volume | PIER Journals

Abstract

Scattering of homogeneous plane waves by a Perfect Electric Conductor half-plane in uniform rectilinear motion in a simple lossless medium is investigated using Wiener-Hopf Technique in the context of Hertzian Electrodynamics. The cases of motion being parallel and perpendicular to the plane are tackled separately. Restrictions on incidence angle vs. speed for the realization of scattering phenomena are investigated in each case. Parallel motion mode reveals the possibility of excitation of surface waves upon reflection, which also contribute to edge diffraction mechanism. Numerical results are illustrated and discussed for scattered fields. Comparative theoretical results for the solution of the same problem using Special Relativity Theory are provided and discussed.

1. Hertz, H., "Uber die Grundgleichungen der Elektrodynamik fur bewegte Korper," Annalen der Physik, Vol. 41, 369-399, 1890.

2. Heaviside, O., "The electrician," Electromagnetic Theory, Vol. 1, Printing and Publishing Company Ltd., 1893.

3. Truesdell, C. and R. Toupin, The Classical Field Theories. In: Flugge, S. (ed.) Prinzipien der klassischen Mechanik und Feldtheorie, Vol. 2, 226-793r, Springe, Handbuch der Physik, 1960.

4. Truesdell, C. and W. Noll, The Non-linear Field Theories of Mechanics, 3rd Ed., Springer, 1965.

5. Frewer, M., "More clarity on the concept of material frame-indifference in classical continuum mechanics," Acta Mech, Vol. 202, 213-246, 2009.

6. Christov, C. I., "On the analogy between the Maxwell electromagnetic field and the elastic continuum," Annuaire de L’Universite de Sofia, Vol. 95, 109-121, 2001.

7. Christov, C. I., "On the material invariant formulation of Maxwell’s displacement current," Foundations of Physics, Vol. 36, No. 11, 1701-1707, 2006.

8. Christov, C. I., "On the nonlinear continuum mechanics of space and the notion of luminiferous medium," Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, No. 12, e2028-e2044, 2009.

9. Christov, C. I., "Frame indifferent formulation of maxwell’s elastic fluid model and the rational continuum mechanics of the electromagnetic field," Mechanics Research Communications, Vol. 38, No. 4, 334-339, 2011.

10. Oldroyd, J. G., "On the formulation of rheological equations of state," Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 200, No. 1063, 523-541, 1950.

11. Polat, B., "On the axiomatic structure of hertzian electrodynamics," TWMS Journal of Applied and Engineering Mathematics, Vol. 2, No. 1, 17-41, 2012.

12. Polat, B., "Scattering by a moving PEC plane and a dielectric half-space in hertzian electrodynamics," TWMS Journal of Applied and Engineering Mathematics, Vol. 2, No. 2, 123-144, 2012.

13. Polat, B., "Scattering by a moving circular cylinder in hertzian electrodynamics," Selcuk Journal of Applied Mathematics, Vol. 13, No. 1, 89-109, 2012.

14. Polat, B. and R. Dasbasi, "Validation of hertzian electromagnetism in a rectangular waveguide with rotating PEC termination," 2019 PhotonIcs & Electromagnetics Research Symposium --- Spring (PIERS-Spring), 2850-2856, Rome, Italy, 2019, doi: 10.1109/PIERS-Spring46901.2019.9017394.

15. Polat, B. and R. Dasbasi, "Plane wave reflection by a PEC plane in harmonic motion," 2020 International Conference on Electrical, Communication, and Computer Engineering (ICECCE), 1-6, Istanbul, Turkey, Jun. 12–13, 2020, doi: 10.1109/ICECCE49384.2020.9179436.

16. Polat, B. and R. Dasbasi, "Hertzian formulation of scattering by moving PEC bodies," IEEE Microwaves, Radar and Remote Sensing Symposium (MRRS-2020), Kharkiv, Ukraine, Sept. 21–25, 2020.

17. Polat, B. and R. Dasbasi, "On conservation of electromotive force in hertzian electrodynamics," 2020 International Conference on Electrical, Communication, and Computer Engineering (ICECCE), 1-6, Istanbul, Turkey, Jun. 12–13, 2020, doi: 10.1109/ICECCE49384.2020.9179200.

18. Noble, B., Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations, Pergamon Press, 1958.

19. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, 1974.

20. Poppe, G. P. M. and C. M. J. Wijers, "More efficient computation of the complex error function," ACM Transactions on Mathematical Software, Vol. 16, No. 1, 38-46, 1990.

21. Abrarov, S. M., B. M. Quine, and R. K. Jagpal, "A sampling-based approximation of the complex error function and its implementation without poles," Applied Numerical Mathematics, Vol. 129, 181-191, 2018.

22. Idemen, M. and A. Alkumru, "Relativistic scattering of a plane wave by a uniformly moving half-plane," EEE Transactions on Antennas and Propagation, Vol. 54, No. 11, 3429-3440, 2006.

23. Van Bladel, J., Relativity and Engineering, Springer-Verlag, 1984.

24. Borkar, S. and R. F. Yang, "Reflection of electromagnetic waves from oscillating surfaces," IEEE Transactions on Antennas and Propagation, Vol. 23, No. 1, 122-127, 1975.

25. Pobedonostsev, L. A., "Experimental studies of the Doppler effect," Journal of Systems Engineering and Electronics, Vol. 6, No. 4, 115-128, 1995.

26. Thim, H. W., "Absence of the relativistic transverse Doppler shift at microwave frequencies," IEEE Transactions on Instrumentation and Measurement, Vol. 52, No. 5, 1660-1664, 2003.

27. Sfarti, A., "Comment on “The case of absence of transverse Doppler effect," IEEE Transactions on Instrumentation and Measurement, Vol. 59, No. 2, 494-495, 2010, doi: 10.1109/TIM.2009.2034324.

28. Thim, H., "Response: The case of absence of transverse Doppler effect," IEEE Transactions on Instrumentation and Measurement, Vol. 59, No. 2, 495-495, 2010, doi: 10.1109/TIM.2009.2034326.

29. Hatch, R. R., Escape from Einstein, 1st Ed., Kneat Kompany, 1992.

Dr. Ramazan Daşbaşı

Prof. Burak Polat