volume | PIER Journals

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

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.

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

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

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

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

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.

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.

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.

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

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.

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.

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.

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.

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.

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

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.

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

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.

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

Prof. Seil S. Sautbekov