Vol. 63
Latest Volume
All Volumes
Vector Circuit Theory for Spatially Dispersive Uniaxial Magneto-Dielectric Slabs
, Vol. 63, 279-294, 2006
We present a general dyadic vector circuit formalism, applicable for uniaxial magneto-dielectric slabs, with strong spatial dispersion explicitly taken into account. This formalism extends the vector circuit theory, previously introduced only for isotropic and chiral slabs. Here we assume that the problem geometry imposes strong spatial dispersion only in the plane, parallel to the slab interfaces. The difference arising from taking into account spatial dispersion along the normal to the interface is briefly discussed. We derive general dyadic impedance and admittance matrices, and calculate corresponding transmission and reflection coefficients for arbitrary plane wave incidence. As a practical example, we consider a metamaterial slab built of conducting wires and split-ring resonators, and show that neglecting spatial dispersion and uniaxial nature in this structure leads to dramatic errors in calculation of transmission characteristics.
Pekka M. T. Ikonen, Mikhail Lapine, Igor Nefedov, and Sergei Tretyakov, "Vector Circuit Theory for Spatially Dispersive Uniaxial Magneto-Dielectric Slabs," , Vol. 63, 279-294, 2006.

1. Felsen, L. B. and N. Marcuvitz, Radiation and Scattering of Waves, IEEE Press, Piscataway, NJ, 1991.

2. Lindell, I. V. and E. Alanen, "Exact image theory for the Sommerfeld haf-space problem, part III: General formulation," IEEE Trans. Antennas Propagat., Vol. AP-32, No. 10, 1027-1032, 1984.

3. Oksanen, M. I., S. A. Tretyakov, and I. V. Lindell, "Vector circuit theory for isotropic and chiral slabs," J. Electromagnetic Waves Appl., Vol. 4, 613-643, 1990.

4. Tretaykov, S., Analytical Modeling in Applied Electromagnetics, Artech House, Norwood, MA, 2003.

5. Viitanen, A. J. and P. P. Puska, "Reflection of obliquely incident plane wave from chiral slab backed by soft and hard surface," IEE Proc. Microwaves, Vol. 146, No. 8, 271-276, 1999.

6. Serdyukov, A., I. Semchenko, S. Tretyakov, and A. Sihvola, Electromagnetics of Bi-anisotropic Materials; Theory and Applications, Gordon and Breach Science Publishers, 2001.

7. 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.

8. 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.

9. Belov, P. A., R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, "Strong spatial dispersion in wire media in the very large wavelength limit," Phys. Rev. B, Vol. 67, No. 3, 113103, 2003.

10. Nefedov, I. S., A. J. Viitanen, and S. A. Tretyakov, "Electromagnetic wave refraction at an interface of a double wire medium," Phys. Rev. B, Vol. 72, 245113, 2005.

11. Kostin, M. V. and V. V. Shevchenko, "Artificial magnetics based on double circular elements," Proc. Bianisotropics'94, 18-20, 1994.

12. Gorkunov, M., M. Lapine, E. Shamonina, and K. H. Ringhofer, "Effective magnetic properties of a composite material with circular conductive elements," Eur. Phys. J. B, Vol. 28, No. 7, 263-269, 2002.

13. Maslovski, S. I., P. Ikonen, I. A. Kolmakov, S. A. Tretyakov, and M. Kaunisto, "Artificial magnetic materials based on the new magnetic particle: Metasolenoid," Progress in Electromagnetics Research, Vol. 54, 61-81, 2005.

14. Maslovski, S. I., "On the possibility of creating artificial media simultaneously possessing negative permittivity and permeability," Techn. Phys. Lett., Vol. 29, No. 1, 32-34, 2003.

15. Belov, P. A. and M. G. Silveirinha, "Resolution of subwavelength transmission devices formed by a wire medium," Phys. Rev. E, Vol. 73, No. 5, 1-9, 2006.

16. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, No. 10, 3966-3969, 2000.

17. Engheta, N.M. Silveirinha, A. Alu, and A. Salandrino, "Scattering and reflection properties of low-epsilon metamaterials shells and bends," Proc. of joint ICEAA'05 and EESC'05 Conf., 12-16, 2005.

18. Gralak, B., S. Enoch, and G. Tayeb, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. B, Vol. 17, No. 6, 1012-1020, 2000.

19. Garcia, N., E. V. Ponizovskaya, and J. Q. Xiao, "Zero permittivity materials: Band gaps at the visible," Appl. Phys. Lett., Vol. 80, No. 2, 1120-1122, 2002.

20. Schwartz, B. T. and R. Piestun, "Total external reflection from metamaterials with ultralow refractive index," J. Opt. Soc. Am. B, Vol. 20, No. 12, 2448-2453, 2003.

21. Enoch, S., G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett., Vol. 89, No. 11, 1-4, 2002.

22. Gorkunov, M. V. and M. I. Ryazanov, "The role of spatial dispersion near zero points of the dielectric function of cubic and uniaxial crystals," Laser Physics, Vol. 8, 502-507, 1997.