The metamaterial slab with low refractive index exhibits directive properties which make it suitable to work as antenna. The characteristics of such a device are affected under the presence of a conducting rod of arbitrary shape placed over the slab. A qualitative and quantitative approach is presented which is possible by implementing the method of auxiliary sources. For the evaluation of the far field quantities the method of stationary phase is employed. A validation example considering a circular rod is solved rigorously with use of the method of moments. Several numerical results are shown and discussed.
2. Mahmoud, S., "A new miniaturized annular ring patch resonator partially loaded by a metamaterial ring with negative permeability and permittivity," IEEE Antennas Wireless Propag. Lett., Vol. 3, No. 10, 19-22, 2004.
3. Alu, A. and N. Engheta, "Achieving transparency with plasmonic and metamaterial coatings," Phys. Rev. E, Vol. 72, 016623, 2005.
4. Baccarelli, P., P. Burghignoli, G. Lovat, and S. Paulotto, "Surface-wave suppression in a double-negative metamaterial grounded slab," IEEE Antennas Wireless Propag. Lett., Vol. 2, 269-272, 2003.
5. Baccarelli, P., P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, "Fundamental modal properties of surface waves on metamaterial grounded slabs," IEEE Trans. Microw. Theory Tech., Vol. 53, No. 4, 1431-1442, 2005.
6. Li, C., Q. Sui, and F. Li, "Complex guided wave solution of grounded dielectric slab made of metamaterials," Progress In Electromagnetics Research, Vol. 66, 239-251, 2006.
7. Ubeda, E., J. Rius, and J. Romeu, "Preconditioning techniques in the analysis of finite metamaterial slabs," IEEE Trans. Antennas Propag., Vol. 54, No. 1, 265-268, 2006.
8. Parazzoli, C. G., R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett., Vol. 90, 107401, 2003.
9. Lovat, G., P. Burghignoli, F. Capolino, D. Jackson, and D. Wilton, "Analysis of directive radiation from a line source in a metamaterial slab with low permittivity," IEEE Trans. Antennas Propag., Vol. 54, No. 3, 1017-1030, 2006.
10. Wu, B., W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk, and J. A. Kong, "A study of using metamaterials as antenna substrate to enhance gain," Progress In Electromagnetics Research, Vol. 51, 295-328, 2005.
11. Pacheco, J., "Theory and application of left-handed metamaterials," 181-216, 181-216, 2004.
12. Wang, W., "Directive antenna using metamaterial substrates," 17-36, 17-36, 2004.
13. Weng, Z.-B., Y.-C. Jiao, and F.-S. Zhang, "Design and experiment of one dimension and two dimension metamaterial structures for directive emission," Progress In Electromagnetics Research, Vol. 70, 199-209, 2007.
14. Zitron, N. and J. Davis, "Scattering of directed radiation by a cylinder," Journal Applied Scientific Research, Vol. 18, No. 1, 280-287, 1968.
15. Felsen, L. and N. Marcuvitz, Radiation and Scattering of Waves, 485-487, 485-487, Wiley-IEEE, New York, 1994.
16. Valagiannopoulos, C. A., "Arbitrary currents on circular cylinder with inhomogeneous cladding and RCS optimization," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 5, 665-680.
17. Pinto, I., V. Galdi, and L. Felsen, Electromagnetics in a Complex World: Challenges and Perspectives, 155-157, 155-157, Springer, Benevento, 2004.
18. Schevchenko, V., Continuous Transitions in Open Waveguides, 24-26, 24-26, Golem, 1971.
19. Leviatan, Y. and A. Boag, "Analysis of electromagnetic scattering from dielectric cylinders using a multifilament current model," IEEE Trans. Antennas Propag., Vol. 35, No. 10, 1119-1128, 1987.
20. Leviatan, Y., P. Li, A. Adams, and J. Perini, "Single-post inductive obstacle in rectangular waveguide," IEEE Trans. Microw. Theory Tech., Vol. 31, No. 10, 806-812, 1983.
21. Leviatan, Y. and A. Boag, "Analysis of electromagnetic scattering from dielectrically coated conducting cylinders using a multifilament current model," IEEE Trans. Antennas Propagat., Vol. 36, No. 11, 1602-1607, 1988.
22. Karkashadze, D., On Status of main singularities in 3D scattering problems, Proceedings of VIth International Seminar/Workshop on DIPED-2001, 81-84, 2001.
23. Stewart, J., Calculus, 575-581, 575-581, Brooks/Cole Publishing Company, 1999.
24. Fikioris, G., "On two types of convergence in the method of auxiliary sources," IEEE Trans. Antennas Propagat., Vol. 54, No. 7, 2022-2033, 2006.
25. Erdelyi, A., Asymptotic Expansions, 50-52, 50-52, Dover Publications, New York, 1956.
26. Li, L., D. You, M. Leong, and T. Yeo, "Electromagnetic scattering by multilayered chiral-media structures: a scattering radiation transform," Progress In Electromagnetic Research, Vol. 26, 249-291, 2000.
27. Abramowitz, M. and I. Stegun, Handbook of Mathematical Functions, 362-364, 362-364, National Bureau of Standards, Washington, 1964.
28. Hildebrand, F., Advanced Calculus for Applications, 549-551, 549-551 Prentice Hall, New Jersey, 1976.
29. Jones, D., Theory of Electromagnetism, 269-271, 269-271, Pergamon Press, Oxford, 1964.
30. Collin, R., Field Theory of Guided Waves, 730-732, 730-732, IEEE Press, New York, 1991.