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WIENER-HOPF ANALYSIS OF THE H-POLARIZED PLANE WAVE DIFFRACTION BY A FINITE SINUSOIDAL GRATING (Invited Paper)

By T. Eizawa and K. Kobayashi

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Abstract:
The diffraction by a finite sinusoidal grating is analyzed for the H-polarized plane wave incidence using the Wiener-Hopf technique combined with the perturbation method. Assuming the depth of the grating to be small compared with the wavelength and approximating the boundary condition on the grating surface, the problem is reduced to the diffraction problem involving a flat strip with a certain mixed boundary condition. Introducing the Fourier transform for the unknown scattered field and applying an approximate boundary condition together with a perturbation series expansion for the scattered field, the problem is formulated in terms of the zero-order and first-order Wiener-Hopf equations. The Wiener-Hopf equations are solved via the factorization and decomposition procedure leading to the exact and asymptotic solutions. Taking the inverse Fourier transform and applying the saddle point method, the scattered field expression is explicitly derived. Scattering characteristics of the grating are discussed in detail via numerical examples of the far field intensity.

Citation:
T. Eizawa and K. Kobayashi, "Wiener-Hopf Analysis of the h -Polarized Plane Wave Diffraction by a Finite Sinusoidal Grating (Invited Paper)," Progress In Electromagnetics Research, Vol. 149, 1-13, 2014.
doi:10.2528/PIER14063007
http://www.jpier.org/PIER/pier.php?paper=14063007

References:
1. Shestopalov, V. P., The Riemann-Hilbert Method in the Theory of Diffraction and Propagation of Electromagnetic Waves, Kharkov University Press, Kharkov, 1971 (in Russian).

2. Nosich, A. I., "Green’s function-dual series approach in wave scattering by combined resonant scatterers," Analytical and Numerical Methods in Electromagnetic Wave Theory, Chapter 9, M. Hashimoto, M. Idemen, and O. A. Tretyakov, Eds., Science House, Tokyo, 1993.

3. Shestopalov, V. P., L. N. Litvinenko, S. A. Masalov, and V. G. Sologub, Diffraction of Waves by Gratings, Kharkov University Press, Kharkov, 1973 (in Russian).

4. Shestopalov, V. P., A. A. Kirilenko, and S. A. Masalov, Convolution-type Matrix Equations in the Theory of Diffraction, Naukova Dumka Publishing, Kiev, 1984 (in Russian).

5. Nosich, A. I., "The method of analytical regularization in wave-scattering and eigenvalue problems: Foundations and review of solutions," IEEE Antennas Propagat. Mag., Vol. 41, No. 3, 34-49, 1999.
doi:10.1109/74.775246

6. Ikuno, H. and K. Yasuura, "Improved point-matching method with application to scattering from a periodic surface," IEEE Trans. Antennas Propagat., Vol. 21, No. 5, 657-662, 1973.
doi:10.1109/TAP.1973.1140592

7. Okuno, Y., "The mode-matching method," Analysis Methods for Electromagnetic Wave Problems, E. Yamashita (ed.), Chapter 4, Artech House, Boston, 1990.

8. Okuno, Y., "An introduction to the Yasuura method," Analytical and Numerical Methods in Electromagnetic Wave Theory, M. Hashimoto, M. Idemen, and O. A. Tretyakov (eds.), Chapter 11, Science House, Tokyo, 1993.

9. Petit, R. (ed.), Electromagnetic Theory of Gratings, Springer-Verlag, Berlin, 1980.
doi:10.1007/978-3-642-81500-3

10. Hinata, T. and T. Hosono, "On the scattering of electromagnetic wave by plane grating placed in homogeneous medium — Mathematical foundation of point-matching method and numerical analysis," Trans. IECE Japan, Vol. J59-B, No. 12, 571-578, 1976 (in Japanese).

11. Yamasaki, T., K. Isono, and T. Hinata, "Analysis of electromagnetic fields in inhomogeneous media by Fourier series expansion methods — The case of a dielectric constant mixed a positive and negative regions," IEICE Trans. Electron., Vol. E88-C, No. 12, 2216-2222, 2005.
doi:10.1093/ietele/e88-c.12.2216

12. Ozaki, R., T. Yamasaki, and T. Hinata, "Scattering of electromagnetic waves by multilayered inhomogeneous columnar dielectric gratings," IEICE Trans. Electron., Vol. E90-C, No. 2, 295-303, 2007.
doi:10.1093/ietele/e90-c.2.295

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

14. Weinstein, L. A., The Theory of Diffraction and the Factorization Method, The Golem Press, Boulder, 1969.

15. Mittra, R. and S.-W. Lee, Analytical Techniques in the Theory of Guided Waves, Macmillan, New York, 1971.

16. Kobayashi, K., "Wiener-Hopf and modified residue calculus techniques," Analysis Methods for Electromagnetic Wave Problems, Chapter 8, E. Yamashita, Ed., Artech House, Boston, 1990.

17. Baldwin, G. L. and A. E. Heins, "On the diffraction of a plane wave by an infinite plane grating," Math. Scand., Vol. 2, 103-118, 1954.

18. Hills, N. L. and S. N. Karp, "Semi-infinite diffraction gratings --- I," Comm. Pure Appl. Math., Vol. 18, No. 1-2, 203-233, 1965.
doi:10.1002/cpa.3160180119

19. Luneburg, E. and K. Westpfahl, "Diffraction of plane waves by an infinite strip grating," Ann. Phys., Vol. 27, No. 3, 257-288, 1971.
doi:10.1002/andp.19714820305

20. Luneburg, E., "Diffraction by an infinite set of parallel half-planes and by an infinite strip grating," Analytical and Numerical Methods in Electromagnetic Wave Theory, M. Hashimoto, M. Idemen, and O. A. Tretyakov (eds.), Chapter 7, Science House, Tokyo, 1993.

21. Serbest, A. H., A. Kara, and E. Luneburg, "Scattering of plane waves at the junction of two corrugated half-planes," Electromagnetics, Vol. 25, No. 1, 21-38, 2005.
doi:10.1080/02726340590522111

22. Idemen, M. and A. Alkumru, "Diffraction of two-dimensional high-frequency electromagnetic waves by a locally perturbed two-part impedance plane," Wave Motion, Vol. 42, 53-73, 2005.
doi:10.1016/j.wavemoti.2004.09.003

23. Ayub, M., M. Ramzan, and A. B. Mann, "Acoustic diffraction by an oscillating strip," Applied Mathematics and Computation, Vol. 214, 201-209, 2009.
doi:10.1016/j.amc.2009.03.089

24. Kobayashi, K., "Diffraction of a plane wave by the parallel plate grating with dielectric loading," Trans. IECE Japan, Vol. J64-B, No. 10, 1091-1098, 1981 (in Japanese).

25. Kobayashi, K., "Diffraction of a plane electromagnetic wave by a parallel plate grating with dielectric loading: The case of transverse magnetic incidence," Can. J. Phys., Vol. 63, No. 4, 453-465, 1985.
doi:10.1139/p85-071

26. Kobayashi, K. and T. Inoue, "Diffraction of a plane wave by an inclined parallel plate grating," IEEE Trans. Antennas Propagat., Vol. 36, No. 10, 1424-1434, 1988.
doi:10.1109/8.8630

27. Kobayashi, K. and K. Miura, "Diffraction of a plane wave by a thick strip grating," IEEE Trans. Antennas Propagat., Vol. 37, No. 4, 459-470, 1989.
doi:10.1109/8.24166

28. Das Gupta, S. P., "Diffraction by a corrugated half-plane," Proc. Vib. Prob., Vol. 3, No. 11, 413-424, 1970.

29. Chakrabarti, A. and S. Dowerah, "Traveling waves in a parallel plate waveguide with periodic wall perturbations," Can. J. Phys., Vol. 62, No. 3, 271-284, 1984.

30. Zheng, J. P. and K. Kobayashi, "Diffraction by a semi-infinite parallel-plate waveguide with sinusoidal wall corrugation: Combined perturbation and Wiener-Hopf analysis," Progress In Electromagnetics Research B, Vol. 13, 75-110, 2009.
doi:10.2528/PIERB08120704

31. Zheng, J. P. and K. Kobayashi, "Combined Wiener-Hopf and perturbation analysis of the H-polarized plane wave diffraction by a semi-infinite parallel-plate waveguide with sinusoidal wall corrugation," Progress In Electromagnetics Research B, Vol. 13, 203-236, 2009.
doi:10.2528/PIERB09021102

32. Kobayashi, K. and T. Eizawa, "Plane wave diffraction by a finite sinusoidal grating," Trans. IECE Japan, Vol. E74, No. 9, 2815-2826, 1991.

33. Kobayashi, K., "Some diffraction problems involving modified Wiener-Hopf geometries," Analytical and Numerical Methods in Electromagnetic Wave Theory, M. Hashimoto, M. Idemen, and O. A. Tretyakov (eds.), Chapter 4, Science House, Tokyo, 1993.

34. Kobayashi, K., "Solutions of wave scattering problems for a class of the modified Wiener-Hopf geometries," IEEJ Transactions on Fundamentals and Materials, Vol. 133, No. 5, 233-241, 2013.
doi:10.1541/ieejfms.133.233

35. Kobayashi, K., "Plane wave diffraction by a strip: Exact and asymptotic solutions," J. Phys. Soc. Japan, Vol. 60, No. 6, 1891-1905, 1991.
doi:10.1143/JPSJ.60.1891

36. Kobayashi, K., "On generalized gamma functions occurring in diffraction theory," J. Phys. Soc. Japan, Vol. 60, 1501-1512, 1991.
doi:10.1143/JPSJ.60.1501


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