The properties of a grounded dielectric slab with double negative (DNG) metamaterials are investigated in this paper. Dramatically different dispersion curves of evanescent surface modes (electromagnetic fields exponentially decay both in air and inside the slab) are observed. They are highly dependent on the medium parameters. As the counterpart of the improper complex leaky modes in a double positive (DPS) medium, the complex modes in a DNG medium are proved to be exclusively proper. They have exponentially decaying fields in the air region and are termed complex surface modes. It is found that there are an infinite number of complex surface modes and they cannot be suppressed. The Poynting vectors of complex surface modes are studied and it is proved that their integrals along the transverse direction are simply zero. The complete mode spectrum of the dielectric slab for both DPS and DNG media are tabled and compared. Surface wave suppression is discussed and its necessary and sufficient conditions are presented.
2. Pendry, J. B., A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett., Vol. 76, No. 6, 4773-4776, 1996.
3. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech., Vol. 47, No. 11, 2075-2084, 1999.
4. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, No. 10, 3966-3969, 2000.
5. Smith, D. R., W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett., Vol. 84, No. 5, 4184-4187, 2000.
6. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, No. 4, 72-79, 2001.
7. Smith, D. R. and N. Kroll, "Negative refractive index in lefthanded materials," Phys. Rev. Lett., Vol. 85, No. 10, 2933-2936, 2000.
8. Markos, P. and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E, Vol. 65, No. 3, 036622, 2002.
9. AlÃ¹, A. and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Microwave Theory Tech., Vol. 51, No. 10, 2558-2571, 2003.
10. AlÃ¹, A. and N. Engheta, "An overview of salient properties of planar guided-wave structures with double-negative (DNG) and single-negative (SNG) layers," Negative-Refraction Metamaterials: F undamental Principles and Applications, 339-380, 2005.
11. Caloz, C. and T. Itoh, "Transmission line approach of left-handed (LH) materials and microstrip implementation of an artificial LH transmission line," IEEE Trans. Microwave Theory Tech., Vol. 52, No. 5, 1159-1166, 2004.
12. Lin, I.-H., M. DeVincentis, C. Caloz, and T. Itoh, "Arbitrary dual band components using composite right/left-handed transmission lines," IEEE Trans. Microwave Theory Tech., Vol. 52, No. 4, 1142-1149, 2004.
13. Mittra, R., K. Rajab, and M. T. Lanagan, Size reduction of microstrip antennas using metamaterials, Proc. IEEE AP-S, No. 7, 2005.
14. Erentok, A. and R. W. Ziolkowski, Development of epsilonnegative (ENG) metamaterials for efficient electrically small antenna applications, Proc. IEEE AP-S, No. 7, 2005.
15. Cory, H. and A. Barger, "Surface-wave propagation along a metamaterial slab," Microwave Opt. Technol. Lett., Vol. 38, No. 9, 392-395, 2003.
16. Dong, H. and T. X. Wu, "Analysis of discontinuities in doublenegative (DNG) slab waveguides," Microwave Opt. Technol. Lett., Vol. 39, No. 12, 483-488, 2003.
17. Nefedov, I. S. and S. A. TretyaKov, "Waveguide containing a backward-wave slab," Radio Sci., Vol. 38, 1101-1109, 2003.
18. Wu, B.-I., T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys., Vol. 93, No. 6, 9386-9388, 2003.
19. Shadrivov, I. W., A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E, Vol. 67, No. 5, 057602, 2003.
20. Suwailam, M. M. B. and Z. D. Chen, "Surface waves on a grounded double-negative (DNG) slab waveguide," Microwave Opt. Technol. Lett., Vol. 44, No. 3, 494-498, 2005.
21. Li, C., Q. Sui, and F. Li, "Complex guided wave solutions of grounded dielectric slab made of metamaterials," Progress In Electromagnetics Research, Vol. 51, 187-195, 2005.
22. Baccarelli, P., P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, "Effects of leaky-wave propagation in metamaterial grounded slabs excited by a dipole source," IEEE Trans. Microwave Theory Tech., Vol. 53, No. 1, 32-44, 2005.
23. Baccarelli, P. P., Burghignoli, G. Lovat, and S. Paulotto, "Surfacewave suppression in a double-negative metamaterial grounded slab," IEEE Antennas Wireless Propag. Lett., Vol. 2, 269-272, 2003.
24. 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. Microwave Theory Tech., Vol. 53, No. 4, 1431-1442, 2005.
25. Landau, L., E. Lifshitz, and L. Pitaevskii, Electrodynamics of Continuous Media, 2nd edition, Butterworth-Heinenann, Oxford, England, 1984.
26. Collin, R. E., Field Theory of Guided Waves, 2nd edition, IEEE Press, Piscataway, NJ, 1991.
27. Chew, W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York, 1990.
28. Oliner, A. A., "Leakage from higher modes on microstrip line with applications to antennas," Radio Sci., Vol. 22, 907-912, 1987.
29. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley & Sons, NJ, 1989.
30. Mahmoud, S. F. and A. J. Viitanen, "Surface wave character on a slab of metamaterial with negative permittivity and permeability," Progress In Electromagnetics Research, Vol. 51, 127-137, 2005.
31. Hanson, G. W. and A. B. Yakovlev, Operator Theory for Electromagnetics, Springer, NY, 2002.
32. Rozzi, T., L. Pierantoni, and M. Farina, "General constraints on the propagation of complex waves in closed lossless isotropic waveguides," IEEE Trans. Microwave Theory Tech., Vol. 46, No. 5, 512-516, 1998.
33. Freire, M. J., F. Mesa, and M. Horno, "Power characteristics of complex modes in both reciprocal and nonreciprocal boxed microstrip lines," Microwave Opt. Technol. Lett., Vol. 18, No. 8, 389-394, 1998.
34. Tamir, T. and A. A. Oliner, The spectrum of electromagnetic waves guided by a plasma layer, Proceedings of the IEEE, Vol. 51, No. 2, 317-332, 1963.
35. Laxpati, S. R. and R. Mittra, "Energy considerations in open and closed waveguides," IEEE Trans. Antenna and Propag., Vol. 18, No. 11, 883-890, 1965.