This paper focuses on the complex guided wave solutions of grounded slab made of metamaterials. Complex solutions of both TE and TM modes have been analyzed. It is found that they are distributed on the proper Riemann sheet. This property differs dramatically from that of a conventional grounded slab. A number of other distribution properties are studied analytically. Some numerical examples are given to verify the analytical results. It is important to take the peculiar complex solutions into account in the problems of microstrip and surface wave excitation.
2. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative refractive index of refraction," Science, Vol. 292, No. 4, 77-99, 2001.
3. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, 3966-3969, 2000.
4. Simovski, C. R. and S. He, "Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting Omega-particles," Phys. Lett. A, Vol. 311, 2003.
5. Huangfu, J. T., et al., "Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns," Applied Physics Letters, Vol. 84, No. 9, 1537-1539, 2004.
6. Nefedov, I. S. and S. A. Tretyakov, "Theoretical study of waveguiding structures containing backward-wave materials," Proc. of XXXVIIth URSI General Assembly, 17-24, 2002.
7. Alu, A. and N. Engheta, "Anomalous mode coupling in guided-wave structures containing metamaterials with negative permittivity and permeability," Proc. IEEE 2002 Nanotechnology Conference, 26-28, 2002.
8. Wu, B.-I., T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary tranverse wave number in a slab waveguide with negative permittivity and permeability," Journal of Applied Physics, Vol. 93, No. 11, 9386-9388, 2003.
9. Ilya V. S., A. A. Sukhorukov, and Yu. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Physical Review E, Vol. 67, No. 5, 057602-1, 2003.
10. Collin, R. E., Field Theory of Guided Waves, 1990., 1990.