This paper is concerned with the analysis of the currents induced on a 2D infinite perfectly conducting plane illuminated by a complex beam obtained from the analytical continuation of the real location of a unit impulse source into a complex one. The main goal considering this well-known problem is to understand the meaning of the analytical continuation and the physical information underlying the complex quantities arising from it,and to investigate the capabilities of operating in complex spaces instead of the original real ones through a simple example. Several complex quantities directly related to this problem are analysed and translated into the real domain,leading to a clear and general description of all the possible behaviours of the currents. These results will provide some new insight to extend the complex analysis methodology to more complicated scattering problems. As expected,complex analysis appears to be a full-meaning tool to obtain parameterizations of EM problems,leading to more general solutions and their physical descriptions.
2. Felsen, L. B., "Complex rays," Philips Res. Repts. Vol. 30, Vol. '' Philips Res. Repts. 30, 187-195, 1975.
3. Ra, J. W., H. L. Bertoni, and L. B. Felsen, "Reflection and transmission of beams at a dielectric interface," SIAM J. Appl. Math., Vol. 24, No. 3, 396-413, 1973.
4. Lu, I. T., L. B. Felsen, and Y. Z. Ruan, "Sp ectral aspects of the Gaussian beam method: reflection from a homogeneous halfspace," Geophys. J. R. Astr. Soc., 915-932, 1987.
5. Dahl, M., "Electromagnetic Gaussian beams and Riemannian geometry," Progress In Electromagnetics Research, Vol. 60, 265-291, 2006.
6. Kaiser, G., "Ph ysical wavelets and their sources: real physics in complex spacetime," J. Phys. A: Math. Gen., Vol. 36, 291-338, 2003.
7. Gonzalez-Morales, M. J., C. Dehesa-Martínez, and E. Gago-Ribas, About complex extensions and their application in electromagnetics, Complex Computing-Networks. A link between Brain-like and Wave-oriented Electrodynamic Algorithms, Vol. 104, 81-86, 2006.
8. Gago-Ribas, E., M. J. Gonzalez-Morales, and C. Dehesa-Martínez, "Analytical parametrization of a 2D real propagation space in terms of complex electromagnetic beams," IEICE Trans. on Electronics, Vol. E80-C, No. 11, 1434-1439, 1997.
9. Gago-Ribas, E. and M. J. Gonzalez-Morales, "2D complex point source radiation problem. I. Complex distances and complex angles," Turkish Journal of Electric Engineering and Computer Sciences, Vol. 10, No. 2, 317-343, 2002.
10. Gonzalez-Morales, M. J. and E. Gago-Ribas, "2D complex point source radiation problem. II. Complex beams," Turkish Journal of Electric Engineering and Computer Sciences, Vol. 10, No. 2, 345-369, 2002.
11. Heyman, E. and L. B. Felsen, "Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics," J. Opt. Soc. Am. A, Vol. 18, No. 7, 1588-1611, 2001.
12. Martini, E., G. Pelosi, and S. Selleri, "Line integral representation of physical optics scattering from a perfectly conducting plate illuminated by a Gaussian beam modeled as a complex point source," IEEE Trans. on AP, Vol. 51, No. 10, 2003.
13. Lin, W., "W. and Z. Yu Existence and uniqueness of the solutions in the SN,DN and CN waveguide Theories," J. of Electromagn. Waves and Appl., Vol. 20, No. 2, 237-247, 2006.
14. Imram, A. and Q. A. Naqvi, "Diffraction of electromagnetic plane wave by an impedance strip," Progress In Electromagnetics Research, Vol. 75, 303-318, 2007.
15. Abo-Seida O. M., "F ar-field due to a vertical magnetic dipole in sea," J. of Electromagn. Waves and Appl., Vol. 20, No. 6, 707-715, 2006.
16. Arnold M. D., "An efficient solution for scattering by a perfectly conducting strip grating," J. of Electromagn. Waves and Appl., Vol. 20, No. 7, 891-900, 2006.
17. Watanabe, K. and K. Yasumoto, "Tw o-dimensional electromagnetic scattering of non-plane incident waves by periodic structures," Progress In Electromagnetics Research, Vol. 74, 241-271, 2007.
18. Hussain, W., "Asymptotic analysis of a line source diffraction by a perfectly conductiong half plane in a bi-isotropic medium," Progress In Electromagnetics Research, Vol. 58, 271-283, 2006.
19. Gago-Ribas, E., M. J. Gonzalez-Morales, and C. Dehesa- Martínez, Challenges and perspectives of complex spaces and complex signal theory analysis in electromagnetics: First steps, Electromagnetics in a Complex World: Challenges and Perspectives, Vol. 96, 175-188, 2003.
20. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Eq. (9.2.3), Do ver Pub., New York, 1965.