The paper is devoted to the study of the interaction of the electromagnetic waves with the structure composed of perfectly conducting strip grating, situated on the plane boundary of metamaterial with effective permittivity, depending on the frequency of the wave of excitation. The rigorous solution to the relevant diffraction boundary value problem is developed. The extensive numerical experiments, performed with a help of corresponding algorithm constructed, allowed to establish several regularities in the complicated process of interaction of electromagnetic waves with grating on dispersive metamaterial. The efficient association of analytical and numerical study has provided the understanding of the nature of resonant phenomena appearing in this process.
2. Bilotti, F., A. Al`u, N. Engheta, and L. Vegni, "Anomalous properties of scattering from cavities partially loaded with double-negative or single-negative metamaterials," Progress in Electromagnetic Research, Vol. 51, 49-63, 2005. doi:10.2528/PIER04041401
3. Lai, A., T. Itoh, and C. Caloz, "Composite right/left-handed transmission line metamaterials," IEEE Microwave Magazine, Vol. 5, No. 3, 34-50, 2004. doi:10.1109/MMW.2004.1337766
4. Lim, S., C. Caloz, and T. Itoh, "Electronically scanned composite right/left handed micro strip leaky-wave antenna," IEEE Microwave and Wireless Components Letters, Vol. 14, No. 6, 277-279, 2004. doi:10.1109/LMWC.2004.828008
5. Antoniades, M. A. and G. V. Eleftheriades, "Compact linear lead/lag metamaterial phase shifters for broadband applications," IEEE Antennas and Wireless Propagation Letters, Vol. 2, No. 6, 103-106, 2003. doi:10.1109/LAWP.2003.815280
6. Engheta, N., "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas and Wireless Propagation Letters, Vol. 1, No. 1, 10-13, 2002. doi:10.1109/LAWP.2002.802576
7. Caloz, C., C.-C. Chang, and T. Itoh, "Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations," Journal of Applied Physics, Vol. 90, No. 11, 5483-5486, 2001. doi:10.1063/1.1408261
8. Pendry, J. B., A. J. Holden, W. J. Stewart, and I. Youhgs, "Extremely low frequency plasmons in metallic structures," Phys. Rew. Lett., Vol. 76, 4773-4776, 1996. doi:10.1103/PhysRevLett.76.4773
9. Shestopalov, V. P. and Yu. K. Sirenko, Dynamic Theory of Gratings, 214, Kiyev, Naukova Dumka, 1989.
10. Poyedinchuk, A. Ye., Yu. A. Tuchkin, N. P. Yashina, J. Chandezon, and G. Granet, "C-method: Several aspects of spectral theory of gratings," Progress In Electromagnetics Research, Vol. 59, 113-149, 2006. doi:10.2528/PIER05050901
11. Brovenko, A. V., P. N. Melezhik, and A. Y. Poyedinchuck, "The method of regularization for one class of duel summatory equations," Ukrainskiy Fizicheskiy Zhurnal, Vol. 53, No. 10, 1320-1327, 2001.
12. Brovenko, A. V., P. N. Melezhik, and A. Y. Poyedinchuck, "The diffraction of plane electromagnetic wave by metal grating with magnetoactive plasma," Isv. VUZov, Vol. 47, No. 8, 638-649, 2004.
13. Shestopalov, V. P., The Method ofthe Riemann-Hilbert Problem in the Theory ofEle ctromagnetic Wave Diffraction and Propagation, 400, Publishing House of Kharkov National University, Kharkov, 1971.
14. Shestopalov, V. P., Y. A. Tuchkin, A. Y. Poyedinchuk, and Y. K. Sirenko, "New solution methods for direct and inverse problems of the diffraction theory," Analytical Regularization of the Boundary-value Problems in Electromagnetic Theory, 1997.
15. Hokhberg, I. Z. and Y. I. Seagul, "Operator generalization of the theorem about logarithmic residue and the Rouche theorem," Collected Papers on Mathematics, Vol. 84, No. 4, 607-629, 1971.