volume | PIER Journals

Abstract

In this article, the diffraction of plane electromagnetic waves by double half-planes with fractional boundary conditions is considered. As particular cases, the diffractions by wedges and corners are considered for different values of fractional orders. The results are compared to the analytical ones. The interesting properties of wedge diffraction are outlined for intermediate fractional orders.

1. Engheta, N., "Use of fractional integration to propose some “fractional” solutions for the scalar Helmholtz Equation," Progress In Electromagnetics Research, Vol. 12, 107-132, 1996.

2. Engheta, N., "Fractional curl operator in electromagnetics," Microwave and Optical Technology Letters, Vol. 17, No. 2, 86-91, 1998.
doi:10.1002/(SICI)1098-2760(19980205)17:2<86::AID-MOP4>3.0.CO;2-E

3. Engheta, N., "Phase and amplitude of fractional-order intermediate wave," Microwave and Optical Technology Letters, Vol. 21, No. 5, 338-343, 1999.
doi:10.1002/(SICI)1098-2760(19990605)21:5<338::AID-MOP10>3.0.CO;2-P

4. Veliev, E. I. and N. Engheta, "Generalization of Green’s theorem with fractional differ-integration," IEEE AP-S International Symposium & USNC/URSI National Radio Science Meeting, 2003.

5. Veliev, E. I., M. V. Ivakhnychenko, and T. M. Ahmedov, "Fractional boundary conditions in plane waves diffraction on a strip," Progress In Electromagnetics Research, Vol. 79, 443-462, 2008.
doi:10.2528/PIER07102406

6. Veliev, E. I., T. M. Ahmedov, and M. V. Ivakhnychenko, "Fractional operators approach and fractional boundary conditions," Electromagnetic Waves, V. Zhurbenko (ed.), IntechOpen, Rijeka, Croatia, 2011, doi: 10.5772/16300.

7. Veliev, E. I., K. Karacuha, E. Karacuha, "Scattering of a cylindrical wave from an impedance strip by using the method of fractional derivatives," XXIIIrd International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), 2018.

8. Karacuha, K., E. I. Veliyev, V. Tabatadze, and E. Karacuha, "Analysis of current distributions and radar cross sections of line source scattering from impedance strip by fractional derivative method," Advanced Electromagnetics, Vol. 8, No. 2, 108-113, 2019.
doi:10.7716/aem.v8i2.981

9. Tabatadze, V., K. Karacuha, and E. I. Veliev, "The fractional derivative approach for the diffraction problems: plane wave diffraction by two strips with the fractional boundary conditions," Progress In Electromagnetics Research, Vol. 95, 251-264, 2019.
doi:10.2528/PIERC19062505

10. Karacuha, K., E. I. Veliyev, V. Tabatadze, and E. Karacuha, "Application of the method of fractional derivatives to the solution of the problem of plane wave diffraction by two axisymmetric strips of different sizes," URSI International Symposium on Electromagnetic Theory (EMTS), May 2019.

11. Veliyev, E. I., V. Tabatadze, K. Karacuha, and E. Karacuha, "The diffraction by the half-plane with the fractional boundary condition," Progress In Electromagnetics Research M, Vol. 88, 101-110, 2020.
doi:10.2528/PIERM19102408

12. Oberhettinger, F., "On the diffraction and reflection of waves and pulses by wedges and corners," Journal of Research of the National Bureau of Standards, Vol. 61, No. 5, November 1958.

13. Ciarkowski, A. D., J. O. Boersma, and R. Mittra, "Plane-wave diffraction by a wedge — A spectral domain approach," IEEE Transactions on Antennas and Propagation, Vol. 32, No. 1, 20-29, 1984.
doi:10.1109/TAP.1984.1143190

14. Umul, Y. Z., "The theory of the boundary diffraction wave for wedge diffraction," Journal of Modern Optics, Vol. 55, No. 9, 1417-1426, 2008.
doi:10.1080/09500340701675197

15. Borovskii, A. V. and A. L. Galkin, "Diffraction on the wedge with an arbitrary angle," Bulletin of the Lebedev Physics Institute, Vol. 41, No. 1, 6-11, 2014.
doi:10.3103/S1068335614010023

16. Ufimtsev, P. Y., Fundamentals of the Physical Theory of Diffraction, John Wiley & Sons, 2014.
doi:10.1002/9781118753767

17. Castro, L. P. and D. Kapanadze, "Wave diffraction by wedges having arbitrary aperture angle," Journal of Mathematical Analysis and Applications, Vol. 421, No. 2, 1295-1314, 2015.
doi:10.1016/j.jmaa.2014.07.080

18. Nethercote, M. A., R. C. Assier, and I. D. Abrahams, "Analytical methods for perfect wedge diffraction: A review," Wave Motion, Vol. 93, 1024-1079, 2020.

19. Veliev, E. I., "Plane wave diffraction by a half-plane: A new analytical approach," Journal of Electromagnetic Waves and Applications, Vol. 13, No. 10, 1439-1453, 1999.
doi:10.1163/156939399X00772

20. Ikiz, T., S. Koshikawa, K. Kobayashi, E. I. Veliev, and A. H. Serbest, "Solution of the plane wave diffraction problem by an impedance strip using a numerical-analytical method: E-polarized case," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 3, 315-340, Jan. 2001.
doi:10.1163/156939301X00481

21. Samko, S. G., A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Science Publishers, 1993.

22. Prudnikov, H. P., Y. H. Brychkov, and O. I. Marichev, Special Functions, Integrals and Series, Vol. 2, Gordon and Breach Science Publishers, 1986.

23. Honl, H., A. W. Maue, and K. Westpfahl, Theorie der Beugung, Springer-Verlag, 1961.

24. YouTube, , , [Online], Available: https://www.youtube.com/watch?v=uyVNQbpx6 M&list=PLsBKZFx kreW8aznSKGKGFVvwy9RRqefwy&index=1 [Accessed: 5-Feb-2020].

Dr. Vasil Tabatadze

Mr. Kamil Karaçuha

Prof. Eldar I. Veliyev

Dr. Ertuğrul Karaçuha