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Abstract

This paper deals with the development of the Wiener-Hopf method for solving the diffraction of waves at fine strip-slotted structures. The classical problem for diffraction of plane wave at a strip is an important canonical problem. The boundary value problem is consecutively solved by a reduction to a system of singular boundary integral equations, and then to a system of Fredholm integral equations of the second kind, which effiectively is solved by one of three presented methods: A reduction to a system of the linear algebraic equations with the help of the etalon integral and the saddle point method numerical discretization based on Gauss quadrature formulas the method of successive approximations. The solution to the problem in the first method contains a denominator that takes into account the resonance process. Moreover, the precision of the main contribution of the short-wave asymptotic solution is ensured down to the quasi-stationary limit. The paper presents also comparisons of with earlier known results.

1. McLachlan, N. W., Ttheory and a Application of Mathieu Functions, Clarendon, Press-Oxford, 1974.

2. Brovenko, A. V., E. D. Vinogradova, P. N. Melezhik, A. Y. Poyedinchuk, and A. S. Troschylo, "Resonance wave scattering by a strip grating attached to a ferromagnetic medium," Progress In Electromagnetics Research B, Vol. 23, 109-129, 2010.
doi:10.2528/PIERB10012203 Google Scholar

3. Millar, R. F., "Diffraction of a wide slit and complementary strip," Proc. of the Cambridge Philosophical Society, Vol. 54, No. 4, 476-511, 1958. Google Scholar

4. Westpfahl, K., "Zur teorie einer klassse von beugungs problem mitteles singular integralgleichungen," Annalen der Physik, Vol. 4, No. 5--6, 283-351, 1959.
doi:10.1002/andp.19594590602 Google Scholar

5. Luneburg, E. and K. Westpfahl, "Bengung am streifen. hoch frequenz asymptotik and kleinmasche losung," Annalen der Physik, Vol. 21, No. 1--2, 12-25, 1968.
doi:10.1002/andp.19684760103 Google Scholar

6. Kieburts, R. B., "Constraction of asymptotic solutions to scattering problems in the Fourier transform representation," Applied Scientific Research, Vol. 12, No. 3, 221-234, 1965.
doi:10.1007/BF00382123 Google Scholar

7. Stockel, H., "Bengung am spalt," Annalen der Physik, Vol. 16, No. 5--6, 209-219, 1965.
doi:10.1002/andp.19654710502 Google Scholar

8. Hansen, E. B., "Scalar diffraction by an infinite strip and a circular disc," Journal of Mathematics and Physics, Vol. 41, No. 3, 229-245, 1962. Google Scholar

9. Grinberg, G. A., "New method of a solution of diffraction problem of electromagnetic waves on a plane with a unlimited rectilinear slot and to related it of problems," JTP, Vol. 27, No. 11, 2595-2605, 1957. Google Scholar

10. Grinberg, G. A., "Method of the solution of diffraction problems ideally conducting plane screens, based on studying of shadow currents induced on screens," JTP, Vol. 28, No. 3, 542-568, 1958. Google Scholar

11. Grinberg, G. A., "Diffraction of electromagnetic waves on a strip of finite width," DAN USSR, Vol. 129, No. 2, 295-298, 1959. Google Scholar

12. Kuritsin, V. N., "To the solution of a key problem for diffraction on ideally conducting strip," JTP, Vol. 31, No. 12, 1485-1490, 1961. Google Scholar

13. Popov, G. Y., "About one approximate expedient solution of the integral equation of diffraction of electromagnetic waves on a strip of finite width," JTP, Vol. 35, No. 3, 381-385, 1965. Google Scholar

14. Khaskind, M. D. and L. A. Weinstein, "Diffraction of plane waves on a slot and a strip," Radiotekhnika i Elektronika, Vol. 9, No. 10, 1800-1811, 1964. Google Scholar

15. Weinstein, L. A., Theory of Diffraction and Method of Factorization, Soviet Radio, Moscaw, 1966.

16. Fialkovski, A. T., "Diffraction of flat electromagnetic waves on a slot and a strip," Radiotekhnika i Elektronika, Vol. 11, No. 32, 178-186, 1966. Google Scholar

17. Nefyodov, E. I. and A. T. Fialkovski, Asymptotical Theory of Diffraction of Electromagnetic Waves on Finite Structures, Soviet Radio, Moscaw, 1972.

18. Borovikov, V. A., Diffraction on Polygons and Polyhedrons, Nauka, 1966.

19. Popichenko, V. A., "Diffraction on a slot and strip: An exactitude of various asymptotic methods," Radiotekhnika i Elektronika, Vol. 22, No. 7, 1341-1349, 1966. Google Scholar

20. Ufimtsev, P. Y., Theory of Edge Diffraction in Electromagnetics, Tech Science Press, 2003.

21. Ufimtsev, P. Y., Fundamentals of the Physical Theory of Diffraction, SciTech Publishing, 2007.
doi:10.1002/0470109017

22. Imran, A., Q. A. Naqvi, and K. Hongo, "Diffraction of electromagnetic plane wave by an impedance strip," Progress In Electromagnetics Research, Vol. 75, 303-318, 2007.
doi:10.2528/PIER07053104 Google Scholar

23. Guiliano, M., P. Nepa, G. Pelosi, and A. Vallecchi, "An approximate solution for skew incidence diffraction by an interior right-angled anisotropic impedance wedge," Progress In Electromagnetics Research, Vol. 45, 45-75, 2004. Google Scholar

24. Jones, D. S., Acoustic and Electromagnetic Waves, Clarendon Press, 1986.

25. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Dover, 1986.

26. Moschovitis, C. G., H. T. Anastassiu, and P. V. Frangos, "Scattering of electromagnetic waves from a rectangular plate using an extended stationary phase method based on fresnel functions (SPM-F)," Progress In Electromagnetics Research, Vol. 107, 63-99, 2010.
doi:10.2528/PIER10040104 Google Scholar

27. Erdelyi, A. and I. H. Bateman, Higher Transcendental Functions, Vol. 1, McGraw-Hill, 1953.

28. Sautbekov, S. S., "Once again about diffraction on a strip and a slot: Wiener-Hoph-Fock method," Radiotekhnika i Elektronika, Vol. 45, No. 45, 1202-1209, 2000. Google Scholar

29. Sautbekov, S. S., Method of Edges Sources in Theories of Electromagnetic Waves Diffraction, Gilim, 2001.

Prof. Seil S. Sautbekov