volume | PIER Journals

Abstract

In this paper, accurate analytical expressions for the impedance of vertical electric and magnetic dipoles which are located over the half-space materials of arbitrary permittivity and permeability are developed. In this regard, the impedance variations are expressed in integral forms. For metamaterial half-space, a proper expression for approximating the Fresnel reflection coefficient is proposed. Using this approximate expression, the impedance integrals are analytically solved, and exact formulas for impedance variations are obtained. The results for the metamaterial half-spaces are compared with the case of natural materials (positive permittivity and permeability), and key differences are explained. The in uences of sign changing in permeability of the half-space material on the impedance of vertical dipole are studied, and the results are validated by comparison with those of numerical solution of integrals. It is shown that for elevated dipoles over materials with high and/or low conductivities, the results of both methods are in complete agreement. For vertical dipoles above low loss materials, the results are somewhat identical. However, a better agreement could be obtained using higher order approximations for the integrand.

1. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of ε and μ," Soviet Physics USPEKHI, Vol. 10, 509, 1968.
doi:10.1070/PU1968v010n04ABEH003699

2. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewart, "Metamaterials with negative parameters, theory, design and microwave applications," Phys. Rev. Lett., Vol. 76, 4773, 1996.
doi:10.1103/PhysRevLett.76.4773

3. Marques, R., F. Martin, and M. Sorolia, Metamaterials with Negative Parameters, Theory, Design and Microwave Applications, Wiley & Sons, 2008.

4. Sarychev, A. K. and V. M. Shalaev, "Electrodynamics of Metamaterials," World Scientific Publishing Company, 2007.

5. Eleftheriades, G. I. and K. G. Balmain, "Negative-refraction metamaterials," Fundamental Principles and Applications, 2005.

6. Zhou, H., Z. Pei, S. Qu, S. Zhang, J. Wang, Q. Li, and Z. Xu, "A planar zero-index metamaterial for directive emission," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 7, 953-962, 2009.
doi:10.1163/156939309788355289

7. Cheng, Q., H. F. Ma, and T. J. Cui, "A complementary lens based on broadband metamaterials," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 1, 93-101, 2010.
doi:10.1163/156939310790322172

8. Shelby, R. A., D. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, No. 77, 2001.

9. Houck, A. A., J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys snells law," Phys. Rev. Lett., Vol. 90, No. 13, 137401, 2003.
doi:10.1103/PhysRevLett.90.137401

10. Grbic, A. and G. V. Eleftheriades, "Overcoming the diffraction limit with a planar left-handed transmission-line lens," Phys. Rev. Lett., Vol. 92, No. 11, 117-403, 2004.
doi:10.1103/PhysRevLett.92.117403

11. Shalaev, V. M., W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Optics Letters, Vol. 30, No. 24, 2005.
doi:10.1364/OL.30.003356

12. Thomas, J. R. and A. Ishimaru, "Wave packet incident on negative-index media," IEEE Trans. on Antennas Propagat., Vol. 53, No. 5, 2005.
doi:10.1109/TAP.2005.846454

13. Ishimaru, A., J. R. Thomas, and S. Jaruwatanadilok, "Electromagnetic waves over half-space metamaterials of arbitrary permittivity and permeability," IEEE Trans. on Antennas Propagat., Vol. 53, No. 3, 2005.
doi:10.1109/TAP.2004.842572

14. Formato, R. A., "New techniques for increasing antenna bandwidth with impedance loading," Progress In Electromagnetics Research B, Vol. 29, 269-288, 2011.
doi:10.2528/PIERB11021904

15. Yu, G. X., T. J. Cui, W. X. Jiang, X. M. Yang, Q. Cheng, and Y. Hao, "Transformation of different kinds of electromagnetic waves using metamaterials," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 5-6, 583-292, 2009.
doi:10.1163/156939309788019723

16. Oraizi, H. and A. Abdolali, "Some aspects of radio wave propagation in double zero metamaterials having the real parts of epsilon and mu equal to zero," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 14-15, 1957-1968, 2009.
doi:10.1163/156939309789932421

17. Fei, T., L. W. Li, T. S. Yeo, H. L. Wang, and Q. Wu, "A comparative study of radio wave propagation over the earth due to a vertical electric dipole," IEEE Trans. on Antennas Propagat., Vol. 55, No. 10, 2007.
doi:10.1109/TAP.2007.905869

18. Wait, J. R., "Characteristics of antenna over lossy earth," Antenna Theory, R. E. Collin and F. J. Zucker, Eds., Part 2, Chapter 23, 386-435, MacGraw-Hill, 1969.

19. Metwally, A. D. M. and S. F. Mahmoud, "Input impedance of vertical dipoles near a lossy half space," Radio Sci., Vol. 16, No. 2, 1981.
doi:10.1029/RS016i002p00179

20. Mahmoud, S. F. and A. D. M. Metwally, "New image representation for dipole near a dissipative earth, 1-discrete image ," Radio Sci., Vol. 16, No. 6, 1981.

21. Mahmoud, S. F. and A. D. M. Metwally, "Exact image method for impedance of antennas above the ground," Radio Sci., Vol. 16, No. 6, 1981.

22. Jarchi, S., J. Rashed-Mohassel, and R. Faraji-Dana, "Analysis of microstrip dipole antennas on a layered metamaterial substrate," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 5-6, 755-764, 2010.
doi:10.1163/156939310791036278

23. Parise, M., "Exact electromagnetic field excited by a vertical magnetic dipole on the surface of a lossy half-space," Progress In Electromagnetics Research B, Vol. 23, 69-82, 2010.
doi:10.2528/PIERB10060707

24. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York Abramowitz, 1964.

Mr. Younes Radi

Prof. Saeid Nikmehr

Dr. Shahram Hosseinzadeh