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Generation of Complex Source Point Expansions from Radiation Integrals (Invited Paper)

By Enrica Martini and Stefano Maci
Progress In Electromagnetics Research, Vol. 152, 17-31, 2015


This paper discusses methods for expanding fields radiated by arbitrary sourcesenclosed by a certain minimum sphere in termsof Complex Source Point (CSP) beams. Two different approaches are reviewed; the first one is based on a spectral radiation integral, where the Fourier-spectrum is obtained by far field matching. The second approach consists of two steps: first, the equivalence principle is applied to a sphere enclosing the real sources, and a continuous equivalent electric current distribution is obtained in terms of spherical waves; then, the continuous current is extended to complex space and its SW components are properly filtered and sampled to generate the discrete set of CSPs. In both cases, the final resultis a compact finite series representation with a number of terms that matches the degrees of freedom of arbitrary radiated fields;it is particularly efficient when the fields are highly directional and the observation domain is limited to a given angular sector. The fact that the CSPs rigorously respect Maxwell's equations ensures the validity of the expansion from near to far zone and allows one to incorporate the CSP representation in a generalized admittance matrix formalism for the analysis of complex problems.


Enrica Martini and Stefano Maci, "Generation of Complex Source Point Expansions from Radiation Integrals (Invited Paper)," Progress In Electromagnetics Research, Vol. 152, 17-31, 2015.


    1. Wylde, R. J., "Millimetre-wave Gaussian beam-mode optics and corrugated feed horns," IEE Proceedings H, Microwaves, Optics and Antennas, Vol. 131, No. 4, 258-262, Aug. 1984, Doi: 10.1049/ip-h-1.1984.0053.

    2. McEwan, N. J. and P. F. Goldsmith, "Gaussian beam techniques for illuminating reflector antennas," IEEE Trans. Antennas Propag., Vol. 37, No. 3, 297-304, Mar. 1989.

    3. Imbriale, W. A. and D. J. Hoppe, "Recent trends in the analysis of quasioptical systems," Millenium Conf. on Antennas Propag., Davos, Switzerland, 2000.

    4. Withington, S., J. A. Murphy, and K. G. Isaak, "Representation of mirrors in beam waveguides as inclined phase-transforming surfaces," Infrared Phys. Technol., Vol. 36, No. 3, 723-734, Apr. 1995.

    5. Siegman, A., "Hermite-Gaussian functions of complex argument as optical-beam eigenfunctions," J. Opt. Soc. Am., Vol. 63, 1093-1094, 1973.

    6. Hern`andez-Figueroa, H. E., M. Zamboni-Rached, and E. Recami (eds.), Localized Waves, Chapter 6, Wiley-Interscience, Hoboken, NJ, 2008.

    7. Steinberg, B. Z., E. Heyman, and L. B. Felsen, "Phase space methods for radiation from large apertures," Radio Sci., Vol. 26, 219-227, 1991.

    8. Shlivinski, A., E. Heyman, A. Boag, and C. Letrou, "A phase-space beam summation formulation for ultrawideband radiation: A multiband scheme," IEEE Trans. Antennas Propag., Vol. 52, No. 8, 2042-2056, Aug. 2004, Doi: 10.1109/TAP.2004.832513.

    9. Shlivinski, A., E. Heyman, and A. Boag, "A phase-space beam summation formulation for ultrawideband radiation — Part II: A multiband scheme," IEEE Trans. Antennas Propag., Vol. 53, No. 3, 948-957, Mar. 2005.

    10. Shlivinski, A., E. Heyman, and A. Boag, "A pulsed beam summation formulation for short pulse radiation based on windowed radon transform (WRT) frames," IEEE Trans. Antennas Propag., Vol. 53, No. 9, 3030-3048, Sep. 2005.

    11. Arnold, J. M., "Phase-space localization and discrete representation of wave fields," J. Opt. Soc. Am. A, Vol. 12, No. 1, 111-123, Jan. 1995.

    12. Chou, H.-T., P. H. Pathak, and R. J. Burkholder, "Application of Gaussian-ray basis functions for the rapid analysis of electromagnetic radiation from reflector antennas," IEE Proc. Microw. Antennas Propag., Vol. 150, 177-183, 2003.

    13. Chou, H.-T. and P. H. Pathak, "Uniform asymptotic solution for electromagnetic reflection and diffraction of an arbitrary Gaussian beam by a smooth surface with an edge," Radio Sci., Vol. 32, No. 4, 1319-1336, Jul./Aug. 1997.

    14. Skokic, S., M. Casaletti, S. Maci, and S Sorensen, "Complex conical beams for aperture field representations," IEEE Trans. Antennas Propag., Vol. 50, No. 2, 611-622, Feb. 2011, Doi: 10.1109/TAP.2010.2096379.

    15. Sarkar, T. K. and O. Pereira, "Using the matrix pencil method to estimate the parameters of a sum of complex exponentials," IEEE Antennas and Propagation Magazine, Vol. 37, No. 1, 48-55, Feb. 1995, Doi: 10.1109/74.370583.

    16. Deschamps, G. A., "The Gaussian beam as a bundle of complex rays," Electron. Lett., Vol. 7, No. 23, 684-685, 1971.

    17. Felsen, L. B., "Complex-source-point solutions of the field equations and their relation to the propagation and scattering of Gaussian beams," Proc. Symp. Math., Vol. 18, 39-56, 1975.

    18. 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.

    19. Yao, D., "Complex source representation of time harmonic radiation from a plane aperture," IEEE Trans. Antennas Propag., Vol. 43, No. 7, 720-723, Jul. 1995.

    20. Chow, Y. L., J. J. Yang, D. G. Fang, and G. E. Howard, "A closed form spatial Green function for the microstrip substrate," IEEE Trans. Microw. Theory Tech., Vol. 39, No. 3, 588-592, Mar. 1991.

    21. He, J., T. Yu, N. Geng, and L. Carin, "Method of moments analysis of electromagnetic scattering from a general three-dimensional dielectric target embedded in a multilayered medium," Radio Sci., Vol. 35, No. 2, 305-313, 2000.

    22. Vipiana, F., A. Polemi, S. Maci, and G. Vecchi, "A mesh-adapted closed-form regular kernel for 3D singular integral equations," IEEE Trans. Antennas Propag., Vol. 56, No. 6, 1687-1698, Jun. 2008.

    23. Bucci, O. and G. Franceschetti, "On the degrees of freedom of scattered fields," IEEE Trans. Antennas Propag., Vol. 37, No. 7, 918-926, 1989, Doi: 10.1109/8.29386.

    24. Bucci, O., "Computational complexity in the solution of large antenna and scattering problems," Radio Sci., Vol. 40, RS6S16, 2005, Doi: 10.1029/2004RS003196.

    25. Stupfel, B. and Y. Morel, "Singular value decomposition of the radiation operator: Application to model-order and far-field reduction," IEEE Trans. Antennas Propag., Vol. 56, No. 6, 1605-1615, 2008, Doi: 10.1109/TAP.2008.923311.

    26. Bogush, Jr., A. J. and R. E. Elkins, "Gaussian field expansions for large aperture antennas," IEEE Trans. Antennas Propag., Vol. 34, No. 2, 228-243, 1986.

    27. Prakash, V. V. S. and R. Mittra, "Characteristic basis function method: A new technique for efficient solution of method of moments matrix equations," Microwave Opt. Technol. Lett., Vol. 36, No. 2, 95-100, 2003.

    28. Matekovits, L., V. Laza, and G. Vecchi, "Analysis of large complex structures with the synthetic-functions approach," IEEE Trans. Antennas Propag., Vol. 55, No. 9, 2509-2521, 2007, Doi: 10.1109/TAP.2007.90407.

    29. Casaletti, M., S. Maci, and G. Vecchi, "Diffraction-like synthetic functions to treat the scattering from large polyhedral metallic object," Appl. Comput. Electromagn. Soc., Vol. 24, No. 2, 161-173, 2009.

    30. Tap, K., P. H. Pathak, and R. J. Burkholder, "Exact complex source point beam expansions for electromagnetic fields," IEEE Trans. Antennas Propag., Vol. 59, No. 9, 3379-3390, 2011, Doi: 10.1109/TAP.2011.2161438.

    31. Martini, E., G. Carli, and S. Maci, "A domain decomposition method based on a generalized scattering matrix formalism and a complex source expansion," Progress In Electromagnetics Research B, Vol. 19, 445-473, 2010.

    32. Norris, A. N. and T. B. Hansen, "Exact complex source representations of time-harmonic radiation," Wave Motion, Vol. 25, 127-141, 1997.

    33. Martini, E. and S. Maci, "A closed-form conversion from spherical-wave- to complex-point-source-expansion," Radio Sci., Vol. 46, RS0E22, 2011, Doi: 10.1029/2011RS004665.

    34. Devaney, A. J. and E. Wolf, "Radiating and nonradiating classical current distributions and the fields they generate," Phys. Rev. D, Vol. 8, 1044-1047, 1973.

    35. Sadourny, R., A. Arakawa, and Y. Mintz, "Integration of the nondivergent barotropic vorticity equation with an icosahedral-hexagonal grid for the sphere," Mon. Wea. Rev., Vol. 96, 351-356, 1968, Doi: http://dx.doi.org/10.1175/1520-0493(1968)096<0351:IOTNBV>2.0.CO;2.

    36. Rumsey, V. H., "Some new forms of Huygens’ principle," IRE Transactions on Antennas and Propagation, Vol. 7, No. 5, 103-116, Dec. 1959, Doi: 10.1109/TAP.1959.1144766.

    37. Harrington, R. F., Time Harmonic Electromagnetics, McGraw-Hill, New York, 1961.

    38. Martini, E., G. Carli, and S. Maci, "An equivalence theorem based on the use of electric currents radiating in free space," IEEE Antennas Wireless Propag. Lett., Vol. 7, 421-424, 2008, Doi: 0.1109/LAWP.2008.2001764.

    39. Hansen, J. E., Spherical Near-field Antenna Measurements, Peter Peregrinus, London, 1988.

    40. Lebedev, V. I., "A quadrature formula for the sphere of the 131st algebraic order of accuracy," Dokl. Math., Vol. 59, No. 3, 477-481, 1999.

    41. Heilpern, T., E. Heyman, and V. Timchenko, "A beam summation algorithm for wave radiation and guidance in stratified media," J. Acoust. Soc. Am., Vol. 121, No. 4, 1856-1864, 2007, Doi: 10.1121/1.2537221.