volume | PIER Journals

Abstract

The plane wave diffraction by an acute-angled wedge located on a perfect electric conducting plane is studied in the frequency and time domains. Only a TMz polarization is explicitly considered in the manuscript since the case of a TEz polarization can be solved in a similar way. At first, the uniform asymptotic physical optics approach is used to obtain the diffraction coefficients in the framework of the uniform geometrical theory of diffraction. The analytical procedure allows one to obtain closed form expressions that are easy to handle and provide reliable results from the engineering viewpoint. The time domain diffraction coefficients are successively determined by applying the inverse Laplace transform to the frequency domain counterparts. The effectiveness of the proposed solutions is proved by means of numerical tests and comparisons with full-wave numerical techniques.

1. 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

2. Riccio, G., "Uniform asymptotic physical optics solutions for a set of diffraction problems," Wave Propagation in Materials for Modern Applications, 33-54, A. Petrin Ed., Intech, Vukovar, HR, 2010. Google Scholar

3. Gennarelli, G. and G. Riccio, "A uniform asymptotic solution for diffraction by a right-angled dielectric wedge," IEEE Trans. Antennas Propagat., Vol. 59, 898-903, 2011.
doi:10.1109/TAP.2010.2103031 Google Scholar

4. Gennarelli, G. and G. Riccio, "Plane-wave diffraction by an obtuse-angled dielectric wedge," J. Opt. Soc. Am. A, Vol. 28, 627-632, 2011.
doi:10.1364/JOSAA.28.000627 Google Scholar

5. Gennarelli, G., M. Frongillo, and G. Riccio, "High-frequency evaluation of the field inside and outside an acute-angled dielectric wedge," IEEE Trans. Antennas Propagat., Vol. 63, 374-378, 2015.
doi:10.1109/TAP.2014.2364305 Google Scholar

6. Frongillo, M., G. Gennarelli, and G. Riccio, "Plane wave diffraction by arbitrary-angled lossless wedges: High-frequency and time-domain solutions," IEEE Trans. Antennas Propagat., Vol. 66, 6646-6653, 2018.
doi:10.1109/TAP.2018.2876602 Google Scholar

7. Berntsen, S., "Diffraction of an electric polarized wave by a dielectric wedge," SIAM J. Appl. Math., Vol. 43, 186-211, 1983.
doi:10.1137/0143013 Google Scholar

8. Rawlins, A. D., "Diffraction by, or diffusion into, a penetrable wedge," Proc. R. Soc. Lond. A, Vol. 455, 2655-2686, 1999.
doi:10.1098/rspa.1999.0421 Google Scholar

9. Burge, R. E., et al. "Microwave scattering from dielectric wedges with planar surfaces: A diffraction coefficient based on a physical optics version of GTD," IEEE Trans. Antennas Propagat., Vol. 47, 1515-1527, 1999.
doi:10.1109/8.805894 Google Scholar

10. Rouviere, J. F., N. Douchin, and P. F. Combes, "Diffraction by lossy dielectric wedges using both heuristic UTD formulations and FDTD," IEEE Trans. Antennas Propagat., Vol. 47, 1702-1708, 1999.
doi:10.1109/8.814950 Google Scholar

11. Seo, C. H. and J. W. Ra, "Plane wave scattering by a lossy dielectric wedge," Microwave Opt. Technol. Lett., Vol. 25, 360-363, 2000.
doi:10.1002/(SICI)1098-2760(20000605)25:5<360::AID-MOP19>3.0.CO;2-I Google Scholar

12. Kim, S. Y., J. W. Ra, and S. Y. Shin, "Diffraction by an arbitrary-angled dielectric wedge: part I - Physical optics approximation," IEEE Trans. Antennas Propagat., Vol. 39, 1272-1281, 1991.
doi:10.1109/8.81474 Google Scholar

13. Kim, S. Y., J. W. Ra, and S. Y. Shin, "Diffraction by an arbitrary-angled dielectric wedge. II. Correction to physical optics solution," IEEE Trans. Antennas Propagat., Vol. 39, 1282-1292, 1991.
doi:10.1109/8.81474 Google Scholar

14. Bernardi, P., R. Cicchetti, and O. Testa, "A three-dimensional UTD heuristic diffraction coefficient for complex penetrable wedges," IEEE Trans. Antennas Propagat., Vol. 50, 217-224, 2002.
doi:10.1109/8.997998 Google Scholar

15. Salem, M. A., A. H. Kamel, and A. V. Osipov, "Electromagnetic fields in presence of an infinite dielectric wedge," Proc. R. Soc. Lond. A, Vol. 462, 2503-2522, 2006.
doi:10.1098/rspa.2006.1691 Google Scholar

16. Daniele, V. and G. Lombardi, "The Wiener-Hopf solution of the isotropic penetrable wedge problem: Diffraction and total field," IEEE Trans. Antennas Propagat., Vol. 59, 3797-3818, 2011.
doi:10.1109/TAP.2011.2163780 Google Scholar

17. Vasilev, E. N. and V. V. Solodukhov, "Diffraction of electromagnetic waves by a dielectric wedge," Radiophysics and Quantum Electronics, Vol. 17, 1161-1169, 1976.
doi:10.1007/BF01036512 Google Scholar

18. Vasilév, E. N., V. V. Solodukhov, and A. I. Fedorenko, "The integral equation method in the problem of electromagnetic waves diffraction by complex bodies," Electromagnetics, Vol. 11, 161-182, 1991.
doi:10.1080/02726349108908271 Google Scholar

19. Budaev, B., Diffraction by Wedges, Longman Scient, 1995.

20. Veruttipong, T. W., "Time domain version of the uniform GTD," IEEE Trans. Antennas Propagat., Vol. 38, 1757-1764, 1990.
doi:10.1109/8.102736 Google Scholar

21. Gennarelli, G. and G. Riccio, "Time domain diffraction by a right-angled penetrable wedge," IEEE Trans. Antennas Propagat., Vol. 60, 2829-2833, 2012.
doi:10.1109/TAP.2012.2194668 Google Scholar

22. Gennarelli, G. and G. Riccio, "Obtuse-angled penetrable wedges: A time domain solution for the diffraction coefficients," Journal of Electromagnetic Waves and Applications, Vol. 27, No. 16, 2020-2028, 2013.
doi:10.1080/09205071.2013.831327 Google Scholar

23. Frongillo, M., G. Gennarelli, and G. Riccio, "TD-UAPO diffracted field evaluation for penetrable wedges with acute apex angle," J. Opt. Soc. Am. A, Vol. 32, 1271-1275, 2015.
doi:10.1364/JOSAA.32.001271 Google Scholar

24. Frongillo, M., G. Gennarelli, and G. Riccio, "Diffraction by a structure composed of metallic and dielectric 90˚ blocks," IEEE Antennas Wireless Propagat. Lett., Vol. 17, 881-885, 2018.
doi:10.1109/LAWP.2018.2820738 Google Scholar

25. Clemmow, P. C., The Plane Wave Spectrum Representation of Electromagnetic Fields, Oxford University Press, 1996.
doi:10.1109/9780470546598

26. Maliuzhinets, G. D., "Inversion formula for the Sommerfeld integral," Soviet Physics Doklady, Vol. 3, 52-56, 1958. Google Scholar

27. Taflove, A. and S. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method, Artech House, 2000.

Dr. Marcello Frongillo

Dr. Gianluca Gennarelli

Professor Giovanni Riccio