volume | PIER Journals

Abstract

A study of the diffraction and scattering of a transverse electric X-wave by conducting bodies is presented based on the timedomain, uniform theory of diffraction method and the pulsed plane wave representation of an X-wave. The latter allows the calculation of the diffraction and scattering of each pulsed plane wave component of the incident X-wave at the observation point. The superposition of the individual diffracted and scattered pulsed plane wave components yields the diffracted and scattered field due to an incident X-wave. First, the scattering from a perfectly conducting infinite wedge is studied. Then, the case of a circular conducting disk is considered as an example of a finite scatterer. Numerical results illustrating the effectiveness of the approach, as well as an estimate of the limits of its applicability, are provided.

1. Lu, J. and J. F. Greenleaf, "Nondiffracting X-waves–Exact solutions to free-space scalar wave equation and their finite aperture realization," IEEE Trans. on Ultrason., Ferroelect. Freq. Contr., Vol. 39, 19-31, 1992.
doi:10.1109/58.166806 Google Scholar

2. Ziolkowski, R. W., "Localized transmission of electromagnetic energy," Phys. Rev. A, Vol. 39, 2005-2033, 1989.
doi:10.1103/PhysRevA.39.2005 Google Scholar

3. Shaarawi, A. M., "Comparison of two localized wave fields generated from dynamic apertures," J. Opt. Soc. Am. A, Vol. 14, 1804-1816, 1997.
doi:10.1364/JOSAA.14.001804 Google Scholar

4. Shaarawi, A. M., I. M. Besieris, R. W. Ziolkowski, and S. M. Sedky, "Generation of approximate focus-wave-mode pulses from wideband dynamic Gaussian apertures," J. Opt. Soc. Am. A, Vol. 12, 1954-1964, 1995.
doi:10.1364/JOSAA.12.001954 Google Scholar

5. Shaarawi, A. M., I. M. Besieris, A. M. Attiya, and E. A. El- Diwany, "Acoustic X-wave reflection and transmission at a planar interface: spectral analysis," J. Acoust. Soc. Am., Vol. 107, 70-86, 2000.
doi:10.1121/1.428345 Google Scholar

6. Attiya, A. M., E. A. El-Diwany, A. M. Shaarawi, and I. M. Besieris, "Reflection and transmission of X-waves in the presence of planarly layered media: the pulsed plane wave representation," Progress In Electromagnetics Research, Vol. 30, 191-211, 2000.
doi:10.2528/PIER99090202 Google Scholar

7. Shaarawi, A. M., I. M. Besieris, A. M. Attiya, and E. A. El-Diwany, "Reflection and transmission of an electromagnetic X-wave incident on a planar air-dielectric interface: spectral analysis," Progress in Electromagnetics Research, Vol. 30, 213-250, 2000.
doi:10.2528/PIER00042502 Google Scholar

8. Attiya, A. M., E. A. El-Diwany, and A. M. Shaarawi, "Transmission and reflection of TE electromagnetic X-wave normally incident on a lossy dispersive half-space," Proceedings of the 17th National Radio Science Conference, NRSC’2000, B11.1-12, Minufiya University, Egypt, 2000. Google Scholar

9. Attiya, A. M., "Transverse (TE) electromagnetic X-waves: propagation, scattering, diffraction and generation problems,", Ph.D. Thesis, Cairo University, May 2001. Google Scholar

10. Saari, P. and K. Reivelt, "Evidence of X-shaped propagationinvariant localized light waves," Phys. Rev. Lett., Vol. 79, 4135-4138, 1997.
doi:10.1103/PhysRevLett.79.4135 Google Scholar

11. Saari, P. and H. S onajalg, "Pulsed bessel beams," Laser Phys., Vol. 7, 32-39, 1997. Google Scholar

12. Donnelly, R. and D. Power, "The behavior of electromagnetic localized waves at a planar interface," IEEE Trans. Antennas Propagat., Vol. 45, 580-591, 1997.
doi:10.1109/8.564083 Google Scholar

13. Hillion, P., "How do focus wave modes propagate across a discontinuity in a medium?," Optik, 93, 67-72, 1993. Google Scholar

14. Power, D., R. Donnelly, and MacIsaac, "Spherical scattering of superpositions of localized waves," Phys. Rev., E, Vol. 48, 1410-1417, 1993.
doi:10.1103/PhysRevE.48.1410 Google Scholar

15. Hillion, P., "Diffraction of time-dependent electromagnetic pulse by a conducting plane screen," Opt. Comm., Vol. 102, 199-204, 1993.
doi:10.1016/0030-4018(93)90381-E Google Scholar

16. Hillion, P., "Diffraction of focus wave modes at a perfectly conducting screen," Opt. Comm., Vol. 123, 215-224, 1996.
doi:10.1016/0030-4018(95)00397-5 Google Scholar

17. Fagerholm, J., A. T. Friberg, J. Huttunen, D. P. Morgan, and M. M. Salomaa, "Angular-spectrum representation of nondiffracting X-waves," Phys. Rev. E, Vol. 54, 4347-4352, 1996.
doi:10.1103/PhysRevE.54.4347 Google Scholar

18. Kouyoumjian, R. G. and P. H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface," Proc. IEEE, Vol. 62, 1448-1461, 1974.
doi:10.1109/PROC.1974.9651 Google Scholar

19. McNamara, D. M., C. W. I. Pistorius, and J. A. G. Malherba, "Introduction to the uniform geometrical theory of diffraction,", Artech House, Boston, 1990. Google Scholar

20. Keller, J. B., "Geometrical theory of diffraction," J. Opt. Soc. Am., Vol. 52, 116-130, 1962.
doi:10.1364/JOSA.52.000116 Google Scholar

21. Michaeli, A., "Equivalent edge currents for arbitrary aspects of observation," IEEE Trans. Antennas and Prop., Vol. 32, 252-258, 1984.
doi:10.1109/TAP.1984.1143303 Google Scholar

22. Rousseau, P. R. and P. H. Pathak, "Time-domain uniform geometrical theory of diffraction for a curved wedge," IEEE Trans. Antennas and Prop., Vol. 43, 1375-1382, 1995.
doi:10.1109/8.475925 Google Scholar

23. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, New York, 1965.

24. Knott, E. and T. Senior, "Comparison of three high-frequency diffraction techniques," Proc. IEEE, Vol. 62, 1468-1474, 1974.
doi:10.1109/PROC.1974.9653 Google Scholar

25. Marsland, D. P., C. A. Balanis, and S. A. Brumley, "Higher order diffractions from a circular disk," IEEE Trans. Antennas and Prop., Vol. 35, 1436-1444, 1987.
doi:10.1109/TAP.1987.1144034 Google Scholar

26. Shirai, H. and L. B. Felsen, "Modified GTD for generating complex resonances for flat strips and disks," IEEE Trans. Antennas and Prop., Vol. 34, 779-790, 1986.
doi:10.1109/TAP.1986.1143889 Google Scholar

27. Dominek, A. K., "Transient scattering analysis for a circular disk," IEEE Trans. Antennas and Prop., Vol. 39, 815-819, 1991.
doi:10.1109/8.86881 Google Scholar

28. Lu, J. and J. F. Greenleaf, "Experimental verification of nondiffracting X-waves," IEEE Trans. on Ultrason., Ferroelect., Freq. Contr., Vol. 39, 441-446, 1992.
doi:10.1109/58.143178 Google Scholar

29. Attiya, A. M., E. A. El-Diwany, and A. M. Shaarawi, "Generation of an approximate TE electromagnetic X-wave in free space using Huygen’s aperture," Proceedings of the 16th National Radio Science Conference, NRSC’99, B3.1-11, Ain Shams University, Cairo, Egypt, 1999. Google Scholar

30. Michaeli, A., "Equivalent edge currents for arbitrary aspects of observation," IEEE Trans. Antennas and Prop., Vol. 32, 252-258, 1984.
doi:10.1109/TAP.1984.1143303 Google Scholar

31. Michaeli, A., "Elimination of infinities in equivalent edge currents, part I: fringe current components," IEEE Trans. Antennas and Prop., Vol. 34, 912-918, 1986.
doi:10.1109/TAP.1986.1143913 Google Scholar

32. Knott, E., "The relationship between Mitzner’s ILDC and Michaeli’s equivalent currents," IEEE Trans. Antennas and Prop., Vol. 33, 112-114, 1985.
doi:10.1109/TAP.1985.1143482 Google Scholar

33. Johansen, P., "Uniform physical theory of diffraction equivalent edge currents for truncated wedge strips," IEEE Trans. Antennas and Prop., Vol. 44, 989-995, 1996.
doi:10.1109/8.504306 Google Scholar

34. Johansen, P., "Time-domain version of the physical theory of diffraction," IEEE Trans. Antennas and Prop., Vol. 47, 261-270, 1999.
doi:10.1109/8.761065 Google Scholar

35. Tiberio, R. and S. Maci, "An incremental theory of diffraction: scalar formulation," IEEE Trans. Antennas and Prop., Vol. 42, 600-611, 1994.
doi:10.1109/8.299558 Google Scholar

36. Tiberio, R., S. Maci, and A. Toccafondi, "An incremental theory of diffraction: electromagnetic formulation," IEEE Trans. Antennas and Prop., Vol. 43, 87-96, 1995.
doi:10.1109/8.366356 Google Scholar

Dr. Ahmed Mohamed Attiya

Dr. Amr Shaarawi

Professor Ioannis Besieris