In a recent study, we proposed improved quasi-static expressions for the electromagnetic field components excited by a vertical electric dipole lying on the surface of a flat and homogeneous lossy half-space. The present paper introduces an analytical approach to derive analogous formulas for the case of the horizontal electric dipole. The procedure is based on the expansion of the integral representations for the fields into power series of the ratio between the wavenumbers in free-space and in the conducting medium. Later, the terms in the expansions up to the second order can be reduced to known tabulated integrals. Numerical results are presented to illustrate the improvement in accuracy that follows from using the second-order approximations for the fields in place of the zeroth-order ones. In the quasi-static frequency range and beyond, use of the new formulation makes it possible to reduce the maximum relative error in the calculation of the fields from about 23% down to less than 7%.
2. Wait, J. R., "The electromagnetic fields of a horizontal dipole in the presence of a conducting half-space," Canadian Journal of Physics, Vol. 39, 1017-1028, 1961.
3. Moore, R. K. and W. E. Blair, "Dipole radiation in a conducting half-space," Journal of Research of the National Bureau of Standards --- D. Radio Propagation, Vol. 65D, No. 6, 547-563, 1961.
4. Bannister, P. R., "Quasi-static fields of dipole antennas at the earth's surface," Radio Science, Vol. 1, No. 11, 1321-1330, 1966.
5. Bannister, P. R., "The quasi-near fields of dipole antennas," IEEE Trans. Antennas and Propag., Vol. 15, No. 5, 618-626, 1967.
6. King, R. W. P., M. Owens, and T. T. Wu, Lateral Electromagnetic Waves: Theory and Applications to Communications, Geophysical Exploration, and Remote Sensing, Springer-Verlag, New York, 1992.
7. King, R. W. P., "New formulas for the electromagnetic field of a vertical electric dipole in a dielectric or conducting half-space near its horizontal interface," Journal of Applied Physics, Vol. 53, 8476-8482, 1982.
8. King, R. W. P., S. S. Sandler, and L. C. Shen, "The electromagnetic field of a vertical electric dipole over the earth or sea," IEEE Trans. Antennas and Propag., Vol. 42, No. 3, 382-389, 1994.
9. King, R. W. P., "Electromagnetic field of a vertical dipole over an imperfectly conducting half-space," Radio Science, Vol. 25, 149-160, 1990.
10. 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.
11. Kong, J. A., Electromagnetic Wave Theory, John Wiley & Sons, New York, 1986.
12. Chew, W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York, 1990.
13. Radi, Y., S. Nikmehr, and S. Hosseinzadeh, "A rigorous treatment of vertical dipole impedance located above lossy DPS, MNG, ENG, and DNG half-space," Progress In Electromagnetics Research, Vol. 116, 107-121, 2011.
14. Parise, M., "A study on energetic efficiency of coil antennas used for RF diathermy," IEEE Antennas and Wireless Prop. Letters, Vol. 10, 385-388, 2011.
15. Zhang, M. and A. Alden, "Calculation of whole-body SAR from a 100MHz dipole antenna," Progress In Electromagnetics Research, Vol. 119, 133-153, 2011.
16. Li, Z. X., G.-F. Li, J.-B. Fan, and Y. Yin, "Quasi-static complex image method for a current point source in horizontally stratified multilayered earth," Progress In Electromagnetics Research B, Vol. 34, 187-204, 2011.
17. Parise, M., "On the use of cloverleaf coils to induce therapeutic heating in Tissues," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 11-12, 1667-1677, 2011.
18. Palacky, G. J., "Resistivity characteristics of geologic targets," Electromagnetic Methods in Applied Geophysics, Vol. 1, 52-129, M. N. Nabighian, Editor, SEG, Tulsa, Oklahoma, 1988.
19. Wait, J. R., Electromagnetic Waves in Stratified Media, Pergamon Press, New York, 1970.
20. Li, K., Electromagnetic Fields in Stratified Media, Zhejiang University Press, Hangzhou; Springer-Verlag, Berlin, Heidelberg, 2009.
21. Parise, M., "Second-order formulation for the quasi-static field from a vertical electric dipole on a lossy half-space," Progress In Electromagnetics Research, Vol. 136, 509-521, 2013.
22. Li, K., Y.-L. Lu, and W.-Y. Pan, "Exact formulas for the lateral electromagnetic pulses generated by a horizontal electric dipole in the interface of two dielectrics," Progress In Electromagnetics Research, Vol. 55, 249-283, 2005.
23. Whittaker, E. T. and G. N. Watson, A Course of Modern Analysis, 4th Ed., Cambridge University Press, Cambridge, England, 1927.
24. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1964.
25. Erdelyi, A., Tables of Integral Transforms, Vol. 2, McGraw-Hill, New York, 1954.
26. Dong, J.-F. and J. Li, "Characteristics of guided modes in uniaxial chiral circular waveguides," Progress In Electromagnetics Research, Vol. 124, 331-345, 2012.
27. Ausserlechner, U., "Closed analytical formulae for multi-pole magnetic rings," Progress In Electromagnetics Research B, Vol. 38, 71-105, 2012.
28. Parise, M., "Fast computation of the forward solution in controlled-source electromagnetic sounding problems," Progress In Electromagnetics Research, Vol. 111, 119-139, 2011.
29. Parise, M. and S. Cristina, "High-order electromagnetic modeling of shortwave inductive diathermy effects," Progress In Electromagnetics Research, Vol. 92, 235-253, 2009.