Effective permittivity and permeability of a medium consisting of an infinite number of ferromagnetic microwires are evaluated in this paper. Analysis is carried out with the help of local and average fields inside a unit cell. In the literature, effective permittivity of the microwire grid is obtained by assuming the grid as an impedance loaded surface. The analysis is applicable only for the case of TMz polarized normally incident wave. Proposed analysis enable us to evaluate all the three diagonal components of effective permittivity and permeability for arbitrarily incident uniform plane wave having arbitrary polarization angle. Numerical results are obtained through MATLAB, and a comparison is done with the results available in the literature for validation. Numerical results have shown a DNG like behaviour of the medium for a TMz polarized incident wave.
2. Pendry, J. B., A. Holden, W. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett., Vol. 76, No. 25, 4773-4776, 1996.
doi:10.1103/PhysRevLett.76.4773
3. Smith, D. R., W. J. Padilla, N. S. C. Nemat, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett., Vol. 84, 4184-4187, 2000.
doi:10.1103/PhysRevLett.84.4184
4. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, 77-79, 2001.
doi:10.1126/science.1058847
5. Walser, R. M., "Electromagnetic metamaterials," Proc. SPIE, Vol. 4467, 1-15, July 9, 2001.
6. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, 1780-1782, 2006.
doi:10.1126/science.1125907
7. Bose, J. C., "On the rotation of plane of polarization of electric waves by a twisted structure," Proc. R. Soc. Lond., Vol. 63, 146-152, January 1, 1898.
8. Kock, W., "Metallic delay lenses," Bell System, Technical J., Vol. 27, 58-82, 1948.
doi:10.1002/j.1538-7305.1948.tb01331.x
9. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Uspekhi, Vol. 10, No. 4, 509-514, 1968.
doi:10.1070/PU1968v010n04ABEH003699
10. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced non-linear phenomena," IEEE Trans. on Microwave Theory Techn., Vol. 47, 2075-2084, 1999.
doi:10.1109/22.798002
11. Belov, P., S. Tretyakov, and A. Viitanen, "Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires," Journal of Electromagnetic Waves and Applications, Vol. 16, No. 8, 1153-1170, 2002.
doi:10.1163/156939302X00688
12. Christodoulou, C. and J. Kauffman, "On the electromagnetic scattering from infinite rectangular grids with finite conductivity," IEEE Transactions on Antennas and Propagation, Vol. 34, No. 2, 144-154, 1986.
doi:10.1109/TAP.1986.1143803
13. He, Y., P. He, V. G. Harris, and V. Carmine, "Role of Ferrites in negative index metamaterials," IEEE Trans. on Magnetics, Vol. 42, No. 10, 2852-2854, 2006.
doi:10.1109/TMAG.2006.879146
14. Carbonell, J., M. H. Garcıa, and D. J. Sanchez, "Double negative metamaterials based on ferromagnetic microwires," Physical Review B, Vol. 81, 024401-1-024401-6, 2010.
15. Carignan, L., A. Yelon, and D. Menard, "Ferromagnetic nanowire metamaterials: Theory and applications," IEEE Trans. Microwave Theory Techn., Vol. 59, No. 10, 2568-2586, 2011.
doi:10.1109/TMTT.2011.2163202
16. Kumar, T., N. Kalyanasundaram, and B. K. Lande, "Analysis of the generalized case of scattering from a ferromagnetic microwire grid," Progress In Electromagnetics Research M, Vol. 35, 1-10, 2014.
doi:10.2528/PIERM13120406
17. Liberal, I., I. S. Nefedov, I. Ederra, R. Gonzalo, and S. A. Tretyakov, "Electromagnetic response and homogenization of grids of ferromagnetic microwires," J. Appl. Phys., Vol. 110, 064909-1-064909-8, 2011.
doi:10.1063/1.3658844
18. Tretyakov, S., Analytical Modeling in Applied Electromagnetics, 69-81, Artech House, Boston, 2003.
19. Balanis, C. A., Advanced Engineering Electromagnetics, 2nd Ed., Chap. 11, 57-606, John Wiley and Sons, 2012.
20. Wilfried, S. and W. Martin, Semiconductor Optics and Transport Phenomena, 32-33, SpringerVerlag, Berlin-Heidelberg, 2002.
21. Reynet, O., A. L. Adenot, S. Deprot, and O. Acher, "Effect of the magnetic properties of the inclusions on the high-frequency dielectric response of diluted composites," Phy. Rev. B, Vol. 66, 094412-1-094412-9, 2002.
22. Acher, O., M. Ledieu, A. L. Adenot, and O. Reynet, "Microwave properties of diluted composites made of magnetic wires with giant magneto-impedance effect," IEEE Trans. on Mag., Vol. 39, No. 5, 3085-3090, 2003.
doi:10.1109/TMAG.2003.816011
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