volume | PIER Journals

Abstract

The diffraction of a uniform unit-amplitude E-polarized plane wave is considered in the case of its normal incidence on a strip periodic metal grating placed on the anisotropic hyrotropic ferromagnetic half-space boundary. The Dirichlet boundary conditions on the grating strips, the medium interface conjugation conditions, the Meixner condition that the energy is finite in any confined volume and the radiation condition are applied, and the boundary value diffraction problem in terms of Maxwell's (Helmholtz) equations is equivalently reduced to the dual system of functional equations with exponential kernel. The system is shown to be the Riemann-Hilbert problem in analytic function theory with the conjugation coefficient differing, in general, from ``-1" and dependent on the incident wave frequency. An analytical regularization procedure based on the Riemann-Hilbert boundary value problem solution with the following use of the Plemelle-Sokhotsky formulas is suggested, resulting in the system of linear algebraic equations of the second kind with a compact operator. For vthese systems, the truncation technique possibility has been shown. Calculation algorithms and simulation packages in terms of C++ language have been developed. As a result, the reflection coefficient performance has been studied over sufficiently wide ranges of frequency and constitutive and geometrical parameters of the electrodynamical systems of interest. The frequency bands of the reflection coefficient resonant behavior have been established and examined. A numerical analytical model of these resonances has been proposed.

1. Jia, H., K. Yasumoto, and H. Toyama, "Reflection and transmission properties of layered periodic arrays of circular cylinders embedded in magnetized ferrite slab," IEEE Trans. Antennas Propag., Vol. 53, No. 3, 1145-1153, 2005.
doi:10.1109/TAP.2004.842654

2. Achmad, M., S. Atsushi, K. Hiroshi, and A. Ikuo, "Application of the 2nd finite difference-frequency domain method for the analysis of the dispersion characteristics of ferrite devices," 33rd European Microwave Conference, 1175-1177, Munich, Germany, 2003.

3. Yeliseeva, S. V. and D. I. Sementsov, "Electromagnetic eigenwave spectrum of a ferromagnetic-semiconductor periodic structure," ZhTF, Vol. 75, No. 7, 106-111, 2005 (in Russian).

4. Masalov, S. A., A. V. Ryzhak, O. I. Sukharevskiy, and V. M. Shkil, "Physical elements of range "Stealth"-type technologies," The Mozhayskiy's VIKU, St. Petersburg, 1999 (in Russian).

5. Nishimura, K. and M. Tsutsumi, "Scattering of millimeter waves by metallic strip gratings on an optically plasma-induced semiconductor slab," IEEE Trans. Microwave Theory and Techniques, Vol. 44, No. 12, 2231-2237, 1996.
doi:10.1109/22.556451

6. Pendry, J. B., "Negative refraction," Contemporary Physics, Vol. 45, No. 3, 191-203, January-February 2004.
doi:10.1080/00107510410001667434

7. Panin, S. B., P. D. Smith, and A. Y. Poyedinchuk, "Elliptical to linear polarization transformation by a grating on a chiral medium," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1885-1899, 2007.

8. Brovenko, A. V., P. N. Melezhik, and A. Y. Poyedinchuk, "Diffraction of a plane electromagnetic wave by a metal grating with a magnetoactive plasma," Izv. VUZov. Radiofizika, Vol. XLVII, No. 8, 638-649, 2004 (in Russian).

9. Brovenko, A. V., P. N. Melezhik, A. Y. Poyedinchuk, N. P. Yashina, and G. Granet, "Surface resonances of a metal strip grating on the plane boundary of metamaterial," Progress In Electromagnetic Research, Vol. 63, 209-222, 2006.
doi:10.2528/PIER06052401

10. Gurevich, A. G. and G. A. Melkov, Magnetic Oscillations and Waves, Fizmatgiz, 1994 (in Russian).

11. Shestopalov, V. P., Riemann-Hilbert Problem Method in Theory of Electromagnetic Wave Diffraction and Propagation, Kharkov State Univ. Press, 1971 (in Russian).

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

13. Shestopalov, V. P., A. A. Kirilenko, S. A. Masalov, and Y. K. Sirenko, Resonance Scattering of Waves, Vol. 1, Diffraction gratings, Naukova Dumka, 1986 (in Russian).

14. Abdulkadyrov, V. A. and G. N. Gestrina, "Reflection features of a system of periodic screens with gyrotropic filling," Electromagnetic Waves and Electron Systems, Vol. 9, 52-58, 2004 (in Russian).

15. Gandel, Y. V. and V. V. Khoroshun, "The vortex lattice method in the electromagnetic wave diffraction on a metal grating with a gyrotropic layer," International Conference on Mathematical Methods in electromagnetic Theory MMET 2000, 578, Kharkov, Ukraine, September 12--15, 2000.

16. Belotserkovskiy, S. M. and I. K. Lifanov, Numerical Methods in Singular Integral Equations, Nauka, 1985 (in Russian).

17. Shestopalov, V. P., Y. A. Tuchkin, A. Y. Poyedinchuk, and Y. K. Sirenko, "New solution methods for direct and inverse problems in diffraction theory," Analytical Regularization of Boundary Value Problems in Electromagnetic Theory, Osnova, Kharkov, 1997 (in Russian).

18. Khoroshun, V. V., "Diffraction of plane electromagnetic waves on a metal grating with a gyromagnetic medium," Radiotekhnika, No. 4, 20-25, Kharkov State Univ. Press, Kharkov, 1967 (in Russian).

19. Brovenko, A. V. and A. Y. Poyedinchuk, "Regularization method for a class of dual series equations in diffraction theory," Int. Conf. on Mathematical Methods in Electromagnetic Theory MMET'98, 775-777, Ukraine, 1998.
doi:10.1109/MMET.1998.709887

20. Brovenko, A. V., P. N. Melezhik, and A. Y. Poyedinchuk, "Regularization method for a class of dual series equations in diffraction theory," Ukr. Math. Zhurnal, Vol. 53, No. 10, 1320-1327, 2001 (in Ukrainian).

21. Brovenko, A. V., P. N. Melezhik, and A. Y. Poyedinchuk, "Electromagnetic wave diffraction by a partially screened," Doklady NAN Ukrainy, No. 2, 89-95, 2002 (in Ukrainian).

22. Brovenko, A. V., P. N. Melezhik, and A. Y. Poyedinchuk, "The H-polarized wave diffraction by a partially screened cylinder with magnetic active plasma properties: The analytical regularization procedure," The 4th International Symposium "Physics and Engineering of Millimeter and Sub-millimeter Waves", 211-213, June Kharkov, Ukraine, June 4--9, 2001.

23. Brovenko, A. V., P. N. Melezhik, and A. Y. Poyedinchuk, "Electromagnetic wave diffraction by a partially screened anisotropic dielectric (plasma) cylinder," Electromagnetic Waves and Electron Systems, Vol. 8, No. 9, 4-11, 2003 (in Russian).

24. Brovenko, A. V., P. N. Melezhik, and A. Y. Poyedinchuk, "The plane H-polarized wave diffraction by a metal grating with a magnetoactive plasma,", 573-575, Ukraine, 2002.

25. Uehara, M., K. Yashiro, and S. Ohkawa, "A method for solving Riemann Hilbert boundary value problems in nonreciprocal wave propagation," J. Math. Phys., Vol. 38, No. 5, 2417-2434, May May 1997.
doi:10.1063/1.532194

26. Uehara, M., K. Yashiro, and S. Ohkawa, "Diffraction of plane waves from a strip grating on a ferrite substrate," Microwave Conference Proceedings, 1997.

27. Mexiner, J., "The behavior of electromagnetic fields at edges," Tech. Rpt. EM-72, Inst. Math. Sci., New York University, New York, 1954.

28. Muskhelishvili, N. I., Singular Integral Equations, Dover, 1992.

29. Pollaczek, F., "Sur une generalisation des polynomes de Legendre," C. R. Acad. Sei., Paris, Vol. 228, 1363-1365, 1949.

30. Lavrent'yev, M. A. and B. V. Shabat, Methods in Complex Variable Theory, GIFML, Moscow, 1958(in Russian).

31. Kantorovich, L. V. and G. P. Akilov, Functional Analysis, Nauka, 1984 (in Russian).

Dr. А. V. Brovenko

Dr. Elena D. Vinogradova

Dr. P. N. Мelezhik

Dr. Anatoly Poyedinchuk

Dr. A. S. Troschylo