This paper investigates the generalized case of scattering from a planar grid, containing an infinite number of axially magnetized ferromagnetic microwires placed parallel to each other in free space. A semi-analytical solution is obtained by calculating the local field at the surface of the reference microwire which is the sum of the scattered field from the other microwires as well as the incident field. Graf's theorem is used to transform the scattered field from one coordinate system to the other. Scattering field coefficients for the reference microwire are obtained by matching the tangential field components at the surface of the reference microwire. Simulated results are expressed in terms of the Reflection, Transmission, and Absorption Coefficients for the (TMz) and (TEz) polarizations. For validation, results of the proposed analysis specialized to the case of normal incidence with TMz polarization are compared with the results available in the literature.
2. Carbonell, J., H. G. Miqule, and J. S. Dehsa, "Double negative metamaterials based on ferromagnetic microwires," Physical Review B, Vol. 81, 024401, 2010.
3. Pendry, J., A. Holden, W. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett., Vol. 76, No. 25, 4773-4776, 1996.
4. Liberal, I., I. Ederra, C. Gomez-Polo, A. Labrador, J. I. Perez Landazabal, and R. Gonzalo, "Theoretical modeling and experimental veri¯cation of the scattering from a ferromagnetic microwire," IEEE Trans. Microwave Theory Techn., Vol. 59, No. 3, 517-526, Mar. 2011, DOI: 10.1109/TMTT.2010.2098037.
5. Eggimann, W. H., "Scattering of a plane wave on a ferrite cylinder at normal incidence," EEE Trans. Microwave Theory Techn., Vol. 8, No. 4, 440-445, Jul. 1960, DOI: 10.1109/TMTT.1960.1124754.
6. Attiya, A. M. and M. A. Alkanhal, "Generalized formulation for the scattering from a ferromagnetic microwire," ACES Journal, Vol. 27, No. 5, 399-407, May 2012.
7. Waldron, R. A., "Electromagnetic wave propagation in cylindrical waveguides containing gyromagnetic media," Journal of the British Institution of Radio Engineers, Vol. 18, No. 10, 597-612, Oct. 1958.
8. 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, 2011.
9. Polewski, M. and J. Mazur, "Scattering by an array of conducting, lossy dielectric, ferrite and pseudochiral cylinders," Progress In Electromagnetics Research, Vol. 38, 283-310, 2002.
10. Christodoulou, C. G. and J. F. Kauffman, "On the electromagnetic scattering from infinite rectangular grids with finite conductivity," IEEE Trans. on Antennas and Propg., Vol. 34, No. 2, 144-154, Feb. 1986.
11. Henin, B. H., A. Z. Elsherbeni, and M. H. Al Sharkawy, "Oblique incidence plane wave scattering from an array of circular dielectric cylinder," Progress In Electromagnetics Research, Vol. 68, 261-279, 2007.
12. 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.
13. Pozar, D. M., Microwave Engineering, 4th Ed., Chapter 9, Wiley-Interscience, New York, 2012.
14. Tretyakov, S., Analytical Modeling in Applied Electromagnetics, Artech House, Norwood, MA, 2003.
15. Balanis, C. A., Advanced Engineering Electromagnetics, 2nd Ed., John Wiley and Sons, 2012.
16. Sang, L., J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications, John Wiely and Sons, 2000, ISBN 0-471-38799-1.
17. Abramowitz, M. and I. Stegun, Handbook of Mathematical Functions, Dover, 1965.
18. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th Ed., Academic Press, 2007.