fractional differintegration. In: IEEE AP-S International Symposium and USNC/URSI National Radio Science Meeting; Ohio, USA; 2003. p. 228.
[6] Ivakhnychenko MV, Veliev EI. Fractional curl operator in radiation problems. In: 10th IEEE International Conference on Mathematical Methods in Electromagnetic Theory; Ukraine; 2004. pp. 231-233. doi 10.1109/MMET.2004.1396991
[7] Veliev EI, Ahmedov TM, Ivakhnychenko MV. Fractional operators approach and fractional boundary conditions. In: Zhurbenko V (editor). Electromagnetic Waves. Rijeka, Croatia: InTech Open, 2011. doi: 10.5772/16300
[8] Veliev EI, Ivakhnychenko MV, Ahmedov TM. Fractional boundary conditions in plane waves diffraction on a strip. Progress in Electromagnetics Research 2008; 79: 443-462. doi: 10.2528/PIER07102406
[9] Ivakhnychenko MV, Veliev EI, Ahmedov TM. Scattering properties of the strip with fractional boundary conditions and comparison with the impedance strip. Progress in Electromagnetics Research 2008; 2: 189-205. doi: 10.2528/PIERC08031502
[10] Veliyev EI, Karaçuha K, Karaçuha E, Dur O. The use of the fractional derivatives approach to solve the problem of diffraction of a cylindrical wave on an impedance strip. Progress in Electromagnetics Research 2018; 77: 19-25.
[11] Samko SG, Kilbas AA, Marichev OI. Fractional Integrals and Derivatives: Theory and Applications. London, UK: CRC Press, 1993.
[12] Oldham K, Spanier J. The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order. New York, NY, USA: Elsevier, 1974.
[13] Hönl H, Maue AW, Westpfahl K. Theorie der Beugung. Berlin, Germany: Springer-Verlag, 1987 (in German).
[14] Bateman H. Higher Transcendental Functions. New York, NY, USA: McGraw-Hill Book Company, 1953.
[15] Prudnikov AP. Integral and Series. New York, NY, USA: Gordon and Breach, 1986.
[16] Ishimaru A. Electromagnetic Wave Propagation, Radiation, and Scattering: From Fundamentals to Applications. Hoboken, NJ, USA: John Wiley and Sons, 2017.
[17] Ji Y, Zhi J, Meihuan Y, Ying Q, Yufeng P. Negative absorption peaks in ultraviolet–visible spectrum of water. ChemistrySelect 2016; 1 (3): 3443-3448.