2020-03-26
The Diffraction by Two Half-Planes and Wedge with the Fractional Boundary Condition
By
Progress In Electromagnetics Research M, Vol. 91, 1-10, 2020
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.
Citation
Vasil Tabatadze, Kamil Karaçuha, Eldar I. Veliyev, and Ertuğrul Karaçuha, "The Diffraction by Two Half-Planes and Wedge with the Fractional Boundary Condition," Progress In Electromagnetics Research M, Vol. 91, 1-10, 2020.
doi:10.2528/PIERM20020503
References

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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.        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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        Google Scholar

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.        Google Scholar

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        Google Scholar

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        Google Scholar

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].